Question

Given the data set: 6, 19, 17, 23, 20, 10. Determine

(i). the percentile rank for each test score,

(ii). test score that corresponds to the 50th percentile.

Answer 1

Formula to calculate percentile rank is-

Where, c_lis the count of all scores less than the score of interest, N is the total number of values in the sample.

Lets first arrange data in increasing order - 6, 10, 17, 19, 20, 23

i) -

By using the formula for percentile, percentile rank for each score -

for 6 -

for 10-

for 17 -

for 19 -

for 20 -

for 23 -

ii) -

We have to calculate the score that corresponds to 50th percentile.

For this. we first rank the values in the data set in order from smallest to largest.

6	10	17	19	20	23
1	2	3	4	5	6

Now, we multiply 50% by N(total number of values in the sample) to get position of number.

So, position of number = 0.5(6) = 3

Hence, 50th percentile for the given scores is 17.