Question

find the standard deviation for following data: 1,2,3,4,5,6,7,8,9
a) 3
b) 2
c) 4.5
d) 2.58​

Answer 1

b) 2 is the answer of sd

Step-by-step explanation:

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Answer 2

Given:

1,2,3,4,5,6,7,8,9

To find:

The standard deviation

Solution:

The standard deviation is 2.58. (Option d)

We can find the value by following the given steps-

We know that the standard deviation can be calculated by finding out the mean of the data.

The mean of the given data is the sum of all the terms divided by the number of terms in the data.

Mean of the data=Sum of all terms/Number of terms

The number of terms in the given data=9

The sum of all the terms=1+2+3+4+5+6+7+8+9

=45

So, the mean=45/9=5

Now, we will obtain the difference of mean from each term of the data.

1-5= -4

2-5= -3

3-5= -2

4-5= -1

5-5=0

6-5=1

7-5=2

8-5=3

9-5=4

Now, we will square each of the differences obtained and add them.

=$(-4)^{2} +(-3)^{2} +(-2)^{2} +(-1)^{2} +0+1^{2} +2^{2} +3^{2} +4^{2}$

=16+9+4+1+0+1+4+9+16

=60

The standard deviation of the data=Root of the sum of the differences between each term and the mean of the data/ Number of terms

The standard deviation of the data=$\sqrt{(60/9)}$

=$\sqrt{6.66}$

=2.58

Therefore, the standard deviation is 2.58.