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10 Questions 10 Marks 10 Mins
Formula used:
Mean: It is the ratio of the sum of all observations and the total
number of observations.
Property of mean:
Let mean of a1, a2, ......an = A, then
- Mean of a1 + k,a2, + k ......an + k = A + k
- Mean of a1 - k, a2 - k ......an - k = A - k
- Mean of ka1, ka2, ......kan = kA
- Mean of a1/k a2/k ......an/k = A/k
Calculation:
Given that, a mean of 10 observations
A = 5.5
According to the question, each observation is multiplied by 4 and
subtracted from 44. Let new mean is A', then using the property of
mean,
⇒ A' = 44 - 4A
⇒ A' = 44 - 4 × 5.5 (∵ A = 5.5)
⇒ A' = 44 - 22
⇒ A' = 22
∴ The required mean is 22.
Alternate Method
Given that,
Mean of 10 observation = 5.5
Let a1, a2, ......a10 are 10 observations.
⇒ (a1 + a2 + ......a10)/10 = 5.5
⇒ (a1 + a2 + ......a10) = 55 ------(1)
According to the question,
Each observation is multiplied by 4 and subtracted from 44. Then,
Mean = [10 ×44 - 4(a1 + a2 + ......a10)]/10
Using equation (1)
Mean = [10 ×44 - 4 × 55]/10
⇒ Mean = (440 - 220)/10
⇒ Mean = 220/10 = 22
∴ The new mean is 22.
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13
Let the observations be x1, x2, x3.........xn
Mean = .....(i)
If each observation is increased by 5, we get,
x1 + 5, x2 + 5, x3 + 5.........xn + 5
New mean
⇒ Mean =
Thus, the mean is also increased by 5.
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Suggest Corrections
4
The mean of 20 observations is 12. If each observation is increased by 5, then find the new observation.
Posted by Maria Jaleel 3 years, 4 months ago
Since mean of 20 observations is 12
Sum of the 20 observations = 12 {tex}\times{/tex} 20 = 240
New sum of 20 observations = 240 +(5 x 20) = 420 + 100 = 520
New mean = 520/20 = 26