**Measures of Dispersion (Part 2)**

__7.2b Interquartile Range 1__**(A) Interquartile Range of Ungrouped Data**

**Example 1:**

Find the interquartile range of the following data.

**(a)**7, 5, 1, 3, 6, 11, 8

**(b)**12, 4, 6, 18, 9, 16, 2, 14

*Solution:***(a)**Rearrange the data according to ascending order.

1 3 5 6 7 8 11

↑ ↑ ↑

lower median upper

quartile quartile

**Interquartile Range**

= upper quartile – lower quartile

= 8 – 3

= **5**

**(b)**Rearrange the data according to ascending order.

2 4 ⁞ 6 9 ⁞ 12 14 ⁞ 16 18

↑ ↑ ↑

lower median upper

quartile quartile

**Interquartile Range**

= upper quartile – lower quartile

=
$\frac{14+16}{2}-\frac{4+6}{2}$

= 15 – 5

=

=

**10****(B) Interquartile Range of Grouped Data (without Class Interval)**

**Example 2:**

The table below shows the marks obtained by a group of Form 4 students in school mid-term science test.

Marks |
1 |
2 |
3 |
4 |
5 |

Number of students |
4 |
7 |
5 |
2 |
6 |

Determine the interquartile range of the distribution.

*Solution:*Lower quartile,

*Q*_{1 }= the $\frac{1}{4}{\left(24\right)}^{\text{th}}$ observation = the 6

^{th}observation = 2

Upper quartile,

*Q*_{3 }= the $\frac{3}{4}{\left(24\right)}^{\text{th}}$ observation = the 18

^{th}observation = 4

Marks |
Frequency |
Cumulative Frequency |

1 |
4 |
4 |

2 |
7 |
11 (Q)_{1} is located here |

3 |
5 |
16 |

4 |
2 |
18 (Q)_{3} is located here |

5 |
6 |
24 |

Interquartile Range

= upper quartile – lower quartile

=

*Q*–_{3}*Q*_{1}= 4 – 2

=

**2**