Question

restaurant guests
12
10
8
6
4
2
0
0 - 9 10 - 19 20 - 29 30 - 39 40 - 49 50 - 59
age (years)
which statement about the data in the histogram must be true?
a the data represent 25 restaurant guests.
b the range of ages is 59.
c the oldest restaurant guest is 59.
d the mean age of restaurant guests is 30.

Explanation:

Step1: Calculate total number of guests

Add the number of guests in each age - group: $1 + 0+0 + 6+8 + 10=25$.

Step2: Analyze range of ages

The age groups are $0 - 9$, $10 - 19$, $20 - 29$, $30 - 39$, $40 - 49$, $50 - 59$. The range is calculated as the difference between the upper - limit of the highest age group and the lower - limit of the lowest age group. The lower - limit of the lowest age group is $0$ and the upper - limit of the highest age group is $59$, so the range is $59-0 = 59$. But we don't know if there are no guests above $59$ or below $0$ in reality, this is just based on the given age - groups.

Step3: Analyze age of oldest guest

We only know the age groups, not the exact ages of the guests. The oldest guest could be less than $59$.

Step4: Analyze mean age

We don't have enough information to calculate the mean age as we don't know the exact ages of the guests within each age - group.

Answer:

A. The data represent 25 restaurant guests.