Subscribe to our YouTube channel for the latest videos, updates, and tips.


Mean

Mean or average or arithmetic mean is one of the representative values of data. We can find the mean of observations by dividing the sum of all the observations by the total number of observations.

Mean of raw data:

If x1, x2, x3, ……. xn are n observations, then

Arithmetic Mean = (x1, x2, x3, ……. xn)/n

= (∑xi)/n

∑ (Sigma) is a Greek letter showing summation


1. Weights of 6 boys in a group are 63, 57, 39, 41, 45, 45. Find the mean weight.

Solution:

Number of observations = 6

Sum of all the observations = 63 + 57 + 39 + 41 + 45 + 45 = 290

Therefore, arithmetic mean = 290/6 = 48.3


Mean of tabulated data:

If x1, x2, x3, x4, ……. xn are n observations, and f1, f2, f3, f4, ……. fn represent frequency of n observations.

Then mean of the tabulated data is given by

= (f1 x1 + f2 x2 + f3 x3 + ……. fn xn)/(f1 + f2 + f3 + …… fn) = ∑(fixi)/∑fi


2. A die is thrown 20 times and the following scores were recorded 6, 3, 2, 4, 5, 5, 6, 1, 3, 3, 5, 6, 6, 1, 3, 3, 5, 6, 6, 2.

Prepare the frequency table of scores on the upper face of the die and find the mean score.

Solution:

Number on the upper
face of die
Number of times it occurs
(frequency)
fixi
1 2 1 × 2 = 2
2 2 2 × 2 = 4
3 5 3 × 5 = 15
4 1 4 × 1 = 4
5 4 5 × 4 = 20
6 6 6 × 6 = 36


Therefore, mean of the data   = ∑(fixi)/∑fi

                                        = (2 + 4 + 15 + 4 + 20 + 36)/20

                                        = 81/20

                                        = 4.05



3. If the mean of the following distribution is 9, find the value of p.

X 4 6 p + 7 10 15
f 5 10 10 7 8


Solution:

Calculation of mean

xi fi xifi
4 5 20
6 10 60
p + 7 10 10(p + 7)
10 7 70
15 8 120


∑fi = 5 + 10 + 10 + 7 + 8 = 40

∑ fixi = 270 + 10(p + 7)

Mean = ∑(fixi)/∑fi

9 = {270 + 10(p + 7)}/40

⇒ 270 + 10p + 70 = 9 × 40

⇒ 340 +10p = 360

⇒ 10p = 360 - 340

⇒ 10p = 20

⇒ p = 20/10

⇒ p = 2



Mean of grouped data:

While calculating the mean of the grouped data, the values x1, x2, x3, ……. xn are taken as the mid-values or the class marks of various class intervals. If the frequency distribution is inclusive, then it should be first converted to exclusive distribution.


4. The following table shows the number of plants in 20 houses in a group

Number of Plants 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 10 - 12 12 - 14
Number of Houses 1 2 2 4 6 2 3

Find the mean number of plans per house

Solution:

We have
   
Number of Plant Number of Houses
(fi)
Class Mark
(xi)
fixi
0 - 2 1 1 1 × 1 = 1
2 - 4 2 3 2 × 3 = 6
4 - 6 2 5 2 × 5 = 10
6 - 8 4 7 4 × 7 = 28
8 - 10 6 9 6 × 9 = 54
10 - 12 2 11 2 × 11 = 22
12 -14 3 13 3 × 13 = 39


∑fi = 1 + 2 + 2 + 4 + 6 + 2 + 3 = 20

∑fi xi =1 + 6 + 10 + 28 + 54 + 22 + 39 = 160

Therefore, mean = ∑(fixi)/ ∑fi = 160/20 = 8 plants

Statistics













From Mean to HOME PAGE




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.



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.




Share this page: What’s this?

Recent Articles

  1. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  2. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More