Question

A researcher decides to split scores on an exam into quartiles. She determines that a score of 64 is at the 25th percentile, a score of 74 is at the 50th percentile, and a score of 80 is at the 75th percentile. What is the interquartile range (IQR) for these data? A. 16 B. 10 C.6 D. There is not enough information to answer this question.

Answer 1

Answer:

Answer : A

Step-by-step explanation:

The given data is 25 th percentile is 64, 50th percentile is 74 and 75 th percentile is 80.

percentage : 25    50   75

  score        : 64    74    80

Median:- The median is obtained by first arranging the data in ascending or descending order and applying the following rule.

If the number of observations is odd, then the median is  observation

$(\frac{n+1}{2}) ^{th}$ term

If the number of observations is even, then the median is  observation and  observations.

$(\frac{n}{2}+1) ^{th}$

given n=3, middle term is '74'

 In this given data the median is (M) = 74

Interquartile range IQR = median of upper half-median of lower half

                                       = 80-64

                                       = 16

                            IQR = 16