lifetime pets\nwhich of the following is most likely true?\nthe mean and median are both in the interval 1…

Explanation:

Step1: Calculate total number of adults

We have the frequencies for each interval: 1 - 5 has 14 adults, 6 - 10 has 9 adults, 11 - 15 has 6 adults and 16 - 20 has 2 adults. So the total number of adults $n=14 + 9+6 + 2=31$.

Step2: Find the median position

Since $n = 31$ (an odd - numbered data set), the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{31+1}{2}=16$-th value.

Step3: Determine the median interval

Counting the frequencies, the first 14 values are in the 1 - 5 interval. Since $14<16$ and $14 + 9=23>16$, the median is in the 6 - 10 interval.

Step4: Estimate the mean

To estimate the mean, we assume the mid - points of each interval: mid - point of 1 - 5 is 3, mid - point of 6 - 10 is 8, mid - point of 11 - 15 is 13 and mid - point of 16 - 20 is 18. The mean $\bar{x}=\frac{14\times3 + 9\times8+6\times13 + 2\times18}{31}=\frac{42+72 + 78+36}{31}=\frac{228}{31}\approx7.35$. So the mean is in the 6 - 10 interval.

Answer:

The mean and median are both in the interval 6 - 10.