Mean or average or arithmetic mean is one of the representative values of data. We can find the mean of observations by dividing the sum of all the observations by the total number of observations.
Mean of raw data:
If x_{1}, x_{2}, x_{3}, ……. x_{n} are n observations, then
∑ (Sigma) is a Greek letter showing summation
1. Weights of 6 boys in a group are 63, 57, 39, 41, 45, 45. Find the mean weight.
Solution:
Number of observations = 6
Sum of all the observations = 63 + 57 + 39 + 41 + 45 + 45 = 290
Therefore, arithmetic mean = 290/6 = 48.3
Mean of tabulated data:
2. A die is thrown 20 times and the following scores were recorded 6, 3, 2, 4, 5, 5, 6, 1, 3, 3, 5, 6, 6, 1, 3, 3, 5, 6, 6, 2.
Prepare the frequency table of scores on the upper face of the die and find the mean score.
Solution:
Number on the upper face of die |
Number of times it occurs (frequency) |
f_{i}x_{i} |
1 | 2 | 1 × 2 = 2 |
2 | 2 | 2 × 2 = 4 |
3 | 5 | 3 × 5 = 15 |
4 | 1 | 4 × 1 = 4 |
5 | 4 | 5 × 4 = 20 |
6 | 6 | 6 × 6 = 36 |
X | 4 | 6 | p + 7 | 10 | 15 |
f | 5 | 10 | 10 | 7 | 8 |
x_{i} | f_{i} | x_{i}f_{i} |
4 | 5 | 20 |
6 | 10 | 60 |
p + 7 | 10 | 10(p + 7) |
10 | 7 | 70 |
15 | 8 | 120 |
Number of Plants | 0 - 2 | 2 - 4 | 4 - 6 | 6 - 8 | 8 - 10 | 10 - 12 | 12 - 14 |
Number of Houses | 1 | 2 | 2 | 4 | 6 | 2 | 3 |
Number of Plant | Number of Houses (f_{i}) |
Class Mark (x_{i}) |
f_{i}x_{i} |
0 - 2 | 1 | 1 | 1 × 1 = 1 |
2 - 4 | 2 | 3 | 2 × 3 = 6 |
4 - 6 | 2 | 5 | 2 × 5 = 10 |
6 - 8 | 4 | 7 | 4 × 7 = 28 |
8 - 10 | 6 | 9 | 6 × 9 = 54 |
10 - 12 | 2 | 11 | 2 × 11 = 22 |
12 -14 | 3 | 13 | 3 × 13 = 39 |
● Statistics
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