wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

3.First 10 multiples of 3

Open in App
Solution

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 13.5182.25
6 10.5110.25
9 7.556.25
12 4.520.25
15 1.52.25
181.52.25
214.520.25
247.556.25
2710.5110.25
3013.5182.25
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.


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Central Tendency
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon