Find the mean and variance for the following data:25, 50, 45, 30

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Statistics

Long Answer Type

481. The frequency distribution of population in males in different age groups is given below:
Calculate the mean deviation about the median.

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Short Answer Type

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482. Find the mean and variance for the following data:
25, 50, 45, 30, 70, 42, 36, 48, 34, 50

top enclose straight x space equals space fraction numerator sum straight x over denominator straight N end fraction equals fraction numerator 25 plus 50 plus 45 plus 30 plus 70 plus 42 plus 36 plus 48 plus 34 plus 50 over denominator 10 end fraction equals 430 over 10 equals 43

sum left parenthesis straight x minus top enclose straight x right parenthesis squared space equals space left parenthesis 25 minus 43 right parenthesis squared plus left parenthesis 50 minus 43 right parenthesis squared plus left parenthesis 45 minus 43 right parenthesis squared plus left parenthesis 30 minus 43 right parenthesis squared plus left parenthesis 70 minus 43 right parenthesis squared

space space space space space plus left parenthesis 42 minus 43 right parenthesis squared plus left parenthesis 36 minus 43 right parenthesis squared plus left parenthesis 48 minus 43 right parenthesis squared plus left parenthesis 34 minus 43 right parenthesis squared plus left parenthesis 50 minus 43 right parenthesis squared

equals space left parenthesis negative 18 right parenthesis squared plus left parenthesis 7 right parenthesis squared plus left parenthesis 2 right parenthesis squared plus left parenthesis negative 13 right parenthesis squared plus left parenthesis 27 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared plus left parenthesis negative 7 right parenthesis squared plus left parenthesis 5 right parenthesis squared plus left parenthesis negative 9 right parenthesis squared plus left parenthesis 7 right parenthesis squared

equals space 324 plus 49 plus 4 plus 169 plus 729 plus 1 plus 49 plus 25 plus 81 plus 49 equals 1480

Hence, Variance

left parenthesis straight sigma squared right parenthesis

=

space space fraction numerator sum left parenthesis straight x minus top enclose straight x right parenthesis squared over denominator straight n end fraction equals 1480 over 10 equals 148

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483. Find the mean and variance for the following data:
6, 7, 10, 12, 13, 4, 8, 12

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Long Answer Type

484. Find the mean and variance of the first n natural numbers.

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Short Answer Type

485. Find the variance and standard deviation of 3, 5, 5, 4, 6, 3, 5, 7,1, 8.

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486. Find the variance and standard deviation of 62,65, 57, 62, 56, 51, 69, 60.

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Long Answer Type

487. Find the mean and variance for the following data:

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488. The scores of 48 children in an intelligency test are shown in the following table:

Calculate: (a) Mean (b) Variance (c) Standard Deviation.

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489. Compute (a) the mean (b) the variance (c) the standard deviation of the following data:

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490. Calculate the mean and standard deviation for the following data:

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