7.1a Mean - SPM Additional Mathematics

7.1a 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}

(B) Grouped Data (Without Class Interval)

Example 2

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

Find the mean marks.

Solution:

\begin{array}{l} Mean marks, \bar{x} \\ \bar{x} = \frac{(50) (6) + (55) (8) + (60) (15) + (65) (10) + (70) (1)}{6 + 8 + 15 + 10 + 1} \\ \bar{x} = \frac{2360}{40} = 59 \end{array}

(C) Grouped Data (With Class Interval)

Example 3

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

Find the mean scores.

Solution:

\begin{array}{l} Mid-point = \frac{5 + 9}{2} = 7 \\ Mean scores, \bar{x} = \frac{\sum f x}{\sum f} = \frac{2290}{100} = 22.9 \end{array}

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