{"id":5672,"date":"2025-11-15T15:02:56","date_gmt":"2025-11-15T09:32:56","guid":{"rendered":"https:\/\/www.tutoroot.com\/blog\/?p=5672"},"modified":"2025-11-15T15:02:56","modified_gmt":"2025-11-15T09:32:56","slug":"probability-and-statistics-for-class-10-a-complete-guide","status":"publish","type":"post","link":"https:\/\/www.tutoroot.com\/blog\/probability-and-statistics-for-class-10-a-complete-guide\/","title":{"rendered":"Probability and Statistics for Class 10: A Complete Guide to Mastering the Basics"},"content":{"rendered":"<p data-start=\"545\" data-end=\"812\"><img loading=\"lazy\" class=\"alignnone wp-image-5676 size-large\" src=\"https:\/\/www.tutoroot.com\/blog\/wp-content\/uploads\/2025\/11\/Probability-and-Statistics-for-Class-10-A-Complete-Guide-to-Mastering-the-Basics-1024x576.png\" alt=\"Probability and Statistics for Class 10 A Complete Guide to Mastering the Basics\" width=\"1024\" height=\"576\" srcset=\"https:\/\/www.tutoroot.com\/blog\/wp-content\/uploads\/2025\/11\/Probability-and-Statistics-for-Class-10-A-Complete-Guide-to-Mastering-the-Basics-1024x576.png 1024w, https:\/\/www.tutoroot.com\/blog\/wp-content\/uploads\/2025\/11\/Probability-and-Statistics-for-Class-10-A-Complete-Guide-to-Mastering-the-Basics-300x169.png 300w, https:\/\/www.tutoroot.com\/blog\/wp-content\/uploads\/2025\/11\/Probability-and-Statistics-for-Class-10-A-Complete-Guide-to-Mastering-the-Basics-768x432.png 768w, https:\/\/www.tutoroot.com\/blog\/wp-content\/uploads\/2025\/11\/Probability-and-Statistics-for-Class-10-A-Complete-Guide-to-Mastering-the-Basics-1536x864.png 1536w, https:\/\/www.tutoroot.com\/blog\/wp-content\/uploads\/2025\/11\/Probability-and-Statistics-for-Class-10-A-Complete-Guide-to-Mastering-the-Basics-2048x1152.png 2048w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p data-start=\"545\" data-end=\"812\"><strong data-start=\"545\" data-end=\"575\">Probability and Statistics<\/strong> are two scoring and practical chapters in <strong data-start=\"618\" data-end=\"636\">Class 10 Maths<\/strong>. Learn them well, and you can gain marks easily. This guide explains the basics in simple words. It also gives solved examples, practice questions, and a quick revision sheet.<\/p>\n<hr data-start=\"814\" data-end=\"817\" \/>\n<h2 data-start=\"819\" data-end=\"857\"><strong data-start=\"822\" data-end=\"857\">What is Probability? (Class 10)<\/strong><\/h2>\n<p data-start=\"859\" data-end=\"1004\">Probability tells us <strong data-start=\"880\" data-end=\"894\">how likely<\/strong> an event is to happen.<br data-start=\"917\" data-end=\"920\" \/>We use it to predict outcomes. For example: coin toss, dice roll, or drawing a card.<\/p>\n<p data-start=\"1006\" data-end=\"1031\"><strong data-start=\"1006\" data-end=\"1029\">Formula (Class 10):<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mtext>Number\u00a0of\u00a0favourable\u00a0outcomes<\/mtext><mtext>Total\u00a0number\u00a0of\u00a0outcomes<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(E) = \\frac{\\text{Number of favourable outcomes}}{\\text{Total number of outcomes}}<\/annotation><\/semantics><\/math>\n<p><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">E<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord text\">Total\u00a0number\u00a0of\u00a0outcomes<\/span><span class=\"mord text\">Number\u00a0of\u00a0favourable\u00a0outcomes<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1123\" data-end=\"1210\"><strong data-start=\"1123\" data-end=\"1132\">Note:<\/strong> Probability is always between 0 and 1.