Given a data set between what values would the middle 50 be

Given a data set, between what values would the middle 50% be included in? Is it between Q1 and Q3?

Solution

For any data set the quartiles Q1, Q2 and Q3 divide the number of observations in 4 parts.

1/4 number of observations before Q1.

1/4 number of observations between Q1 and Q2.

1/4 number of observations between Q2 and Q3.

1/4 number of observations after Q3.

(Note: Q2 is the median)

Between Q1 and Q3 there are (1/4 + 1/4) number of observations.

Between Q1 and Q3 there are 1/2 number of observations.i.e middle 50% of the observations.