Chi Square Formula

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Chi square is a statistical measure of difference between actual counts and expected counts in an

experiment. These experiments may be binomial or multinomial statistical experiment. In the experiment the

observations helps to tell the actual count and the expected count is found by mathematical models. The Chi

square formula is given by:

∑n k=1 (e – f ) ^ 2 / e, where k = 1, 2 ,....n. e = expected count, f = observed count.

When Chi square is zero that means the difference between actual and observed is zero or meaning both are

same. It is also known as “goodness of fit”



Example 1:- Find the Chi square for the given data

Actual: 3, 15, 30, and 20

Expected: 10, 30, and 40.


Solution 1:- In the given problem

 Find = (e – f)^2/e and then find the sum for all the 4 values.

(10-3)^2/10 + (30-15)^2/30 + (40-30)^2/40 + (30-20)^2/30

 4.9 + 7.5 + 2.5 + 3.33 = 18.23

 The Chi square for the given data will be 18.23


Example 2:- Find the Chi square for the given data

Actual : 8, 42, 28, 45

Expected : 10, 45, 30, 50


Solution 2:- In the given problem

 Find = (e – f)^2/e and then find the sum for all the 4 values.

 (10-8)^2/10 + (45-42)^2/45 + (30-28)^2/30 + (50-45)^2/50

 0.4 + 0.20 + 0.133 + 0.5 = 1.233

 The Chi square for the given data will be 1.233

 

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