8.2.1 Mean and Median - SPM Mathematics

8.2.1a Mean
1. The mean of the data is an average value obtained by using the formula:
Mean= Total data values Number of data

(A) Ungrouped Data

Example 1

(a) Find the mean for the set of data 2, 4, 7, 10, 13, 16 and 18.

(b) A value of xis added into the above set of data, the mean for this new data is 9.5. Determine the value of x.

Solution:
(a)

\begin{array}{l} \bar{x} = \frac{2 + 4 + 7 + 10 + 13 + 16 + 18}{7} \\ \bar{x} = \frac{70}{7} = 10 \end{array}

(b)

\begin{array}{l} New mean = 9.5 \\ \frac{70 + x}{8} = 9.5 \\ 70 + x = 76 \\ x = 6 \end{array}

8.2.1b 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

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