7.1c Median

Posted on April 21, 2020 by user

7.1c Median

1. The median of a group of data refers to the value which is at the middle of the data after the data has been arranged according to grouped data and ungrouped data.

(A) Ungrouped Data

Example 1:

Find the median for each of the sets of data given below.

(a) 15, 18, 21, 25, 20, 18

(b) 13, 6, 9, 17, 11

Solution:
(a) Arrange the data in the ascending order

15, 18, 18, 20, 21, 25

$Median = T_{\frac{n + 1}{2}} = T_{\frac{6 + 1}{2}} = T_{3 \frac{1}{2}} = \frac{18 + 20}{2} = 19$

(b) 6, 9, 11, 13, 17

$Median = T_{\frac{n + 1}{2}} = T_{\frac{5 + 1}{2}} = T_{3} = 11$

(B) Grouped Data (without Class Interval)

Example 2:

The frequency table shows the marks obtained by 40 students in a biology test.

Solution:

$Median = T_{\frac{n + 1}{2}} = T_{\frac{40 + 1}{2}} = T_{20 \frac{1}{2}} = 60 \leftarrow (20 \frac{1}{2} th term is 60)$

(C) Grouped Data (with Class Interval)

m = median

L = Lower boundary of median class

N = Number of data

F = Total frequency before median class

f_m = Total frequency in median class

c = Class size = (Upper boundary – lower boundary)

1. The median can be determined from an accumulative frequency table and the ogive.

2. The ogive is an accumulative graph; the median, quartiles and the range between quartiles can be determined from it.

Example 3:

The grouped frequency distribution was obtained from 100 students regarding the scores in their test shown as below.

Find the median.

Solution:
Method 1: using formula

$\begin{array}{l} S t e p 1 \\ Median class is given by T_{\frac{n}{2}} = T_{\frac{100}{2}} = T_{50} \\ ∴ Median class is the class 20 - 24 \\ S t e p 2 \\ m = L + (\frac{\frac{N}{2} - F}{f_{m}}) c \\ m = 19.5 + (\frac{\frac{100}{2} - 33}{26}) 5 \\ m = 19.5 + 3.269 = 22.77 \end{array}$