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
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Question : 1

Mean of a set of observations is the value which ____________________

Right Option : C
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Question : 2

The mean of 8, 11, 6, 14, x and 13 is 16. Find the value of the observation x.

Right Option : C
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Explanation
Question : 3

If each entry of a data is increased by 5, then the arithmetic mean ____________________

Right Option : B
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Explanation
 
 


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