The mean of a set of observation is ¯¯¯x .If each observation is

Sail E0 Webinar

Question

The mean of a set of observation is

¯ ¯ ¯ x

.If each observation is divided by

α α \neq 0

, and then is increased by 10,
then the mean of the new set is

Options:

A . ¯¯¯xα

B . ¯¯¯x+10α

C . ¯¯¯x+10αα

D . α¯¯¯x+10

Answer: Option C
:
C
Let

x_{1}, x_{2} \dots \dots, x_{n}

be n observations.

Then ¯ ¯ ¯ x = \frac{1}{n} \sum x_{i}

let y_{i} = \frac{x_{i}}{α} + 10

¯ ¯ ¯ y = \frac{1}{n} n \sum i y_{i}

And, ¯ ¯ ¯ y = \frac{1}{n} [(n \sum i \frac{x_{i}}{α} + 10. n]

\Rightarrow ¯ ¯ ¯ y = \frac{1}{α} ¯ ¯ ¯ x + 10

= \frac{¯ ¯ ¯ x + 10 α}{α} .

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. The mean of 5 numbers is 18. If one number is excluded, their mean becomes 16. Then the excluded number is....

Question 2. If a variable takes the discrete values α+4,α−72,α−52,α−3,α−2,....a variable takes the discrete values α+4,α−72,α−52,α−3,α−2,α+12,α−12,α+5(α>0),then the median is

Question 3. If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is....

Question 4. The mean deviation of 2, 4, 6, 8, 10 about its mean is....

Question 5. The mean and S.D. of the marks of 200 candidates were found to be 40 and 15 respectively. Later, it was discovered ....wrongly read as 50. The correct mean and S.D. respectively are

Question 6. The mean of n items is ¯¯¯x. If the first term is increased by 1 second by 2 and so on, then ne....1 second by 2 and so on, then new mean is

Question 7. If the mean of the number 27+x,31+x,89+x,107+x,156+x is 82, then the mean of 130+x,126+x,68+x,50+x,1+x is....

Question 8. The variance of the data 2, 4, 6, 8, 10 is:....

Question 9. Suppose a population A has 100 observations 101, 102,……200 and another population B has 100 ....the variances of the two populations respectively, then VAVB is

Question 10. Mean deviation of the series a, a + d, a + 2d, a + 2nd from its mean is....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0