﻿ Quartile Worksheet | Problems & Solutions

# Quartile Worksheet

Quartile Worksheet
• Page 1
1.
The number of games won by a famous basketball team each year from the year 1991 to the year 2000 are 20, 25, 20, 45, 35, 50, 35, 45, 30 and 35. Find the difference of the lower quartile and the upper quartile of the data set.
 a. 25 b. 20 c. 15 d. None of the above

#### Solution:

The increasing order of the data is 20, 20, 25, 30, 35, 35, 35, 45, 45 and 50.

So, the least value of the data set is 20, the greatest value of the data set is 50 and the middle value of the data set is (35+35) / 2 = 35.

So, the lower quartile of the data set is the median of the lower half and is 25.

So, the upper quartile of the data set is the median of the upper half and is 45.

So, difference between the lower quartile and the upper quartile is 45 - 25 = 20.

2.
The rate of an article changed in six consecutive months. Its rate each month was 16, 13, 11, 8, 18, 3. Find the lower and the middle quartile in the data set.
 a. 8, 12 b. 16, 18 c. 8, 16 d. None of the above

#### Solution:

The increasing order of the data is 3, 8, 11, 13, 16, 18.

The least value of the data set is 3, greatest value is 18 and the middle value is (11+13) / 2 = 12.

The lower quartile in the data set is the value between the middle and the least value.

So, lower quartile is 8.

So, the lower quartile is 8 and the middle quartile is 12.

3.
The owner of a super market recorded the number of customers who came into his store each hour in a day. The results were 11, 7, 9, 6, 14, 2, 5, 6, 11, 7 and 8. Find the lower quartile and upper quartile from the data.
 a. 6, 11 b. 6, 9 c. 9, 11 d. None of the above

#### Solution:

The ascending order of the data is 2, 5, 6, 6, 7, 7, 8, 9, 11, 11, 14

The least value in the data is 2 and the greatest value in the data is 14.

The middle value in the data is 7.

The lower quartile is the value that is in between the middle value and the least value in the data set.

So, lower quartile is 6.

The upper quartile is the value that is in between the middle value and the greatest value in the data set.

So, upper quartile is 11.

4.
Find the lower quartile and the upper quartile from the data.
 Component Quantity Hard disk 240 Monitors 330 Keyboards 200 Mouse 160 Speakers 380

 a. 160, 380 b. 160, 240 c. 200, 330 d. None of the above

#### Solution:

The increasing order of the data is 160, 200, 240, 330, 380

The least value = 160 and the greatest value = 380.

The middle value = 240.

The lower quartile is the value between the least value and the middle value.

So, lower quartile of the data set is 200.

The higher quartile is the value between the greatest value and the middle value.

So, the higher quartile of the data set is 330.

5.
Find the average of the lower quartile and the upper quartile from the data.
 Component Quantity Harddisk 260 Monitors 290 Keyboards 210 Mouse 180 Speakers 350
 a. 290 b. 250 c. 210 d. None of the above

#### Solution:

The increasing order of the data is 180, 210, 260, 290, 350

The least value of the data is 180 and the greatest value of the data is 350.

The middle value of the data is 260.

The lower quartile is the value that is between the least value and the middle value.

So, lower quartile is 210.

The higher quartile is the value that is between the greatest value and the middle value.

So, higher quartile is 290.

The average of the lower quartile and the higher quartile is (210+290) / 2 = 250.

6.
Find the average of the lower, the middle and the upper quartiles of the data.
15, 18, 23, 12, 10, 0, 6, 7, 22 and 12
 a. 12.333 b. 9.333 c. 15.333 d. 16.633

#### Solution:

The data values in the ascending order are 0, 6, 7, 10, 12, 12, 15, 18, 22 and 23

Middle quartile is the median of the entire data values.

So, middle quartile of the data = 12+12 / 2
[As there are 10 values, middle quartile is the average of 5th and 6th values.]

= 12
[Divide.]

Lower quartile is 7 and the upper quartile is 18.
[Middle value of lower half is the 3rd value and that of upper half is 8th value.]

Average of all the quartiles = 12+7+18 / 3
[Average = sum of valuescount of values]

= 373

= 12.333
[Divide.]

So, average of all the quartiles is 12.333.

7.
Find the lower quartile of the data set.
8, 4, 17, 32, 34, 14, 29, 23 and 21
 a. 8 b. 14 c. 11 d. 21

#### Solution:

The data set in the ascending order is 4, 8, 14, 17, 21, 23, 29, 32 and 34.

The lower quartile is the middle value in the lower half of the data set.

So, the lower quartile of the data is the mean value of 8 and 14.

= 8 + 142
[Formula for the mean.]

= 22 / 2
[Add the numbers in the numerator.]

= 11
[Divide.]

So, the lower quartile of the data set is 11.

8.
Annie conducted a math test for her students. The scores they got in the test are 16, 19, 9, 14, 31, 9, 24, 16, 19, 14 and 31. Find the difference between the lower quartile and the middle quartile of the data.
 a. 9 b. 14 c. 16 d. 2

#### Solution:

The data in the ascending order is 9, 9, 14, 14, 16, 16, 19, 19, 24, 31 and 31.

Middle quartile is the middle data value, which is 16.
[As there are 11 data values, middle value is 6th data value.]

Lower quartile is the middle data value in the lower half of the data.

Lower quartile of the data is 14.
[Middle value in the lower half is the 3rd data value.]

The difference between the middle quartile and the lower quartile = 16 - 14 = 2.
[Subtract the lower quartile value from the middle quartile value.]

9.
The salaries (in hundreds of dollars) of the employees at a local company are 7, 4, 10, 18, 7, 3, 15, 34, 21, 30 and 18. What is the sum of the lower quartile and the upper quartile?
 a. 14 b. 7 c. 28 d. 21

#### Solution:

Lower quartile is the middle data value of the lower half of the data and upper quartile is the middle data value of the upper half of the data.

The data values in the ascending order are 3, 4, 7, 7, 10, 15, 18, 18, 21, 30 and 34.
[Arrange from the least to the greatest.]

There are 11 data values in the data set. So, middle value is the 6th data value.

Lower quartile of the data is the 3rd data value, which is 7.
[Middle data value of the lower half.]

Upper quartile of the data is the 9th data value, which is 21.
[Middle data value of the upper half.]

The sum of the lower quartile and the upper quartile = 7 + 21 = 28

10.
The table shows the number of immigrants to the U.S. from various countries during 1981- 1990. Find the sum of the lower, the middle and the upper quartiles of the data.

 a. 830 b. 1082 c. 1081 d. 1000

#### Solution:

The data values in the ascending order are 159, 251, 252, 281, 334, 549 and 1656.
[Arrange from the least to the greatest.]

Middle quartile is the middle value of the data, which is 281.

Lower quartile is the middle value of the lower half of the data = 251

Upper quartile is the middle value of the upper half of the data = 549

Sum of all quartiles = 281 + 251 + 549 = 1081.