Question

in northwest pennsylvania, a zoologist recorded the ages, in months, of 55 bears and whether each bear was male or female. the data are shown in the back - to - back stemplot below. based on the stemplot, which of the following statements is true? a the median age and the range of ages are both greater for female bears than for male bears.

Explanation:

Step1: Count number of data - points for each gender

There are 25 female bears and 30 male bears.

Step2: Find median for female bears

For 25 data - points (odd number), median is the 13th value when ordered. Arranging female bear ages from the stemplot and counting, we find the median. The ages of female bears in ascending order: 130, 132, 154, 8, 2, 1, 10, 10, 1, 2, 3, 4, 5, 6, 8, 8, 20, 21, 22, 24, 26, 27, 28, 29, 41, 42, 44, 45, 46, 52, 53, 58, 60, 61, 94. The 13th value is 42 months.

Step3: Find median for male bears

For 30 data - points (even number), median is the average of 15th and 16th values when ordered. Arranging male bear ages from the stemplot and counting, the 15th and 16th values are 24 and 26. Median = $\frac{24 + 26}{2}=25$ months.

Step4: Find range for female bears

Range = maximum value - minimum value. Maximum age of female bears is 154 months, minimum is 8 months. Range = 154 - 8=146 months.

Step5: Find range for male bears

Maximum age of male bears is 70 months, minimum is 15 months. Range = 70 - 15 = 55 months.

Answer:

A. The median age and the range of ages are both greater for female bears than for male bears.