<br data-start=\"1171\" data-end=\"1174\" \/>0 means impossible. 1 means certain.<\/p>\n<hr data-start=\"1212\" data-end=\"1215\" \/>\n<h2 data-start=\"1217\" data-end=\"1249\"><strong data-start=\"1220\" data-end=\"1249\">Easy Probability Examples<\/strong><\/h2>\n<p data-start=\"1251\" data-end=\"1415\"><strong data-start=\"1251\" data-end=\"1279\">Example 1 \u2014 Dice (Basic)<\/strong><br data-start=\"1279\" data-end=\"1282\" \/>Question: What is the probability of rolling a 5 on a fair six-sided dice?<br data-start=\"1356\" data-end=\"1359\" \/>Solution: Favourable outcomes = 1. Total outcomes = 6.<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>6<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P = \\frac{1}{6}<\/annotation><\/semantics><\/math>\n<p><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">61<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1439\" data-end=\"1584\"><strong data-start=\"1439\" data-end=\"1467\">Example 2 \u2014 Coin (Basic)<\/strong><br data-start=\"1467\" data-end=\"1470\" \/>Question: What is the probability of getting a Head when you toss a coin?<br data-start=\"1543\" data-end=\"1546\" \/>Solution: Favourable = 1. Total = 2.<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P = \\frac{1}{2}<\/annotation><\/semantics><\/math>\n<p><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">21<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1608\" data-end=\"1775\"><strong data-start=\"1608\" data-end=\"1638\">Example 3 \u2014 Cards (Tricky)<\/strong><br data-start=\"1638\" data-end=\"1641\" \/>Question: What is the probability of drawing a red ace from a 52-card deck?<br data-start=\"1716\" data-end=\"1719\" \/>Solution: Red aces = 2 (hearts, diamonds). Total = 52.<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mn>2<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>26<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P = \\frac{2}{52} = \\frac{1}{26}<\/annotation><\/semantics><\/math>\n<p><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">522<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\">261<\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1815\" data-end=\"1883\"><strong data-start=\"1815\" data-end=\"1823\">Tip:<\/strong> Always count outcomes carefully. Write them down if needed.<\/p>\n<hr data-start=\"1885\" data-end=\"1888\" \/>\n<h2 data-start=\"1890\" data-end=\"1927\"><strong data-start=\"1893\" data-end=\"1927\">What is Statistics? (Class 10)<\/strong><\/h2>\n<p data-start=\"1929\" data-end=\"2033\">Statistics helps us <strong data-start=\"1949\" data-end=\"1985\">collect, organise, and interpret<\/strong> numerical data.<br data-start=\"2001\" data-end=\"2004\" \/>In Class 10 you mainly learn:<\/p>\n<ul data-start=\"2035\" data-end=\"2120\">\n<li data-start=\"2035\" data-end=\"2057\">\n<p data-start=\"2037\" data-end=\"2057\"><strong data-start=\"2037\" data-end=\"2045\">Mean<\/strong> (average)<\/p>\n<\/li>\n<li data-start=\"2058\" data-end=\"2087\">\n<p data-start=\"2060\" data-end=\"2087\"><strong data-start=\"2060\" data-end=\"2070\">Median<\/strong> (middle value)<\/p>\n<\/li>\n<li data-start=\"2088\" data-end=\"2120\">\n<p data-start=\"2090\" data-end=\"2120\"><strong data-start=\"2090\" data-end=\"2098\">Mode<\/strong> (most frequent value)<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"2122\" data-end=\"2195\">These tools help us understand data from surveys, tests, and experiments.