Question

Calculate the standard deviation for the following data:5, 8,7,11, 9,10,8,2,4,6​

Answer 1

Answer:

5+7+8+11+9+10+8+2+4+6=70

70/no of observation

70/10

7

Step-by-step explanation:

7 is the answer

X. d(x-a)(a=9).

5. -4

7 -2

8. -1

11. 2

9. 0

10. 1

8. -1

2. -7

4. -5

6. -3

deviation mean = sum of d / no. of observation + A

mean= (-23)/ 10+ 9

=7

Answer 2

Answer:

The standard deviation of the data is $7$

Step-by-step explanation:

First, lets find the arithmetic mean of the given data.

Mean $=\frac{sum}{number of terms}$

$=\frac{5+8+7+11+9+10+8+2+4+6}{10}$

$=\frac{70}{10}\\\\ =7$

Now, find the difference between each term from the mean :

( No need to consider negative sign as we're only considering the magnitude)

$5 -7=2$

$8-7=1\\7-7=0\\11-7=4\\9-7=2\\10-7=3\\8-7=1\\2-7=5\\4-7=3\\6-7=1$

Now, to find the standard deviation :

Find the squares of these differences and add them :

$2^2+1^2+0^2+4^2+2^2+3^2+1^2+5^2+3^2+1^2=70$

Find the mean of this value i.e. divide this sum by the number of terms :

$\frac{70}{10}=7$

Hence, the standard deviation is $7$