{"id":1162,"date":"2025-02-06T12:15:09","date_gmt":"2025-02-06T06:45:09","guid":{"rendered":"https:\/\/leverageedu.com\/questions-answers\/?p=1162"},"modified":"2025-02-06T12:20:52","modified_gmt":"2025-02-06T06:50:52","slug":"using-empirical-formula-calculate-the-mode-of-the-following-data","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/questions-answers\/using-empirical-formula-calculate-the-mode-of-the-following-data\/","title":{"rendered":"Using Empirical Formula Calculate the Mode of the Following Data: 17, 16, 25, 23, 22, 23, 28, 25, 25, 23.\u00a0"},"content":{"rendered":"\n

Answer:<\/strong> The mode of the given data (17, 16, 25, 23, 22, 23, 28, 25, 25, 23) is 23.6, which corresponds to option C<\/strong>. 23.6 . In statistics, the mode is the most frequently occurring number in a given dataset. It represents the value that appears most often.<\/p>\n\n\n\n

Complete Answer:<\/strong><\/p>\n\n\n\n

Step 1: Arrange the Data in Ascending Order<\/strong><\/p>\n

Given data: 17, 16, 25, 23, 22, 23, 28, 25, 25, 23<\/strong><\/p>\n

Arranging in order:
16, 17, 22, 23, 23, 23, 25, 25, 25, 28<\/strong><\/p>\n

Step 2: Find the Mean<\/strong><\/p>\n

The mean<\/strong> (average) is calculated as:<\/p>\n

\n \n \n Mean\n =\n \n Sum\u00a0of\u00a0all\u00a0values\n Total\u00a0number\u00a0of\u00a0values\n \n \n \\text{Mean} = \\frac{\\text{Sum of all values}}{\\text{Total number of values}}\u00a0\u00a0\u00a0\u00a0\n \n <\/span><\/span><\/p>\n

<\/span>\u00a0\n \n =\n \n \n 16\n +\n 17\n +\n 22\n +\n 23\n +\n 23\n +\n 23\n +\n 25\n +\n 25\n +\n 25\n +\n 28\n \n 10\n \n \n = \\frac{16 + 17 + 22 + 23 + 23 + 23 + 25 + 25 + 25 + 28}{10}\u00a0\u00a0\u00a0\u00a0\n <\/span><\/span><\/span><\/span><\/p>\n

\u00a0\u00a0\n \n =\n \n 227\n 10\n \n =\n 22.7\n \n = \\frac{227}{10} = 22.7\u00a0\u00a0\u00a0\u00a0\n <\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Step 3: Find the Median<\/strong><\/p>\n

The median<\/strong> is the middle value of an ordered dataset.<\/p>\n

Since there are 10 numbers<\/strong>, the median is the average of the 5th and 6th values:<\/p>\n

\n \n \n Median\n =\n \n \n 23\n +\n 23\n \n 2\n \n =\n \n 46\n 2\n \n =\n 23\n \n \\text{Median} = \\frac{23 + 23}{2} = \\frac{46}{2} = 23\u00a0\u00a0\u00a0\u00a0\n \n <\/span><\/span><\/p>\n

Step 4: Apply the Empirical Formula<\/strong><\/p>\n

\n \n \n Mode\n =\n 3\n \u00d7\n Median\n \u2212\n 2\n \u00d7\n Mean\n \n \\text{Mode} = 3 \\times \\text{Median} \u2013 2 \\times \\text{Mean}\u00a0\u00a0\u00a0\u00a0\n \n <\/span><\/span><\/p>\n

<\/span>\u00a0\n \n =\n 3\n \u00d7\n 23\n \u2212\n 2\n \u00d7\n 22.7\n \n = 3 \\times 23 \u2013 2 \\times 22.7\u00a0\u00a0\u00a0\u00a0\n <\/span><\/span><\/p>\n

<\/span> \n \n \n =\n 69\n \u2212\n 45.4\n \n = 69 \u2013 45.4\u00a0\u00a0\u00a0\u00a0\n \n <\/span><\/span><\/p>\n

\n \n \n =\n 23.6\n \n = 23.6\u00a0\u00a0\u00a0\u00a0\n \n <\/span><\/span><\/span><\/p>\n

Thus, the correct answer is 23.6<\/strong> (Option C<\/strong>).<\/p>\n\n\n\n

Fun Fact\u00a0<\/strong><\/p>\n\n\n\n

Did you know that in some cases, data can have no mode, one mode (unimodal), or multiple modes (bimodal or multimodal)? When no value repeats, we say the dataset is mode-less!<\/p>\n\n\n\n

Common Doubts in Maths<\/strong><\/p>\n\n\n\n

How Many Thousands Make a Million?<\/strong><\/a><\/td>The Smallest 7- Digit Number is<\/strong><\/a><\/td><\/tr>
1 km is Equal to How Many Miles?<\/strong><\/a><\/td>Write the Smallest and the Largest Six-Digit Numbers<\/strong><\/a><\/td><\/tr>
Convert 1 gallon into liters<\/strong><\/a><\/td>One cusec is Equal to How Many Litres?<\/strong><\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n","protected":false},"excerpt":{"rendered":"Answer: The mode of the given data (17, 16, 25, 23, 22, 23, 28, 25, 25, 23) is…\n","protected":false},"author":90,"featured_media":1173,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[3],"tags":[],"class_list":{"0":"post-1162","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-math"},"yoast_head":"\nUsing Empirical Formula Calculate the Mode of the Following Data: 17, 16, 25, 23, 22, 23, 28, 25, 25, 23.\u00a0<\/title>\n<meta name=\"description\" content=\"Using Empirical Formula, Calculate the Mode of the Following Data - 17, 16, 25, 23, 22, 23, 28, 25, 25, 23, corresponding to option C. 23.6.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/leverageedu.com\/questions-answers\/using-empirical-formula-calculate-the-mode-of-the-following-data\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Using Empirical Formula Calculate the Mode of the Following Data: 17, 16, 25, 23, 22, 23, 28, 25, 25, 23.\u00a0\" \/>\n<meta property=\"og:description\" content=\"Using Empirical Formula, Calculate the Mode of the Following Data - 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