<\/p>\n<hr data-start=\"2197\" data-end=\"2200\" \/>\n<h2 data-start=\"2202\" data-end=\"2232\"><strong data-start=\"2205\" data-end=\"2232\">Key Statistics Formulas<\/strong><\/h2>\n<p data-start=\"2234\" data-end=\"2262\"><strong data-start=\"2234\" data-end=\"2260\">Mean (Ungrouped data):<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mtext>Mean<\/mtext><mo>=<\/mo><mfrac><mrow><mo>\u2211<\/mo><mi>x<\/mi><\/mrow><mi>n<\/mi><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Mean} = \\frac{\\sum x}{n}<\/annotation><\/semantics><\/math>\n<p><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord text\"><span class=\"mord\">Mean<\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">n<\/span><span class=\"mop op-symbol small-op\">\u2211<\/span><span class=\"mord mathnormal\">x<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"2301\" data-end=\"2314\"><strong data-start=\"2301\" data-end=\"2312\">Median:<\/strong><\/p>\n<ul data-start=\"2315\" data-end=\"2397\">\n<li data-start=\"2315\" data-end=\"2346\">\n<p data-start=\"2317\" data-end=\"2346\">If n is odd \u2192 middle value.<\/p>\n<\/li>\n<li data-start=\"2347\" data-end=\"2397\">\n<p data-start=\"2349\" data-end=\"2397\">If n is even \u2192 average of the two middle values.<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"2399\" data-end=\"2410\"><strong data-start=\"2399\" data-end=\"2408\">Mode:<\/strong><\/p>\n<ul data-start=\"2411\" data-end=\"2448\">\n<li data-start=\"2411\" data-end=\"2448\">\n<p data-start=\"2413\" data-end=\"2448\">The number that appears most often.<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"2450\" data-end=\"2476\"><strong data-start=\"2450\" data-end=\"2474\">Mean (Grouped data):<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mover accent=\"true\"><mi>x<\/mi><mo>\u02c9<\/mo><\/mover><mo>=<\/mo><mfrac><mrow><mo>\u2211<\/mo><msub><mi>f<\/mi><mi>i<\/mi><\/msub><msub><mi>x<\/mi><mi>i<\/mi><\/msub><\/mrow><mrow><mo>\u2211<\/mo><msub><mi>f<\/mi><mi>i<\/mi><\/msub><\/mrow><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\bar{x} = \\frac{\\sum f_i x_i}{\\sum f_i}<\/annotation><\/semantics><\/math>\n<p><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord accent\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">x<\/span><span class=\"accent-body\"><span class=\"mord\">\u02c9<\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mop op-symbol small-op\">\u2211<\/span><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"mop op-symbol small-op\">\u2211<\/span><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"2525\" data-end=\"2581\">(Where <span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>x<\/mi><mi>i<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">x_i<\/annotation><\/semantics><\/math>\n<p><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> = class midpoint and <span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msub><mi>f<\/mi><mi>i<\/mi><\/msub><\/mrow><annotation encoding=\"application\/x-tex\">f_i<\/annotation><\/semantics><\/math>\n<p><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> = frequency)<\/p>\n<hr data-start=\"2583\" data-end=\"2586\" \/>\n<h2 data-start=\"2588\" data-end=\"2621\"><strong data-start=\"2591\" data-end=\"2621\">Solved Statistics Examples<\/strong><\/h2>\n<p