Question

The table shows the number of hours Hazel worked per week at her part-time job for the last 20 weeks. 9 22 16 12 16 10 22 16 17 8 20 18 10 20 25 6 14 10 14 20 Identify the five number summary (lowest value, first quartile, median, third quartile, and highest value) for the corresponding box plot. A. 6, 12, 16, 20, 25 B. 6, 10, 17, 22, 25 C. 6, 12, 18, 22, 25 D. 6, 10, 16, 20, 25

Answer 1

Answer:

• lowest value is: 6

• highest value is: 25.

• Median ($Q_{2}$) is 16.

• lower quartile ($Q_{1}$) is: 10.

• third quartile ($Q_{3}$) is: 20.

Step-by-step explanation:

We are given a set of the data as:

9 22 16 12 16    10 22 16 17 8    20 18 10 20 25  6 14 10 14    20

on arranging this data in ascending order we have:

6    8     9    10    10    10    12    14   14    16    16    16    17     18      20    20    20   22   22    25

Hence, the lowest value is: 6

The highest value is: 25.

Now the data is divided into 3 quartiles.

Median ($Q_{2}$) is defined as the central tendency of a data i.e. the middle value of the data.

Hence the median here will lie between: 16 and 16.

Hence the median ($Q_{2}$) is 16.

Now the lower set of data is:

6    8     9    10    10   10    12    14   14  

Hence, the lower quartile($Q_1$) is the median of the lower set of data i.e. the middle term in the following lower set of data.

Hence, the lower quartile ($Q_{1}$) is: 10

Similarly the upper set of data is given as:

16    17     18      20    20    20   22   22    25

Hence, the third quartile ($Q_3$) is the median of the lower set of data i.e. the middle term in the following lower set of data.

Hence, the third quartile ($Q_{3}$) is: 20