# Quartile for Ungrouped Data

Introduction

Quartiles are the values that divide the data arranged in ascending or descending order into four equal parts. A distribution can be divided into four equal parts by three quartiles.

-      The first or lower quartile (Q1) is the point below which 25% of the items lie and above which 75% of the items lie.

-      The second quartile (Q2) is the point below which 50% of the items lie and above which 50% of the items lie. Of course, the second quartile is the median.

-      The third or upper quartile (Q3) is the point below which 75% of the items lie and above which, 25% of the items lie.

At end of the lesson the student are expected to :

a. Illustrate the following measures of position: Quartile

b. Calculate quartile as measures of position of a set of a data.

c. Solve problems involving quartile as measure of position.

Process

Formulas :Mendenhell and Sincich method

Position of  Q1 =¼ (n +1)

Position of Q2  =½ (n+1)

Position of Q3 = ¾ (n +1)

Interquartile range (IQR) Formula  =  Q3-Q1

Example 1.A random sample of 15 patients yielded the following data on the length of stay (in days) in the hospital.

5, 6, 9, 10, 15, 10, 14, 12, 10, 13, 13, 9, 8, 10, 12.

Find quartiles.

The formula for ith quartile is :

Q1 Value of  ( i (n+1)4)  observation, i=1,2,3

where n is the total number of observations.

Arrange the data in ascending order

5, 6, 8, 9, 9, 10, 10, 10, 10, 12, 12, 13, 13, 14, 15

First Quartile Q1

The first quartile Q1 can be computed as follows:

`       Q1=Value of (1(n+1)/4)th `

`         =Value of (1(15+1)/4)th `

`         =Value of (4)th `

`         =9`

Thus, 25 % of the patients had length of stay in the hospital less than or equal to 9 days.

Second Quartile Q2

The second quartile Q2 can be computed as follows:

`       Q2=Value of (2(n+1)/4)th .`

`        =Value of (2(15+1)/4)th `

`        =Value of (8)th `

`        =10`

Thus, 50 % of the patients had length of stay in the hospital less than or equal to 10 days.

Third Quartile Q3

The third quartile Q3 can be computed as follows:

`      Q3=Value of (3(n+1)4)th`

`        =Value of (3(15+1)4)th `

`        =Value of (12)th `

`        =13`

Thus, 75 % of the patients had length of stay in the hospital less than or equal to 13 days.

Please see videos for more examples.

Evaluation

1.Blood sugar level (in mg/dl) of a sample of 20 patients admitted to the hospitals are as follows:

75,89,72,78,87, 85, 73, 75, 97, 87, 84, 76,73,79,99,86,83,76,78,73.

Find the value of Q1, Q2 and Q3.

2.The following data are the heights, correct to the nearest centimeters, for a group of children:

`126, 129, 129, 132, 132, 133, 133, 135, 136, 137, 137, 138, 141, 143, 144, 146, 147, 152, 154, 161 `

Find the value of Q1, Q2 and Q3.

3.The rice production (in Kg) of 10 acres is given as: 1120, 1240, 1320, 1040, 1080, 1720, 1600, 1470, 1750, and 1885. Find the quartiles for the given data.

Find the value of Q1, Q2 and Q3.

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