data-start=\"2623\" data-end=\"2712\"><strong data-start=\"2623\" data-end=\"2651\">Example 1 \u2014 Mean (Basic)<\/strong><br data-start=\"2651\" data-end=\"2654\" \/>Data: 6, 12, 18, 24<br data-start=\"2673\" data-end=\"2676\" \/>Sum = 60, n = 4<br data-start=\"2691\" data-end=\"2694\" \/>Mean = 60 \u00f7 4 = 15<\/p>\n<p data-start=\"2714\" data-end=\"2800\"><strong data-start=\"2714\" data-end=\"2744\">Example 2 \u2014 Median (Basic)<\/strong><br data-start=\"2744\" data-end=\"2747\" \/>Data: 3, 8, 9, 15, 17 \u2192 Middle value = 9 \u2192 Median = 9<\/p>\n<p data-start=\"2802\" data-end=\"2869\"><strong data-start=\"2802\" data-end=\"2830\">Example 3 \u2014 Mode (Basic)<\/strong><br data-start=\"2830\" data-end=\"2833\" \/>Data: 4, 4, 5, 6, 6, 6, 7 \u2192 Mode = 6<\/p>\n<p data-start=\"2871\" data-end=\"2910\"><strong data-start=\"2871\" data-end=\"2910\">Example 4 \u2014 Mean (Grouped \u2014 Tricky)<\/strong><\/p>\n<div class=\"_tableContainer_1rjym_1\">\n<div class=\"group _tableWrapper_1rjym_13 flex w-fit flex-col-reverse\" tabindex=\"-1\">\n<table class=\"w-fit min-w-(--thread-content-width)\" data-start=\"2912\" data-end=\"3120\">\n<thead data-start=\"2912\" data-end=\"2952\">\n<tr data-start=\"2912\" data-end=\"2952\">\n<th data-start=\"2912\" data-end=\"2920\" data-col-size=\"sm\">Class<\/th>\n<th data-start=\"2920\" data-end=\"2936\" data-col-size=\"sm\">Frequency (f)<\/th>\n<th data-start=\"2936\" data-end=\"2952\" data-col-size=\"sm\">Midpoint (x)<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"2995\" data-end=\"3120\">\n<tr data-start=\"2995\" data-end=\"3036\">\n<td data-start=\"2995\" data-end=\"3003\" data-col-size=\"sm\">0\u201310<\/td>\n<td data-start=\"3003\" data-end=\"3020\" data-col-size=\"sm\">2<\/td>\n<td data-start=\"3020\" data-end=\"3036\" data-col-size=\"sm\">5<\/td>\n<\/tr>\n<tr data-start=\"3037\" data-end=\"3078\">\n<td data-start=\"3037\" data-end=\"3045\" data-col-size=\"sm\">10\u201320<\/td>\n<td data-start=\"3045\" data-end=\"3062\" data-col-size=\"sm\">3<\/td>\n<td data-start=\"3062\" data-end=\"3078\" data-col-size=\"sm\">15<\/td>\n<\/tr>\n<tr data-start=\"3079\" data-end=\"3120\">\n<td data-start=\"3079\" data-end=\"3087\" data-col-size=\"sm\">20\u201330<\/td>\n<td data-start=\"3087\" data-end=\"3104\" data-col-size=\"sm\">5<\/td>\n<td data-start=\"3104\" data-end=\"3120\" data-col-size=\"sm\">25<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<p data-start=\"3122\" data-end=\"3212\">Compute <span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mo>\u2211<\/mo><msub><mi>f<\/mi><mi>i<\/mi><\/msub><msub><mi>x<\/mi><mi>i<\/mi><\/msub><mo>=<\/mo><mn>2<\/mn><mo>\u00d7<\/mo><mn>5<\/mn><mo>+<\/mo><mn>3<\/mn><mo>\u00d7<\/mo><mn>15<\/mn><mo>+<\/mo><mn>5<\/mn><mo>\u00d7<\/mo><mn>25<\/mn><mo>=<\/mo><mn>10<\/mn><mo>+<\/mo><mn>45<\/mn><mo>+<\/mo><mn>125<\/mn><mo>=<\/mo><mn>180<\/mn><\/mrow><annotation encoding=\"application\/x-tex\"> \\sum f_i x_i = 2\u00d75 + 3\u00d715 + 5\u00d725 = 10 + 45 + 125 = 180<\/annotation><\/semantics><\/math>\n<p><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop op-symbol small-op\">\u2211<\/span><span class=\"mord\"><span class=\"mord mathnormal\">f<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mord\"><span class=\"mord mathnormal\">x<\/span><span class=\"msupsub\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">i<\/span><\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">3<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord\">15<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">5<\/span><span