Question

Calculate standard deviation from the two sets of income distribution of six and seven person respectively.
Income
Distribution
2200
2400
2600
2700
2800
2900
1CRS​

Answer 1

Given : Income Data

2200

2400

2600

2700

2800

2900

To Find : Standard deviation

Solution:

Mean μ = ( 2200 + 2400 + 2600 + 2700 + 2800 + 2900)/6

= 2600

x                | xi - μ |          ( | x - μ |)²

2200             400                   160000

2400             200                    40000

2600              0                       0

2700             100                    10000    

2800             200                    40000

2900           300                    90000

                                              340000

$\sigma={\sqrt {\frac {\sum(x_{i}-{\mu})^{2}}{N}}}$

= √(340000/6)

=  238.01

≈ 238

standard deviation = 238

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Answer 2

Answer:

238.01

Explanation:

Standard deviation can be calculated through the following steps;

Calculate the average of the given data set;

Average of 2200

,2400

,2600

,2700

,2800

,2900 is 2600

Now Subtract the mean from each number;

(-400) , (-200) , (0) , (100) , (200) , (300) ,

Taking square of each and Add up all of the results

= 340000

Divide the sum of squares by the number of numbers

= (340000)/ (6)

=56666

Taking the square root

=238.01

Hence standard deviation is 238.01