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