class=\"mbin\">\u00d7<\/span><\/span><span class=\"base\"><span class=\"mord\">25<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">10<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">45<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">125<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">180<\/span><\/span><\/span><\/span><br data-start=\"3189\" data-end=\"3192\" \/>Total frequency = 10<\/p>\n<p data-start=\"3214\" data-end=\"3234\">Mean = 180 \u00f7 10 = 18<\/p>\n<hr data-start=\"3236\" data-end=\"3239\" \/>\n<h2 data-start=\"3241\" data-end=\"3272\"><strong data-start=\"3244\" data-end=\"3272\">Common Mistakes to Avoid<\/strong><\/h2>\n<ul data-start=\"3274\" data-end=\"3498\">\n<li data-start=\"3274\" data-end=\"3319\">\n<p data-start=\"3276\" data-end=\"3319\">Not arranging data before finding median.<\/p>\n<\/li>\n<li data-start=\"3320\" data-end=\"3379\">\n<p data-start=\"3322\" data-end=\"3379\">Mixing up favourable and total outcomes in probability.<\/p>\n<\/li>\n<li data-start=\"3380\" data-end=\"3418\">\n<p data-start=\"3382\" data-end=\"3418\">Skipping steps; lose method marks.<\/p>\n<\/li>\n<li data-start=\"3419\" data-end=\"3455\">\n<p data-start=\"3421\" data-end=\"3455\">Wrong midpoint for grouped data.<\/p>\n<\/li>\n<li data-start=\"3456\" data-end=\"3498\">\n<p data-start=\"3458\" data-end=\"3498\">Not checking totals in frequency tables.<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"3500\" data-end=\"3503\" \/>\n<h2 data-start=\"3505\" data-end=\"3542\"><strong data-start=\"3508\" data-end=\"3542\">Practice Questions (Try These)<\/strong><\/h2>\n<p data-start=\"3544\" data-end=\"3561\"><strong data-start=\"3544\" data-end=\"3559\">Probability<\/strong><\/p>\n<ol data-start=\"3562\" data-end=\"3795\">\n<li data-start=\"3562\" data-end=\"3645\">\n<p data-start=\"3565\" data-end=\"3645\">A bag has 4 red and 6 blue balls. Find the probability of picking a blue ball.<\/p>\n<\/li>\n<li data-start=\"3646\" data-end=\"3717\">\n<p data-start=\"3649\" data-end=\"3717\">Two coins are tossed. What is the probability of exactly one head?<\/p>\n<\/li>\n<li data-start=\"3718\" data-end=\"3795\">\n<p data-start=\"3721\" data-end=\"3795\">Pick a letter from \u201cMATHEMATICS\u201d. Find the probability of getting a vowel.<\/p>\n<\/li>\n<\/ol>\n<p data-start=\"3797\" data-end=\"3813\"><strong data-start=\"3797\" data-end=\"3811\">Statistics<\/strong><\/p>\n<ol data-start=\"3814\" data-end=\"3998\">\n<li data-start=\"3814\" data-end=\"3853\">\n<p data-start=\"3817\" data-end=\"3853\">Find the mean: 12, 18, 20, 25, 30.<\/p>\n<\/li>\n<li data-start=\"3854\" data-end=\"3890\">\n<p data-start=\"3857\" data-end=\"3890\">Find the median: 7, 3, 9, 1, 4.<\/p>\n<\/li>\n<li data-start=\"3891\" data-end=\"3931\">\n<p data-start=\"3894\" data-end=\"3931\">Find the mode: 2, 2, 4, 4, 4, 6, 8.<\/p>\n<\/li>\n<li data-start=\"3932\" data-end=\"3998\">\n<p data-start=\"3935\" data-end=\"3998\">For grouped data: (0\u20135:3), (5\u201310:5), (10\u201315:2) \u2014 find the mean.<\/p>\n<\/li>\n<\/ol>\n<p data-start=\"4000\" data-end=\"4049\">(Answers available on request or in class notes.)