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Find the mean, variance and standard deviation using short-cut method$$\begin{array}{|l|c|c|c|c|c|c|c|c|c|}\hline \begin{array}{l}\text { Height } \\\text { in cms }\end{array} & 70-75 & 75-80 & 80-85 & 85-90 & 90-95 & 95-100 & 100-105 & 105-110 & 110-115 \\\hline \begin{array}{l}\text { No. of } \\\text { children }\end{array} & 3 & 4 & 7 & 7 & 15 & 9 & 6 & 6 & 3 \\\hline\end{array}$$

Intro Stats / AP Statistics

Chapter 15

Statistics

Section 2

Measures of Dispersion

Descriptive Statistics

Missouri State University

University of North Carolina at Chapel Hill

Piedmont College

Boston College

Lectures

0:00

10:13

Find the variance and stan…

06:42

04:57

04:43

00:50

Find the mean and the stan…

09:08

$$\begin{array}{|c|c|}\hli…

01:54

01:09

05:01

07:42

03:27

04:14

05:50

09:05

00:36

05:51

01:21

Find the mean and standard…

01:37

It is believed that the me…

01:22

The given values represent…

06:15

hill in this problem we have to find mean variance and standard deviation using shortcut method. So here we have given the following information. Now we will find the mid values of this class interval that is exiled. So we get 72.5 77.5 82.5 87.5 92.5 97.5. 102.5, 107.5 and 112.5 let's assume mean is equal to 92.5. Now, in order to find the mean, first of all, we will find you. Y it is equals two X I minus assumed mean that is 92.5 upon five. So it would be minus full minus three minus two minus one, zero, bun two, three and four. Now we will find a fi ey it would be trained to minus four is minus 12. For into mine history is minus 12. Seven to minus two is minus 14, 17 to minus one is minus seven. 15 to 0 is 09 into one is nine six. Enter two is 12, 16 to 3 is 18 and three and 248 12. And the submission of f i U i s six. Similarly, we will find a fei yu chi square, It would be 48 36 28 seven, zero nine, 24 54 48. And the submission of f i U S square is 254. Now we know that mean is equal to a plus sigma, F I E Y upon and into act Here it is the height of the class interval. Now, by substituting the known values, we get men as equals two 92.5 plus six upon 60 into five. By simplifying it, we get 9.3. Similarly, we will find variants which is equal to it's square opponents square into an into sigma, f i UK square minus sigma, f i u I whole square by substituting the noon values. We get variances equals two five square, about 60 square into 60 into 250 for minus six square. It would be equal to 25 upon 3600 until 15,204 which is equal to 105.58 Now we will find standard deviation that is equal to underwrote variance. Therefore we get standard deviation is equals two under route 105.58 which is equals two, 10.27 Hence we get mean is equal to 9.3, variances equals two 105.58 And standard deviation is equal to 10.27

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