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 |

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

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.

Correct answer : (2)

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 |

The least value of the data set is 3, greatest value is 18 and the middle value is

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.

Correct answer : (1)

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 |

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.

Correct answer : (1)

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 |

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.

Correct answer : (3)

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 |

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

Correct answer : (2)

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

15, 18, 23, 12, 10, 0, 6, 7, 22 and 12

a. | 12.333 | ||

b. | 9.333 | ||

c. | 15.333 | ||

d. | 16.633 |

Middle quartile is the median of the entire data values.

So, middle quartile of the data =

[As there are 10 values, middle quartile is the average of 5

= 12

[Divide.]

Lower quartile is 7 and the upper quartile is 18.

[Middle value of lower half is the 3

Average of all the quartiles =

[Average =

=

[Add numbers in the numerator.]

= 12.333

[Divide.]

So, average of all the quartiles is 12.333.

Correct answer : (1)

7.

Find the lower quartile of the data set.

8, 4, 17, 32, 34, 14, 29, 23 and 21

8, 4, 17, 32, 34, 14, 29, 23 and 21

a. | 8 | ||

b. | 14 | ||

c. | 11 | ||

d. | 21 |

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.

=

[Formula for the mean.]

=

[Add the numbers in the numerator.]

= 11

[Divide.]

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

Correct answer : (3)

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 |

Middle quartile is the middle data value, which is 16.

[As there are 11 data values, middle value is 6

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 3

The difference between the middle quartile and the lower quartile = 16 - 14 = 2.

[Subtract the lower quartile value from the middle quartile value.]

Correct answer : (4)

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 |

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 6

Lower quartile of the data is the 3

[Middle data value of the lower half.]

Upper quartile of the data is the 9

[Middle data value of the upper half.]

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

[Add both quartiles.]

Correct answer : (3)

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 |

[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.

[Add all the quartiles.]

Correct answer : (3)