Question

unit 4 test: graphs and describing distributions multiple choice

1. to locate the median of 24 observations, you would count up to what position after arranging the data in order from smallest to largest?

(a) half - way between the 12th and 13th in the ordered list.
(b) 50th in the ordered list.
(c) 71st in the ordered list.
(d) 75th in the ordered list.
(e) half - way between the 71st and 72nd in the ordered list

Explanation:

Step1: Recall the formula for median position

When \(n\) (number of observations) is even, the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered values. Here \(n = 24\) (even).

Step2: Calculate \(\frac{n}{2}\) and \(\frac{n}{2}+1\)

\(\frac{n}{2}=\frac{24}{2}=12\), \(\frac{n}{2}+1=\frac{24}{2}+1 = 13\)

Answer:

A. Half - way between the \(12^{th}\) and \(13^{th}\) in the ordered list.