1

Problem

Suppose you have a dataset of students' ages and their corresponding heights. The table below shows the number of students in different age groups and their average heights: Calculate the weighted average height of the students in this dataset.

2

Step

The weighted average height takes into account the number of students in each age group. To calculate it, we multiply the average height of each age group by the number of students in that group, sum those products, and then divide by the total number of students.

3

Step

From the table you provided, we can calculate the weighted average height as follows:

4

Step

Multiply the average height of each age group by the number of students in that group:

→ \$(135 cm \times 15 "students") = 2025 cm\$

→ \$(145 cm \times 20 "students") = 2900 cm\$

→ \$(160 cm \times 25 "students") = 4000 cm\$

5

Step

Sum the products

2025 cm + 2900 cm + 4000 cm = 8925 cm

6

Step

The total number of students

15 students + 20 students + 25 students = 60 students

7

Step

\$"Weighted average height" = "Sum of weighted terms" / "Total number of terms"\$

8

Step

The weighted average height is

\$(8925 cm )/ (60 "students")\$ = 148.75 cm

9

Solution

Therefore, the weighted average height of the students in this dataset is approximately 148.75 cm.

10

Sumup

Please summarize steps

Choices

11

Choice-A

This is the correct answer. It considers the number of students in each age group (weighting) when calculating the average height

Correct 148.75cm

12

Choice-B

This option is significantly lower than what we’d expect for the weighted average height. The average heights in the table (135cm, 145cm, 160cm) are already baseline averages for each age group. The weighted average considers the number of students, and because there are likely to be more students with heights closer to the initial averages, the overall weighted average wouldn’t be this low

Wrong 123.50cm

13

Choice-C

This value is too low. Even the youngest age group (10-12) would likely have an average height significantly higher than 83.25cm. The weighted average would be a combination of all three age groups and wouldn’t be this low

Wrong 83.25cm

14

Choice-D

This value is simply too low to be a realistic average height for any age group listed in the table (typically students in these ranges would be much taller than 60cm). It’s likely a result of a miscalculation or a misunderstanding of the scale used for height (e.g., centimeters vs meters)

Wrong 60.00cm

15

Answer

Option

A

16

Sumup

Please summarize choices