Form a hypothesis concerning a potential set of data. For instance, out of 100 people who buy a car from a particular dealership that has red, blue white and black cars, you might hypothesize that 40 people will buy a white car, 30 will buy a blue car, 20 people will buy a black car and 10 people will buy a red car.
Make observations and record the data. For instance, when you actually keep records concerning car purchases, you might find that 40 people bought a blue car, 25 bought a white car, 20 bought a red car and 15 bought a black car.
Determine the deviation for each category by subtracting the hypothesized value from the observed value. Therefore the deviation for blue cars would be 10, white cars would be -15, red cars would be 10 and the black cars would be -5.
Square the deviations; that is, multiply the number times itself. The squared deviation for blue cars would be 100, 225 for white cars, 100 for red cars and 25 for black cars.
Divide the values you found in Step 4 by each hypothesized ("expected") value from Step 1. Therefore, you would divide 100 by 30 for blue cars to get 3.33. Divide 225 by 40 for white cars to get 5.625. Divide 100 by 10 for red cars to get 10. Divide 25 by 20 for black cars to get 1.25.
Add your answers from Step 5 to find the chi-square. For this example, 3.33 + 5.625 + 10 + 1.25 = 20.205. Therefore the value of the chi-square would be 20.205.