7.1a Mean

Posted on April 21, 2020 by user

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)