Properties Questions on Arithmetic Mean

Here using the properties we will solve the different properties questions on arithmetic mean. Follow the steps to understand the explanations on how to solve the problems based on properties.



Worked-out examples on properties questions on arithmetic mean:

1. The mean of eight numbers is 25. If five is subtracted from each number, what will be the new mean?

Solution:

Let the given numbers be x1, x2, . . ., x8.

Then, the mean of these numbers = (x1 + x2 + ...+ x8)/8.

Therefore, (x1 + x2+...+x8)/8 = 25

⇒ (x1 + x2 + ... + x8) = 200 ……. (A)

The new numbers are (x1 - 5), (x2 - 5), …… ,(x8 - 5)

Mean of the new numbers = {(x1 - 5) + (x1 - 5) + …… + (x8 - 5)}/8

= [(x1 + x2 + ... + x8) - 40]/8

= (200 - 40)/8, [using (A)]

= 160/8

= 20

Hence, the new mean is 20.


2. The mean of 14 numbers is 6. If 3 is added to every number, what will be the new mean?

Solution:

Let the given numbers be x1, x2, x3, ….. x14.

Then, the mean of these numbers = x1 + x2 + x3+ ….. x14/14

Therefore, (x1 + x2 + x3 + ….. x14)/14 = 6

⇒ (x1 + x2 + x3 + ….. x14) = 84 ………………. (A)

The new numbers are (x1 + 3), (x2 + 3), (x3 + 3), …. ,(x14 + 3)

Mean of the new numbers

= (x1 + 3), (x2 + 3), (x3 + 3), …. ,(x14 + 3)/14

= (x1 + x2 + x3 + ….. x14) + 42

= (84 + 42)/14, [Using (A)]

= 126/14

= 9

Hence, the new mean is 9.

Statistics

Arithmetic Mean

Word Problems on Arithmetic Mean

Properties of Arithmetic Mean

Problems Based on Average

Properties Questions on Arithmetic Mean










9th Grade Math

From Properties Questions on Arithmetic Mean to HOME PAGE


New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.



Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

RSS

  1. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Dec 01, 23 01:16 AM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  2. Days of the Week | 7 Days of the Week | What are the Seven Days?

    Nov 30, 23 10:59 PM

    Days of the Weeks
    We know that, seven days of a week are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. A day has 24 hours. There are 52 weeks in a year. Fill in the missing dates and answer the questi…

    Read More

  3. Types of Lines |Straight Lines|Curved Lines|Horizontal Lines| Vertical

    Nov 30, 23 01:08 PM

    Types of Lines
    What are the different types of lines? There are two different kinds of lines. (i) Straight line and (ii) Curved line. There are three different types of straight lines. (i) Horizontal lines, (ii) Ver…

    Read More