Question

here again is the histogram showing the distribution of 50 ages at death due to trauma (accidents and homicides) that occurred in a certain hospital during a week. for the data described by the above histogram, (a) the median will be bigger than the mean. (b) the median will be smaller than the mean. (c) the median and the mean will be about the same. (d) the median and the range will be about the same. (e) both (b) and (d) are correct.

Explanation:

Step1: Determine age intervals and frequencies

Intervals (10-20,20-30,...80-90); frequencies: 3,18,12,6,5,3,2,1 (sum=50).

Step2: Calculate median

n=50, median=25th/26th values. Cumulative freq: 3,21,33... → 30-40 class. Median≈30+[(25-21)/12]×10≈33.33.

Step3: Calculate mean

Midpoints:15,25,...85. Mean=(3×15+18×25+...+1×85)/50=1890/50=37.8.

Step4: Compare median and mean

Median≈33.33 < Mean=37.8 → (b) correct.

Answer:

B. the median will be smaller than the mean.