Page 252 - ICSE Math 7

Example 2: The mean of six numbers is 15. If five of them are 9, 12, 13, 18 and 21, find the sixth
number.
Solution: Let the sixth number be x.
9 + 12 + 13 + 18 + 21 + x
Mean =
6
73 + x
⇒ 15 =
6
⇒ 90 = 73 + x
⇒ x = 90 – 73 = 17
Thus, the sixth number is 17.

Example 3: Find the mean of first eight odd natural numbers.
Solution: First eight odd natural numbers are 1, 3, 5, 7, 9, 11, 13 and 15.
1 + 3 + 5 + 7 + 9 + 11 + 13 + 15
Mean =
8
64
⇒ Mean = = 8
8
Arithmetic mean of grouped data
In the previous section we have learnt to find the arithmetic mean of series of individual observations
also called raw data. If the data consists of a large number of observations, we know it can be
converted into frequency distribution. In a frequency table, we have observations x , x , x , ..., x with
2
1
n
3
corresponding frequencies f , f , f , ..., f .
n
1
3
2
x f + x f + x f + ... + x f
Mean = 1 1 2 2 3 3 n n
f + f + f + ... + f n
3
2
1
Thus, mean is the sum of the products of the observations with their corresponding frequencies divided
by the sum of the frequencies.
Example 4: Find the mean from the given table.
Score 27 25 30 40 50
Frequency 4 2 3 5 4

Solution: Score (x ) Frequency (f ) x × f i
i
i
i
27 4 27 × 4 = 108
25 2 25 × 2 = 50
30 3 30 × 3 = 90
40 5 40 × 5 = 200
50 4 50 × 4 = 200

Total 18 648

x f + x f + x f + ... + x f 108 + 50 + 90 + 200 + 200 648
Mean = 1 1 2 2 3 3 n n = = = 36
f + f + f + ... + f n 18 18
2
1
3
238