Question

The exam scores (out of 100 points) for all students taking an introductory Statistics course are used to construct the following boxplot. Based on this boxplot, the interquartile range is closest to 50. 25. 80. 10.

Answer 1

Answer:

The inter quartile range is 55

Step-by-step explanation:

Interquartile range:-

Definition:-

The inter quartile range is the difference between the upper (Q3) and lower(Q1) quartiles, and describes the middle  50% of values when ordered from lowest to highest.

Interquartile range = higher quartile - lower quartile

given data 50.25.80.10

write the ascending order 10 25 50 80

Step:-1

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

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

Step2:-

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 even, then the median is $({\frac{n}{2} })^{th}$

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

In given data the number of observations is '4'(even)

If the number of observations is even, then the median is $({\frac{n}{2} })^{th}$

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

median is $({\frac{4}{2} })^{th}$ is 2 observations and $({\frac{4+1}{2} })^{th}$ is 2.5 observations.

so we have to select average of these two observations.

therefore the median is '3' observation

median of the given data = 50

Step:3

Interquartile range = higher quartile - lower quartile

                                  = 80-25

                                  =55