Question

1. in which data set or sets below does the median equal 100?

a. 50, 100, 100, 200
b. 50, 100, 200, 200
c. 500, 400, 100, 100
d. 500, 400, 200, 100

Explanation:

Step1: Sort each data set

A: $50, 100, 100, 200$ (already sorted)
B: $50, 100, 200, 200$ (already sorted)
C: $100, 100, 400, 500$ (sorted)
D: $100, 200, 400, 500$ (sorted)

Step2: Calculate median for 4 values

For even $n=4$, median = $\frac{\text{2nd value} + \text{3rd value}}{2}$

• A: $\frac{100 + 100}{2} = 100$
• B: $\frac{100 + 200}{2} = 150$
• C: $\frac{100 + 400}{2} = 250$
• D: $\frac{200 + 400}{2} = 300$

Answer:

A. 50, 100, 100, 200