Question

for a particular sample of 77 scores on a psychology exam, the following results were obtained:
first quartile=44, third quartile= 71, standard deviation=6, range=45, mean=64,median=57, mode=32, midrange=60

a)according to chevyshev's theorem how many students scored between 48 and 88?

b) assume that the distribution is normal. based on the empirical rule, how many students scored between 46 and 82?

* i came up with 12 for a and 24 for b, is that correct?
please help and show where i went wrong. thank you

Answer 1

From the data, mode = 32, median = 57 and mean 64, the distribution is definitely positively skewed (to the right).

Unfortunately, I don't know Chevyshev's theorem, and I would not assume the distribution to be normal.

However, for a normal distribution, Z = (score-mean)/SD

Find the Z scores for 46 and 82, then Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportions related to those Z scores and multiply those proportions by 77.