Question

Answer the following questions in about 125 words:
(iii) Explain the process of computing Standard Deviation with the help of an
imaginary example.

Answer 1

Answer:

Standard deviation is a number used to tell how measurements for a group are spread out from the average (mean), or expected value. A low standard deviation means that most of the numbers are close to the average. A high standard deviation means that the numbers are more spread out

Answer 2

Answer:

Explanation:

the standard deviation is a measure of data which determines how much data is closer to the mean of it.it is useful in comparing the sets of data having same mean.

the process of computing standard deviation is

step 1: find the mean of the given data i.e,

mean= sum of the values÷total no of values in the data

step 2:then subtract each value of  the data with the mean,and square the result

step 3: then again find out the mean of the squared differences

step 4: then finally find out the square root of the value of the final mean obtained.

standard deviation formula is given by √(1/n(∑x-α)²).

let us consider an example to  understand more better

let the data given be 9,5,2,4

find the mean to the given data =(9+5+2+4)/4=5

the mean of the data is 5

then subtract each value with the mean and square them i.e,

9-5=4=>(4)^2=16

5-5=0=>(0)^2=0

2-5=-3=>(-3)^2=9

4-5=-1=>(-1)^2=1

now find the mean of all the resultant values =>

(16+0+9+1)/4=26/4=13/2=6.5

now find out the square root of 6.5

√6.5=2.549

therefore the standard deviation of the given data is 2.549.