Question

If you have a set of data that is normally distributed, interpret the mean as a percentile, a quartile, and a standard score.

Answer 1

Answer)

As the data is normally distributed, we can use standard normal z table to answer this question.

Z = (x-mean)/standard deviation

Now here we need to interpret mean

That is x is = mean

Z = (mean - mean)/s.d

Z = 0

Z is nothing but our standard score

Standard score is 0

From z table p(z<0) = 0.50

That is 50% of the data lies below the standard score 0 or mean

So, percentile of mean is 0.5 or 50%

And standard score is 0

Quartile is the 25 percentile

Or a standard score which corresponds to 0.25.

Below the quartile 25% of the data lies.