Question

A quantitative data set of size 70 has mean 45 And standard deviation 4. At least how many observations lie between 29 And 61?

At least _______ observations lie between 29 And 61.

Answer 1

Solution:

From the given information, we have

Mean - k*SD = 45 - 4*4 = 29

Mean + k*SD = 45 + 4*4 = 61

So, we have k = 4

So, according to Chebyshev’s theorem, we have

Required probability = 1 - (1/k^2) = 1 - (1/4^2) = 1 - (1/16) = 1 - 0.0625 = 0.9375

We are given

Total number of observations = 70

So, the number of observations lies between 29 and 61 is given as below:

Number of observations lies between 29 and 61 = 70*0.9375 = 65.625 ≈ 66

At least 66 observations lie between 29 and 61.