the histogram shown summarizes the responses of 100 people when asked, \what was the price of the last meal…

Explanation:

Step1: Calculate cumulative frequencies

First, find the cumulative frequencies for each price - point. The total number of data points is $n = 100$.

Price ($)	Frequency	Cumulative Frequency
5	8	8
9	13	8 + 13=21
13	11	21+11 = 32
17	14	32 + 14=46
21	8	46+8 = 54
25	5	54+5 = 59
29	3	59+3 = 62
33	2	62+2 = 64
37	0	64+0 = 64
41	1	64+1 = 65
45	1	65+1 = 66

Step2: Find the first quartile ($Q_1$) position

The position of $Q_1$ is $L_{Q_1}=\frac{n + 1}{4}=\frac{100+1}{4}=25.25$. The value of $Q_1$ lies in the class where the cumulative - frequency first exceeds 25.25. Looking at the cumulative frequencies, 25.25 lies in the class with a price of $9$ (since the cumulative frequency up to the class with price $9$ is 21 and up to the class with price $13$ is 32). We can approximate $Q_1$ using the formula for the first quartile in a grouped data set (if needed, but for a rough estimate, we know it's in the $9$ - $13$ range and closer to $9$). A simple estimate is that $Q_1\approx9$.

Step3: Find the third quartile ($Q_3$) position

The position of $Q_3$ is $L_{Q_3}=\frac{3(n + 1)}{4}=\frac{3\times(100 + 1)}{4}=75.75$. The value of $Q_3$ lies in the class where the cumulative - frequency first exceeds 75.75. Looking at the cumulative frequencies, 75.75 lies in the class with a price of $21$ (since the cumulative frequency up to the class with price $17$ is 46 and up to the class with price $21$ is 54). A simple estimate is that $Q_3\approx21$.

Step4: Calculate the inter - quartile range (IQR)

The inter - quartile range is $IQR = Q_3-Q_1$. $IQR=21 - 9=12$. The closest value to 12 among the given options is $10$.

Answer:

C. $10$