Question

The steps to make a box plot of the given data are as follows. Find the error in the steps.

Given data: 30, 35, 40, 50, 60, 65, 70

• A. Draw the box from Q1 to Q2
  
• B. Arrange the data in ascending order and find median (Q2). Median = 50.
• C. Find the quartiles Q1 and Q3. Q1 = 35, Q3 = 65
• D. Draw the box from Q1 to Q3.

Answer 1

The correct option is A Draw the box from Q1 to Q2


The given data set is

30, 35, 40, 50, 60, 65, 70

To make a box plot,
we have to arrange the data in ascending order and find the median(Q2).

The first step given is "Arrange the data in ascending order and find median (Q2). Median = 50."
Hence, the first step given is correct.


The next step is to find the lower quartile Q1( median of lower half data), upper quartile Q3(median of upper half data).

Median of the data set = 50
When we divide the data into two halves, we get,
Lower half data = 30, 35, 40
Median(Q1) = 35
Upper half data = 60, 65, 70
Median(Q3) = 65

Hence, the next step "Find the quartiles Q1 and Q3. Q1 = 35, Q3 = 65" is correct.


The next step to create a box plot is to draw a box from Q1 to Q3.

But the next step given is "Draw the box from Q1 to Q2"

Hence, the error in the given steps is "Draw the box from Q1 to Q2".