7.1a Mean

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)
x ¯ = 2 + 4 + 7 + 10 + 13 + 16 + 18 7 x ¯ = 70 7 = 10
(b)
New mean  = 9.5 70 + x 8 = 9.5 70 + x = 76 x = 6


(B) Grouped Data (Without Class Interval)

Example 2
The frequency table shows the marks obtained by 40 students in a Biology test.

Marks
50
55
60
65
70
Number of students
6
8
15
10
1

Find the mean marks.
Solution: 
Mean marks,  x ¯ x ¯ = ( 50 ) ( 6 ) + ( 55 ) ( 8 ) + ( 60 ) ( 15 ) + ( 65 ) ( 10 ) + ( 70 ) ( 1 ) 6 + 8 + 15 + 10 + 1 x ¯ = 2360 40 = 59


(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.

Scores
Frequency
5 – 9
4
10 – 14
10
15 – 19
19
20 – 24
26
25 – 29
21
30 – 34
12
35 – 39
8
Find the mean scores.

Solution:

Scores
Frequency f
Midpoint x
fx
5 – 9
4
7
28
10 – 14
10
12
120
15 – 19
19
17
323
20 – 24
26
22
572
25 – 29
21
27
567
30 – 34
12
32
384
35 – 39
8
37
296
Total

100
2290
Mid-point = 5 + 9 2 = 7 Mean scores,  x ¯ = f x f = 2290 100 = 22.9

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