Question

How do you draw a box-and-whisker plot for the following unordered data. 49,57,53,54,49,67,51,57,56,59,57,50,49,52,53,50,58?
 (a) Arranging in descending order
(b) Arranging in ascending order
(c) Finding the largest number
(d) None of these

Answer 1

Hint: To start with, we have the given problem as, following unordered data. To start with, we will arrange them into ascending order. Then checking them into two halves and finding the two different medians we will get the box-and-whisker plot. Hence, we will get our needed solution.

Complete step by step solution:
According to the question, we are to draw a box-and-whisker plot for the following unordered data. 49,57,53,54,49,67,51,57,56,59,57,50,49,52,53,50,58.
We will have to start it by arranging them into an ascending order.
49,49,49,50,50,51,52,53,53,54,56,57,57,57,58,59,67.
So, we can now see, 49 is the smallest number among them.
53 is our given median which we will call M.
And 67 is the largest one.
Now, we will try to consider each half differently and try to analyze them .
So, the first half goes,
49,49,49,50,50,51,52,53.
From this half now, we are to find the value of the median of the given terms.
The median is now, ${{M}_{1}}=\dfrac{50+50}{2}=50$
For the second half, 54,56,57,57,57,58,59,67.
From this second half now, we are also finding the value of the median of the given terms.
The median is now, ${{M}_{2}}=\dfrac{57+57}{2}=57$
Thus, we get the box-and-whisker plot looks like:

This is our needed solution.
Hence, we have our solution as, (b) Arranging in ascending order.

Note: Median is the middle number in a sorted list of numbers. To determine the median value in a sequence of numbers, the numbers must first be sorted, or arranged, in value order from lowest to highest or highest to lowest. The median can be used to determine an approximate average, or mean, but is not to be confused with the actual mean.