Question

A boxplot helps to visualize the variability of a distribution. Five statistics form a boxplot, often referred to as the five-number summary for the distribution. How much of the data is between the first and third quartiles?
a. 75% of the data is between the first and third quartiles
b. 50% of the data is between the first and third quartiles
c. 25% of the data is between the first and third quartiles
d. 66% of the data is between the first and third quartiles

Answer 1

The 5 statistics that can be directly observed from the box plot are Minimum Value, First Quartile, Median, Third Quartile and Maximum Value. Box Plot is also known as 5 Number Summary plot.

25% of the data values lie below the First Quartile and 75% of the data values lie below the Third Quartile. From this we can conclude that in between First and Third Quartile 50% of the data lies.

Another approach: Each interval in the box plot contains 25% of the data values. 1st interval is from minimum to First Quartile, 2nd interval is from First Quartile to Median, 3rd interval is from Median to Third Quartile and the 4th interval is from Third Quartile to Maximum.

Since going from First Quartile to Third Quartile, two intervals are covered and each interval contains 25% of the data, we can conclude that 50% of the data is between First and Third Quartile.

Therefore the correct answer is option B. 50% of the data is between the first and third quartiles

Answer 2

The five-number summary of the box plot consists of the following values:
1) minimum
2) 1st quartile
3) median
4) 3rd quartile
5) maximum

The data between the first and third quartiles is: b. 50% of the data is between the first and third quartiles