Loading [MathJax]/jax/output/HTML-CSS/jax.js

Subscribe to our YouTube channel for the latest videos, updates, and tips.


Range and Interquartile Range

The variates of a data are real numbers (usually integers). So, thay are scattered over a part of the number line. An investigator will always like to know the nature of the scattering of the variates. The arithmetic numbers associated with distributions to show the nature of scattering are known as measures of dispersion. Simplest of them are:

(i) Range

(ii) Interquartile Range.


Range: The difference of the greatest variate and the smallest variate in a distribution is called the range of the distribution.

Interquartile Range: The interquartile range of a distribution is Q3 - Q1, where Q1 = lower quartile and Q3 = upper quartile.


12(Q3 - Q1) is known as semi-interquartile range.


Solved Examples on Range and Interquartile Range:

1. The following data represent the number of books issued by a library on 12 different days.

96, 180, 98, 75, 270, 80, 102, 100, 94, 75, 200, 610.

Find the (i) interquartile range, (ii) semi-interquartile range and (iii) range.

Solution:

Write the data in ascending order, we have

75, 75, 80, 94, 96, 98, 100, 102, 180, 200, 270, 610.

Here, N = 12.

So, N4 = 124 = 3, which is an integer.

Therefore, the mean of the 3rd and 4th variates is Q1 80+942 = 1742 = 87.

So, 3N4 = 3×124

                                = 364

                                = 9, i.e., 3N4 is an integer.

Therefore, the mean of the 9th and 10th variates is Q3 (the upper quartile).

Therefore, Q3 = 180+2002

                     = 3802

                     = 190.

(i) Interquartile Range = Q3 - Q1 = 190 - 87 = 103

(ii) Semi-interquartile Range = 12(Q3 - Q1)

                                          = 12(190 - 87)

                                          = 1032

                                          = 51.5.

(iii) Range = Highest Variate -  Lowest Variate 

                = 610 - 75

                = 535.

Range and Interquartile Range


2. Marks obtained by 70 students in an examination are given below.

Find the interquartile range.


Marks

25

50

35

65

45

70

Number of Students

6

15

12

10

18

9


Solution:

Arrange the data in ascending order, the cumulative-frequency table is constructed as below.


Marks

25

35

45

50

65

70

Frequency

6

12

18

15

10

9

Cumulative Frequency

6

18

36

51

61

70


Here, N4 = 704 = 352 = 17.5.

Cumulative frequency just greater than 17.5 is 18.

The variate whose cumulative frequency is 18, is 35. 

So, Q1 = 35.


Again, 3N4 = 3×704 = 1054 = 52.5.

Cumulative frequency just greater than 52.5 is 61.

The variate whose cumulative frequency is 61, is 65.

Therefore, Q3 = 65.


Thus, Interquartile Range = Q3 - Q= 65 - 35 = 30.






9th Grade Math

From Range & Interquartile Range to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  2. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  3. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  4. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More

  5. Worksheet on Rounding Off Number | Rounding off Number | Nearest 10

    May 15, 25 05:12 PM

    In worksheet on rounding off number we will solve 10 different types of problems. 1. Round off to nearest 10 each of the following numbers: (a) 14 (b) 57 (c) 61 (d) 819 (e) 7729 2. Round off to

    Read More