3.First 10 multiples of 3
It is given that the data is first 10 multiples of 3, i.e. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
The formula to calculate the mean is the ratio of sum of observations to the number of observations.
x ¯ = 1 n ∑ i = 1 n x i (1)
The sum of observations is,
∑ i = 1 n x i = 3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 = 165
Since the total number of observation is 10, thus substitute 10 for n and 165 for ∑ i = 1 n x i in equation (1).
x ¯ = 1 10 ( 165 ) = 16.5
Therefore, the mean of the given data is 16.5.
The formula to calculate the variance is,
σ 2 = 1 n ∑ i = 1 n ( x i − x ¯ ) 2 (2)
Substitute 16.5 for x ¯ and 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 for x i respectively in x i − x ¯ and make a table to evaluate the variance.
x i x i − x ¯ ( x i − x ¯ ) 2 3 − 13.5 182.25 6 − 10.5 110.25 9 − 7.5 56.25 12 − 4.5 20.25 15 − 1.5 2.25 18 1.5 2.25 21 4.5 20.25 24 7.5 56.25 27 10.5 110.25 30 13.5 182.25 ∑ i = 1 n x i = 165 ∑ i = 1 n ( x i − x ¯ ) 2 = 742.5
Substitute 10 for n and 742.5 for ∑ i = 1 n ( x i − x ¯ ) 2 in equation (2).
σ 2 = 742.5 10 = 74.25
Thus, the variance of the given data is 74.25.
It is given that the data is first 10 multiples of 3, i.e. 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
The formula to calculate the mean is the ratio of sum of observations to the number of observations.
The sum of observations is,
Since the total number of observation is 10, thus substitute 10 for n and 165 for
Therefore, the mean of the given data is 16.5.
The formula to calculate the variance is,
Substitute 16.5 for
| | | |
| 3 | | 182.25 |
| 6 | | 110.25 |
| 9 | | 56.25 |
| 12 | | 20.25 |
| 15 | | 2.25 |
| 18 | 1.5 | 2.25 |
| 21 | 4.5 | 20.25 |
| 24 | 7.5 | 56.25 |
| 27 | 10.5 | 110.25 |
| 30 | 13.5 | 182.25 |
| | |
Substitute 10 for n and 742.5 for
Thus, the variance of the given data is 74.25.
