Question

Pls help me to answer this​

Answer 1

Answers:

Sample Variance = 31.03

Sample Standard Deviation = 5.57

See the table below.

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Explanation:

M refers to the midpoint of each interval. The midpoint is $M = \frac{a+b}{2}$ where a,b are the left and right endpoints.

For example, $M = \frac{0+4}{2} = \frac{4}{2} = 2$ in the first row.

Multiply the frequency with the midpoint to get the third column. Summing this column of values leads to 4+49+180+153+154 = 540 shown at the bottom of that column.

Divide this sum over the sum of the frequencies (2+7+15+9+7 = 40) and we arrive at $\overline{x} = \frac{540}{40} = 13.5$ which is the sample mean xbar.

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After we determine xbar, we subtract it from each value of M. Then we square the result to get $(M - \overline{x})^2$. Multiply that with the column f to get the new column $f(M-\overline{x})^2$.

This column is added to arrive at 1210 shown in the table below. Divide this over the sum of the frequencies minus 1. So we divide by n-1 = 40-1 = 39 to get roughly 31.03

This is the sample variance.

The square root of this is sqrt(31.03) = 5.57 and this is the approximate sample standard deviation.