Question

the histogram below shows the number of cans each student brought in during one day of the canned food drive.

1. how many students are included in this graph?
2. which is greater: the mean of the data set or the median of the data set? explain.
3. what is the ratio of students who brought in at least 15 cans to students who brought in less than 15 cans?
4. if 120 students participated in the canned food drive, how many would you expect to have brought in at least 15 cans on this day?

Explanation:

Step1: Sum all student counts

$1 + 2 + 2 + 4 + 6 = 15$

Step2: Calculate mean (use midpoints)

Midpoints: 2.5, 7.5, 12.5, 17.5, 22.5
$\text{Mean} = \frac{(1 \times 2.5) + (2 \times 7.5) + (2 \times 12.5) + (4 \times 17.5) + (6 \times 22.5)}{15}$
$= \frac{2.5 + 15 + 25 + 70 + 135}{15} = \frac{247.5}{15} = 16.5$

Step3: Find median (8th value)

Ordered data: 2.5, 7.5,7.5,12.5,12.5,17.5,17.5,17.5,17.5,22.5,22.5,22.5,22.5,22.5,22.5
Median = 17.5

Step4: Compare mean and median

$17.5 > 16.5$, so median > mean

Step5: Count students for ratio

At least 15 cans: $4 + 6 = 10$; Less than 15 cans: $1 + 2 + 2 = 5$
Ratio: $\frac{10}{5} = 2:1$

Step6: Calculate expected students

Proportion of ≥15 cans: $\frac{10}{15} = \frac{2}{3}$
Expected: $120 \times \frac{2}{3} = 80$

Answer:

1. 15
2. The median is greater. The mean is 16.5 and the median is 17.5; the data is left-skewed, so the median is higher than the mean.
3. $2:1$
4. 80