Mean of Ungrouped Data


 
 
Concept Explanation
 

Mean of Un-grouped Data

Mean of Un-grouped Data:

The mean or average of a number of observations is the sum of the value of all the observations divided by the total number of observations.

Definition:  If x_{1},x_{2},x_{3},.....,x_{n}  are n values of a variable X , then the arithmetic mean or simply the mean of these values is denoted large bar{x}  and is defined as

          bar{x}=frac{x_{1}+x_{2}+x_{3}+...+x_{n}}{n}=frac{sum_{i=1}^{n}x_{i}}{n}

Here, the symbol sum_{i=1}^{n}x_{i}  denotes the sum x_{1}+x_{2}+x_{3}.....x_{n}.

In other words, the arithmetic mean of a set of observations is equal to their sum divided by the total number of observations.

Illustration 1:   If the heights of 5 persons are 144 cm, 152 cm, 151 cm, 158 cm and 155 cm respectively. Find the mean height.

Solution:    To calculate mean we will find the sum of observations and divide it with number of observations

Mean;height=frac{144+152+151+158+155}{5}=frac{760}{5};cm=152;cm

Illustration 2: The mean of 6, 10, X and 12 is 8. Find the value of x.

Solution: Using the definition

bar{x}=frac{x_{1}+x_{2}+x_{3}+...+x_{n}}{n}

 8=frac{6+10+X+12}{4}

8=frac{28+X}{4}

8times 4=28+X

32=28+X

X = 32-28

X=4

So , the value of x is 4.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

20 years ago, when my parents got married, their average age was 23 years, now the average of my family, consisting of myself and my parents only is 35 years. My present age is

Right Option : D
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Explanation
Question : 2

The mean of 994, 996, 998, 1000 and 1002 is ________________

Right Option : C
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Explanation
Question : 3

The mean of 6, y, 7, x and 14 is 8. Then

Right Option : A
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Explanation
 
 


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