{"id":639685,"date":"2023-06-26T06:48:52","date_gmt":"2023-06-26T01:18:52","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/question\/the-mean-of-the-following-distribution-is-48-and-sum-of-all-the-frequencies-is-50-find-the-missing-frequencies-x-and-y\/"},"modified":"2025-06-26T17:37:24","modified_gmt":"2025-06-26T12:07:24","slug":"the-mean-of-the-following-distribution-is-48-and-sum-of-all-the-frequencies-is-50-find-the-missing-frequencies-x-and-y","status":"publish","type":"questions","link":"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-mean-of-the-following-distribution-is-48-and-sum-of-all\/","title":{"rendered":"The mean of the following distribution is 48 and sum of all the frequencies is 50. Find the missing frequencies x and y."},"content":{"rendered":"","protected":false},"author":1,"template":"","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"The mean of the following distribution is 48 and sum of all the frequencies is 50. Find the missing frequencies x and y.","custom_permalink":"question\/mathematics\/the-mean-of-the-following-distribution-is-48-and-sum-of-all\/"},"categories":[],"acf":{"question":"

The mean of the following distribution is 48 and sum of all the frequencies is 50. <\/span><\/p>

\"\"<\/p>

Find the missing frequencies x and y.<\/span><\/p>

<\/p>

<\/p><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt\"><\/spanstyle=\"-aw-import:ignore\"><\/pstyle=\"margin-top:0pt;margin-bottom:0pt\">","options":[{"option":"15 and 10","correct":false},{"option":"10 and 15","correct":false},{"option":"13 and 12","correct":false},{"option":"12 and 13 <\/span>","correct":true}],"solution":"Given that the mean of the following distribution is 48 and sum of all the frequencies is 50.<\/span>
\"\"We know that the frequency is generally the total sum of all the data divided by the total number of data present in the following table.<\/span>
And mean is the measure of central tendency as it indicates the average value of the data.<\/span>
Find the value of x and y. <\/span>
\"\"\u2211<\/mo><\/mrow><\/mrow><\/munderover><\/mrow>f<\/mi><\/mrow>i<\/mi><\/mrow><\/msub>=<\/mo>25<\/mn>+<\/mo>x<\/mi>+<\/mo>y<\/mi>=<\/mo>50<\/mn><\/math>.<\/span>
\u21d2<\/mo>x<\/mi>=<\/mo>25<\/mn>-<\/mo>13<\/mn><\/math>
\u21d2<\/mo>x<\/mi>=<\/mo>12<\/mn><\/math>
Substitute the value of x into the equation.<\/span>
Mean<\/mi>=<\/mo>a<\/mi>+<\/mo>\u2211<\/mo><\/mrow><\/mrow><\/munderover><\/mrow>f<\/mi><\/mrow>i<\/mi><\/mrow><\/msub>u<\/mi><\/mrow>i<\/mi><\/mrow><\/msub><\/mrow>\u2211<\/mo><\/mrow><\/mrow><\/munderover><\/mrow>f<\/mi><\/mrow>i<\/mi><\/mrow><\/msub><\/mrow><\/mfrac><\/mrow><\/mfenced>\u00d7<\/mo>h<\/mi><\/math>
In the formula, a is the<\/span>  <\/span>assumed mean, <\/span>f<\/mi><\/mrow>i <\/mi><\/mrow><\/msub> <\/mi><\/math>is the frequency of <\/span>i<\/mi><\/mrow>th <\/mi><\/mrow><\/msup><\/math>class, <\/span>X<\/mi>-<\/mo>a <\/mi><\/math>is the deviation of <\/span>i<\/mi><\/mrow>th <\/mi><\/mrow><\/msup><\/math> class, <\/span>x<\/mi><\/mrow>i<\/mi><\/mrow><\/msub><\/math> = class mark = <\/span>(<\/mo>Upper class limit <\/mi>+<\/mo> lower class limit<\/mi><\/mrow>2<\/mn><\/mrow><\/mfrac><\/math>, <\/span>u<\/mi><\/mrow>i<\/mi><\/mrow><\/msub>=<\/mo>x<\/mi><\/mrow>i<\/mi><\/mrow><\/msub>-<\/mo>a<\/mi><\/mrow>h<\/mi><\/mrow><\/mfrac><\/math>  <\/span>, <\/span>\u2211<\/mo><\/mrow><\/mrow><\/munderover><\/mrow>f<\/mi><\/mrow>i<\/mi><\/mrow><\/msub>=<\/mo>N<\/mi>=<\/mo> <\/mi><\/math>Total number of observations.<\/span>
\u21d2<\/mo>48<\/mn>=<\/mo>45<\/mn>+<\/mo>2<\/mn>y <\/mi>-<\/mo> <\/mi>11<\/mn><\/mrow>50<\/mn><\/mrow><\/mfrac><\/mrow><\/mfenced>\u00d7<\/mo>10<\/mn><\/math>
\u21d2<\/mo>48<\/mn>-<\/mo>45<\/mn>=<\/mo>2<\/mn>y <\/mi>-<\/mo> <\/mi>11<\/mn><\/mrow>5<\/mn><\/mrow><\/mfrac><\/mrow><\/mfenced><\/math>
\u21d2<\/mo>48<\/mn>-<\/mo>45<\/mn>=<\/mo>2<\/mn>y <\/mi>-<\/mo> <\/mi>11<\/mn><\/mrow>5<\/mn><\/mrow><\/mfrac><\/mrow><\/mfenced><\/math>
 <\/span>\u21d2<\/mo>15<\/mn>=<\/mo>2<\/mn>y<\/mi>-<\/mo>11<\/mn><\/math>
\u21d2<\/mo>y<\/mi>=<\/mo>13<\/mn><\/math>
Considering the calculated values above,<\/span>  <\/span>the value of x and y is 12 and 13 respectively.<\/span>
Hence, option 4 is correct. <\/span>
 <\/span>","subject":"Mathematics"},"yoast_head":"\nThe mean of the following distribution is 48 and sum of all the frequencies is 50. Find the missing frequencies x and y. - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"The mean of the following distribution is 48 and sum of all the frequencies is 50. Find the missing frequencies x and y.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/question\/mathematics\/the-mean-of-the-following-distribution-is-48-and-sum-of-all\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The mean of the following distribution is 48 and sum of all the frequencies is 50. 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