Here are the calculations for Q1 (25th percentile) of histogram c. The cumulative percentage at the top right of each histogram rectangle shows that the second rectangle contains the 25th percentile because 25% is between 20% and 60%. Here is a blowup of the second rectangle of the histogram: 60 + 20% 25% 60% Since the widths and areas of rectangles | v v v of the same height are proportional, 40 + +-+-------------+ w1 / w2 = a1 / a2. Therefore | | | | 30 + | | | Q1 - 1 25 - 20 | | | | ------ = ------- 20 + | | | 2 - 1 60 - 20 | | | | 10 + | | | (m - 1) / 1 = 5 / 40 | | | | m - 1 = 0.125 0 + +---------------+ median = m = 1.125 ^ ^ ^ 1 Q1 2 Here are the calculations for Q3 (75th percentile) of histogram c. The cumulative percentage at the top right of each histogram rectangle shows that the third rectangle contains the 75th percentile because 75% is between 60% and 90%. Here is a blowup of the third rectangle of the histogram: 60% 75% 90% V V V 60 + +---+---+ Since the widths and areas of rectangles | | | | of the same height are proportional, 40 + | | | w1 / w2 = a1 / a2. Therefore | | | | 30 + | | | Q1 - 1 25 - 20 | | | | ------ = ------- 20 + | | | 2 - 1 60 - 20 | | | | 10 + | | | (m - 1) / 1 = 5 / 40 | | | | m - 1 = 0.125 0 + +---+---+ median = m = 1.125 ^ ^ ^ 1 Q1 2