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

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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Question : 2

The mean of x, x + 3, x + 6, x + 9 and x + 12 is _______________

Right Option : A
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Explanation
Question : 3

The average weight of sample of 10 apples is 52 g. Later it was found that the weighing machine had shown the correct average apple 10g less. The correct average weight of an apple is

Right Option : A
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