Question

In a distribution of 10 observations, the value of mean and standard deviation are given as 20 and 8. By mistake, two values are taken as 12 and 6 instead of 8 and 16. Find out the value of correct mean and variance. *
1 point
19.6, 7.32
20.6, 7.32
20.6, 8.01
19.6, 8.01​

Answer 1

bug you but I don't know what I want

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

In a distribution of 10 observations, the value of mean and standard deviation are given as 20 and 8. By mistake, two values are taken as 12 and 6 instead of 8 and 16. Find out the value of correct mean and standard deviation

• 19.6 , 7.32

• 20.6 , 7.32

• 20.6 , 8.01

• 19.6 , 8.01

EVALUATION

Number of observations = 10

In the initial case mean = 20

Initial total = 10 × 20 = 200

Since by mistake two values are taken as 12 and 6 instead of 8 and 16

Correct total

= 200 - 12 - 6 + 8 + 16

= 206

So correct mean

$\sf \: = \dfrac{206}{10}$

$\sf \: = 20.6$

Again

$\displaystyle \sf \: SD = \sqrt{ \frac{ \sum {x}^{2} }{n} - { \bigg( \frac{ \sum x}{n} \bigg)}^{2} }$

$\displaystyle \sf \implies 8 = \sqrt{ \frac{ \sum {x}^{2} }{10} - { \bigg( \frac{200}{10} \bigg)}^{2} }$

$\displaystyle \sf \implies \frac{ \sum {x}^{2} }{10} - { \bigg( 20 \bigg)}^{2} = 64$

$\displaystyle \sf \implies \frac{ \sum {x}^{2} }{10} - 400 = 64$

$\displaystyle \sf \implies \frac{ \sum {x}^{2} }{10} = 464$

$\displaystyle \sf \implies \sum {x}^{2} = 4640$

Since by mistake two values are taken as 12 and 6 instead of 8 and 16

$\displaystyle \sf Correct \: value \: of \: \: \sum {x}^{2}$

$\displaystyle \sf = 4640 - {12}^{2} - {6}^{2} + {8}^{2} + {16}^{2}$

$\displaystyle \sf = 4640 - 144 - 36 + 64 + 256$

$\displaystyle \sf = 4780$

Hence correct SD

$\displaystyle \sf \: = \sqrt{ \frac{ \sum {x}^{2} }{n} - { \bigg( \frac{ \sum x}{n} \bigg)}^{2} }$

$\displaystyle \sf \: = \sqrt{ \frac{ 4780 }{10} - { \bigg( 20.6 \bigg)}^{2} }$

$\displaystyle \sf \: = \sqrt{ 478 - 424.36}$

$\displaystyle \sf \: = \sqrt{ 53.64}$

$\displaystyle \sf \: = 7.32$

FINAL ANSWER

Hence the correct option is 20.6 , 7.32

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