Question

The mean score of the maths test is 70 with a standard deviation if 12. Calculate the z-score of a student who got 55 marks. Interpret the result.

Answer 1

Z = -1.2 ( It is below the group mean), The sudent performed less than average.

Explanation:

From the question,

Applying

Z = (x-μ)/σ........................ Equation 1

Where Z = z-score, x = observed score or raw score, μ = mean of the score, σ = standard deviation of the score

Given: x = 55 marks, μ = 70, σ = 12

Substitute these values into equation 1

Z = (55-70)/12

Z = -15/12

Z = -1.25

Hence the z- score is negative, meaning it is below the group mean, I.e the student who get 55 marks, performed less than average