Find the mean and variance for each of the data.
$$
\begin{array}{|l|l|l|r|l|r|r|r|}
\hline x_{i} & 6 & 10 & 14 & 18 & 24 & 28 & 30 \\
\hline f_{i} & 2 & 4 & 7 & 12 & 8 & 4 & 3 \\
\hline
\end{array}
$$

Answer

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Intro Stats / AP Statistics

NCERT Class 11 - Math

Chapter 15

Statistics

Section 2

Measures of Dispersion

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Problem 1

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Problem 7

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Problem 9

Problem 10

Video Transcript

hell in this problem we have to find mean and variance for each of the given data. So here, in this table we have given the following data. Now we will find a Phi XI, so it will be 602 is 12. Turning to four is 40 14 into seven is 98, 18 into 12 is 216, 24 into eight is 192, 2018- four is 112 and 13- three is 90. And the submission of FIXi is 760. Now we will find mean, it would be equal to one upon end Sigma. If I excite where I goes from one to end by substituting the known values, we get mean as equals two, One upon 40 into 760, which is equals 2 19. Now, in order to find variants, first of all, we will find absolute value of deviation from me, It would be XI -19. So here we have 6 -19 is -13 In -19 is -9, 14 -19 is -5, 18 -19 is -1, 24 -19 is five, 28 -19 is nine and 30 -19 is 11. Now we will find the square of absolute value of deviation from me, So the square of -13 is 169. Square off -9 is 81. Square off -5 is 25 Squared off -1 is fun Square or five. Square of nine is 81, And Square of 11 is 121. Now we will find if I into square of absolute value of deviation, So two into 169 is 338, four into 81 is 324, 17- 25 is 175, 12 and to one is 12, 18 to 25 is 200 four into 81 is 324, and three into 121 is 363 And the submission is 1736. Now we know that variance is equal to run upon in sigma, f i into square of absolute value of the aviation. Well, I goes from 1 to N. By substituting the known values. We get variance is equal to Run upon 40 into 1,736, which is equals two 43.4. Hence we get variance as equals two, What Day?

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