Mean of Ungrouped Data


 
 
Concept Explanation
 

Mean of Ungrouped  Data

Mean of Ungrouped  Data:

The most common representative value of a group of data is the arithmetic mean.To understand this let us take the following example:

Two vessels contain 20 litres and 60 litres of milk  respectively. What is the amount that each vessel would have, if both share the milk equally? When we ask this question we are seeking  the arithmetic mean. In this case, the average  or the arithmetic mean would be

frac{Total;quantity;of;milk}{Number;of;vessels}=frac{20+60}{2}=40;litres.

Thus, each vessels would have 40 litres of milk.

The average or Arithmetic Mean (A.M) or simply means defined as follows:

Arithmetic ;mean=frac{Sum;of;all;observations}{number;of;observations}

Illustration 1: Ashish studies for 4 hours, 5 hours and 3 hours respectively on three consecutive days. How many hours does he study daily on an average?

Solution: The average study time of Ashish would be

frac{Total;number;of;study;hours}{Number;of;days;for ;which;he;studied}=frac{4+5+3}{3};hours=4;hours;per;day

Thus, we can say that Ashish studies for 4 hours daily on an average.

Thus, the mean for ungrouped data is obtained by dividing the sum of all values by the number of values in the data set. The mean of data indicate how the data are distributed around the central part of the distribution.

Mean Of Raw Data: The mean (or arithmetic mean) of n observations (variates) small _{x_{1}}, _{x_{2}},_{x_{3}},_{x_{4}},....._{x_{n}} is given by

  small Mean= frac{x_{1}+x_{2}+x_{3}+x_{4}+....+x_{n}}{n} 

Or; we; can ; say;that ; Mean =frac{Sum ;of; the; Variables}{Total; Number ;of; Variates}

Illustration 2: A student scored 80%, 72%, 50%, 64% and 74% marks in five subjects in an examination. Find the mean percentage of marks obtained by him.

Solution: Here, observations in percentage are x1 = 80, x2 = 72, x3 = 50, x4 = 64 and x5 = 74 . Therefore, theirMean; =frac{ x1+x2+x3+x4+x5}{5}

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Sample Questions
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Question : 1

The mean of 6, 8, x + 2, 10, 2x - 1, and 2 is 9. Find the value of x

Right Option : C
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Question : 2

Mean of a set of observations is the value which ____________________

Right Option : C
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Question : 3

The mean of first ten whole numbers is _____________

Right Option : D
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