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:
If x_{1}, x_{2}, x_{3}, x_{4}, ……. x_{n} are n observations, and f_{1}, f_{2}, f_{3}, f_{4}, ……. f_{n} represent frequency of n observations.
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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