Question

Which statement is true about the box plots? Both the ranges and the interquartile ranges for the data sets are the same. Neither the ranges nor the interquartile ranges for the data sets are the same. The interquartile ranges for the box plots are the same

Answer 1

Answer:

Neither the ranges nor the interquartile ranges for the data sets are the same.

Step-by-step explanation:

In a visual display, the boxplot presents five sample statistics: the minimum, the lower quartile, the median, the upper quartile and the maximum, and the box length gives an indication of the sample variability and the line across the box shows where the sample is centred, with an end at each quartile. The length of the box is thus the interquartile range of the sample and, whether the sample is symmetric or skewed, either to the right or left, the "shape" of the sample, and by implication, the shape of the population from which it was drawn, considering appropriate analyses of the data.

Answer 2

The question is incomplete! The complete question along with answer and explanation is provided below.  

Question:  

Which statement is true about the box plots? (attached in the image)

A Both the ranges and the interquartile ranges for the data sets are the same.

B. Neither the ranges nor the interquartile ranges for the data sets are the same.

C. The interquartile ranges for the box plots are the same, but their ranges are different.

D. The ranges for the box plots are the same, but their interquartile ranges are different.

Answer:

D. The range of both box-pots is same (9) but the interquartile range of box-plots is different (6 and 5)

Step-by-step explanation:

To answer this question, first we have to understand what a box plot is!

A box plot is a type of graph which shows 5 statistical characteristics of a data set.

1. Maximum and 2. Minimum values of data

3. Upper Interquartile and 4. Lower interquartile of data

5. Median of the data

Now lets analyze the attached box-plot so that we can conclude what is true about them and what is not!

We have two box-plots for two teacher's classes Marc and Sue and they show the number of incorrect questions in exam.

For Sue's class: (on the bottom)

As you can see the maximum and minimum values are

Maximum = 12 and Minimum = 3

So the Range becomes = 12 - 3 = 9

The upper quartile Q3 is 10 and lower quartile Q1 is 5

So the Interquartile Range becomes = 10 - 5 = 5

This Interquartile Range represents the 25 to 75 percentile of the data

There is little vertical line skewed to the right represents the Median = 9

So to summarize Sue's class

Range = 9

Interquartile Range = 5

Median = 9

For Marc's class: (on the top)

As you can see the maximum and minimum values are

Maximum = 10 and Minimum = 1

So the Range becomes = 10 - 1 = 9

The upper quartile Q3 is 9 and lower quartile Q1 is 3

So the Interquartile Range becomes = 9 - 3 = 6

This Interquartile Range represents the 25 to 75 percentile of the data

There is little vertical line skewed to the left represents the Median = 5

So to summarize Marc's class

Range = 9

Interquartile Range = 6

Median = 5

Conclusion:

The range of both box-pots is same (9) but the interquartile range of box-plots is different (6 and 5).

Therefore, we can confidently conclude that option D is the correct answer.