The mean of 20 observations is 12 if each observation is increased by 5, then find the new mean

Free

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.

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free Download App

Trusted by 3.4 Crore+ Students

13

Let the observations be x1, x2, x3.........xn

Mean =

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.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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