<\/p>\n<hr data-start=\"4051\" data-end=\"4054\" \/>\n<h2 data-start=\"4056\" data-end=\"4083\"><strong data-start=\"4059\" data-end=\"4083\">Quick Revision Sheet<\/strong><\/h2>\n<p data-start=\"4085\" data-end=\"4297\"><strong data-start=\"4085\" data-end=\"4101\">Probability:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mi>E<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mtext>favourable<\/mtext><mtext>total<\/mtext><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">P(E) = \\dfrac{\\text{favourable}}{\\text{total}}<\/annotation><\/semantics><\/math>\n<p><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">E<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord text\">total<\/span><span class=\"mord text\">favourable<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br data-start=\"4154\" data-end=\"4157\" \/><strong data-start=\"4157\" data-end=\"4178\">Mean (ungrouped):<\/strong> <span class=\"katex\"><span class=\"katex-mathml\"><\/p>\n<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mstyle displaystyle=\"true\" scriptlevel=\"0\"><mfrac><mrow><mi mathvariant=\"normal\">\u03a3<\/mi><mi>x<\/mi><\/mrow><mi>n<\/mi><\/mfrac><\/mstyle><\/mrow><annotation encoding=\"application\/x-tex\">\\dfrac{\\Sigma x}{n}<\/annotation><\/semantics><\/math>\n<p><\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mfrac\"><span class=\"vlist-t vlist-t2\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"mord mathnormal\">n<\/span>\u03a3<span class=\"mord mathnormal\">x<\/span><\/span><span class=\"vlist-s\">\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br data-start=\"4204\" data-end=\"4207\" \/><strong data-start=\"4207\" data-end=\"4218\">Median:<\/strong> Middle value (if even, average of two middles)<br data-start=\"4265\" data-end=\"4268\" \/><strong data-start=\"4268\" data-end=\"4277\">Mode:<\/strong> Most frequent value<\/p>\n<hr data-start=\"4299\" data-end=\"4302\" \/>\n<h2 data-start=\"4304\" data-end=\"4341\"><strong data-start=\"4307\" data-end=\"4341\">How to Study These Topics Fast<\/strong><\/h2>\n<ul data-start=\"4343\" data-end=\"4612\">\n<li data-start=\"4343\" data-end=\"4400\">\n<p data-start=\"4345\" data-end=\"4400\">Read the concept. Then practice 5\u201310 questions daily.<\/p>\n<\/li>\n<li data-start=\"4401\" data-end=\"4458\">\n<p data-start=\"4403\" data-end=\"4458\">Start with basic problems. Move to tricky ones later.<\/p>\n<\/li>\n<li data-start=\"4459\" data-end=\"4518\">\n<p data-start=\"4461\" data-end=\"4518\">Always write steps clearly. Teachers give method marks.<\/p>\n<\/li>\n<li data-start=\"4519\" data-end=\"4570\">\n<p data-start=\"4521\" data-end=\"4570\">Use past year papers for board-style questions.<\/p>\n<\/li>\n<li data-start=\"4571\" data-end=\"4612\">\n<p data-start=\"4573\" data-end=\"4612\">Review mistakes and fix the weak spots.<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"4614\" data-end=\"4617\" \/>\n<h2 data-start=\"4619\" data-end=\"4670\"><strong data-start=\"4622\" data-end=\"4670\">Why Tutoroot Helps You Master Class 10 Maths<\/strong><\/h2>\n<p data-start=\"4672\" data-end=\"4832\">Tutoroot makes learning simple and personal. Our tutors explain every step. They use clear examples and regular tests. We focus on concept clarity and practice.<\/p>\n<p data-start=\"4834\" data-end=\"4862\"><strong data-start=\"4834\" data-end=\"4860\">With Tutoroot you get:<\/strong><\/p>\n<ul data-start=\"4863\" data-end=\"5060\">\n<li data-start=\"4863\" data-end=\"4899\">\n<p data-start=\"4865\" data-end=\"4899\"><a href=\"https:\/\/www.tutoroot.com\/\"><strong>One-on-one Online Tuition Classes<\/strong><\/a>.