Question

1. in a classroom there are 6 students who are 5 1/2 feet tall, 2 students who are 4 1/2 feet tall, 4 students who are 4 1/4 feet tall, and 2 students who are 6 foot tall. which expression represents the mean height of the students in the classroom?

a. 6×2×4×2 / 6(5 1/2)+2(4 1/2)+4(4 1/4)+2(6)
b. 6 + 2+4 + 2 / 6(5 1/2)+2(4 1/2)+4(4 1/4)+2(6)
c. 6(5 1/2)+2(4 1/2)+4(4 1/4)+4(6) / 6 + 2+4 + 2
d. 6(4 1/2)+2(5 1/2)+4(6)+4(4 1/4) / 6 + 2+4 + 2

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}$, where $x_{i}$ is the value and $f_{i}$ is the frequency.
We have 6 students of height $5\frac{1}{2}$ feet, 2 students of height $4\frac{3}{4}$ feet, 4 students of height $4\frac{1}{4}$ feet and 2 students of height 6 feet.
The sum of the products of height - frequency is $6\times(5\frac{1}{2})+2\times(4\frac{3}{4})+4\times(4\frac{1}{4})+2\times6$.
The sum of the frequencies is $6 + 2+4 + 2$.

Step2: Identify the correct expression

The expression for the mean height is $\frac{6(5\frac{1}{2})+2(4\frac{3}{4})+4(4\frac{1}{4})+2(6)}{6 + 2+4 + 2}$.

Answer:

C. $\frac{6(5\frac{1}{2})+2(4\frac{3}{4})+4(4\frac{1}{4})+2(6)}{6 + 2+4 + 2}$