Question

1. the median of which data set is 5?

a. 4, 5, 6, 7
b. 2, 6, 8
c. 5, 4, 4, 5
d. 3, 4, 5, 6, 7

Explanation:

Step1: Recall median formula

For a data set with \( n \) values:

• If \( n \) is odd, median is the \( \frac{n + 1}{2} \)-th value (when sorted).
• If \( n \) is even, median is the average of the \( \frac{n}{2} \)-th and \( (\frac{n}{2}+ 1) \)-th values (when sorted).

Step2: Analyze Option a

Data set: \([4, 5, 6, 7]\) (already sorted), \( n = 4 \) (even).
Median = \(\frac{5 + 6}{2}=\frac{11}{2} = 5.5\).

Step3: Analyze Option b

Data set: \([2, 6, 8]\) (already sorted), \( n = 3 \) (odd).
Median is the \( \frac{3 + 1}{2}=2 \)-nd value, which is \( 6 \).

Step4: Analyze Option c

First, sort the data set: \([4, 4, 5, 5]\), \( n = 4 \) (even).
Median = \(\frac{4 + 5}{2}=\frac{9}{2}=4.5\).

Step5: Analyze Option d

Data set: \([3, 4, 5, 6, 7]\) (already sorted), \( n = 5 \) (odd).
Median is the \( \frac{5+ 1}{2}=3 \)-rd value, which is \( 5 \).

Answer:

d. [3, 4, 5, 6, 7]