<\/p>\n<\/li>\n<li data-start=\"4900\" data-end=\"4950\">\n<p data-start=\"4902\" data-end=\"4950\">Simple lessons for Probability and Statistics.<\/p>\n<\/li>\n<li data-start=\"4951\" data-end=\"4990\">\n<p data-start=\"4953\" data-end=\"4990\">Live doubt clearing in every class.<\/p>\n<\/li>\n<li data-start=\"4991\" data-end=\"5026\">\n<p data-start=\"4993\" data-end=\"5026\">Custom practice sets and tests.<\/p>\n<\/li>\n<li data-start=\"5027\" data-end=\"5060\">\n<p data-start=\"5029\" data-end=\"5060\">Progress tracking and feedback.<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"5062\" data-end=\"5224\">Join <strong data-start=\"5067\" data-end=\"5152\">Tutoroot\u2019s <a href=\"https:\/\/www.tutoroot.com\/maths-online-tuition\">Maths Online Tuition<\/a><\/strong> to get personalised help. Learn faster. Score better. Build confidence.<\/p>\n<p><strong>Visit Tutoroot Social Platforms \u2013<\/strong><\/p>\n<p><a href=\"https:\/\/www.linkedin.com\/company\/tutoroot-com\/\"><img loading=\"lazy\" class=\"\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/8\/81\/LinkedIn_icon.svg\/1024px-LinkedIn_icon.svg.png\" alt=\"File:LinkedIn icon.svg - Wikimedia Commons\" width=\"48\" height=\"48\" \/><\/a>\u00a0<a href=\"https:\/\/www.facebook.com\/Tutoroot-2155210911160419\/\"><img loading=\"lazy\" class=\"\" src=\"https:\/\/img.freepik.com\/premium-vector\/facebook-logo-vector-facebook-official-logo-vector-facebook-logo-illustrator_1002350-1803.jpg?semt=ais_hybrid&amp;w=740&amp;q=80\" alt=\"Page 2 | Facebook logo Images - Free Download on Freepik\" width=\"45\" height=\"45\" \/><\/a><a href=\"https:\/\/instagram.com\/tutoroot?utm_medium=copy_link\"><img loading=\"lazy\" class=\"alignnone\" src=\"https:\/\/img.freepik.com\/free-psd\/instagram-application-logo_23-2151544102.jpg?semt=ais_hybrid&amp;w=740&amp;q=80\" alt=\"Page 2 | Instagram logo Images - Free Download on Freepik\" width=\"60\" height=\"60\" \/><\/a><a href=\"https:\/\/www.youtube.com\/@tutoroot\"><img loading=\"lazy\" class=\"\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/0\/09\/YouTube_full-color_icon_%282017%29.svg\/1280px-YouTube_full-color_icon_%282017%29.svg.png\" alt=\"File:YouTube full-color icon (2017).svg - Wikimedia Commons\" width=\"57\" height=\"40\" \/><\/a>\u00a0<a href=\"https:\/\/x.com\/tutoroot\"><img loading=\"lazy\" class=\"\" src=\"https:\/\/img.freepik.com\/free-vector\/twitter-new-2023-x-logo-white-background-vector_1017-45422.jpg?semt=ais_hybrid&amp;w=740&amp;q=80\" alt=\"Twitter x logo Images - Free Download on Freepik\" width=\"63\" height=\"63\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Probability and Statistics are two scoring and practical chapters in Class 10 Maths. Learn them well, and you can gain marks easily. This guide explains the basics in simple words. &hellip; <a href=\"https:\/\/www.tutoroot.com\/blog\/probability-and-statistics-for-class-10-a-complete-guide\/\" class=\"more-link\">Read More<\/a><\/p>\n","protected":false},"author":10,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[475,473,53,102,474],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v19.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Probability and Statistics for Class 10 | Complete Guide<\/title>\n<meta name=\"description\" content=\"Simple guide to Probability and Statistics for Class 10. 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