Question

What is the sd of the following values. 7,7,7,7,7​

Answer 1

Given :- What is the sd of the following values. 7,7,7,7,7 ?

Solution :-

→ Mean of given data = 7 + 7 + 7 + 7 + 7 = 7 * 5 / 5 = 7

now,

→ sum of (difference between mean and each data)² = (7 - 7)² + (7 - 7)² + (7 - 7)² + (7 - 7)² + (7 - 7)² = 0 + 0 + 0 + 0 + 0 = 0

then,

→ SD = √(sum of (difference between mean and each data)² / (N - 1)

→ SD = √0/4

→ SD = 0 (Ans.)

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Answer 2

SOLUTION

TO DETERMINE

The SD of the values 7 , 7 , 7 , 7 , 7

EVALUATION

Here the given observations are

7 , 7 , 7 , 7 , 7

Number of observations = 5

$\displaystyle \sf{ \sum x_i = 7 + 7 + 7 + 7 + 7 = 35 }$

$\displaystyle \sf{ Mean = \bar{x} = \frac{\sum x_i}{n} = \frac{35}{5} = 7}$

Now

$\displaystyle \sf{ S.D. = \sqrt{ \frac{ \sum \: {(x_i - \bar{x})}^{2} }{n} } }$

$\displaystyle \sf{ \implies \: S.D. = \sqrt{ \frac{ \displaystyle \sf{} \sum_{i = 1}^{5} \: {(7- 7)}^{2} }{5} } \: \: \bigg( \because \: x_{i} = 7 \: \: \forall \: i \: \bigg)}$

$\displaystyle \sf{ \implies \: S.D. = \frac{0}{5} }$

$\displaystyle \sf{ \implies \: S.D. = 0}$

FINAL ANSWER

Hence the required S. D. = 0

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