 Mean is the most commonly used central tendency measure. In Mathematics, there are various types of means but in Statistics, the mean is the sum of observations divided by the total number of observations. Also, there are other names for mean like arithmetic mean, average. Practicing Mean of Raw Data word problems can make you solve any kind of questions in exams easily. So, Answer all the questions provided in this Worksheet on Mean of Ungrouped Data PDF and gain extra knowledge on finding the arithmetic mean.

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Practice Question on Mean for Ungrouped Data Worksheet PDF

Example 1:

The heights of five students are 155 in, 140 in, 150 in, 160 in, and,165 in respectively. Find the mean height of the students.

Solution:

Given heights of 5 students are 155 in, 140 in, 150 in, 160 in, and,165 in
Sum of the heights of five students = (155+140+150+160+165) = 770
Using Mean Formula,
Mean = {Sum of Observation} ÷ {Total numbers of Observations}
= 770 ÷ 5
= 154 in

Example 2:

Find the mean of the following.
(i) The first five positive integers.
(ii) 4, 11, 3, 5, 10, 15, 40

Solution:

(i) The first five positive numbers are 1, 2, 3, 4, 5
Mean of the five positive numbers = Sum of five positive numbers ÷ Total number
= 1+2+3+4+5 ÷ 5
= 15 ÷ 5
= 3
Hence, the mean of the first five positive numbers is 3.
(ii) Given list of observations are 4, 11, 3, 5, 10, 15, 40
To find the mean, use the mean formula and apply the given observations;
Mean = Sum of Observations ÷ Number of Observations
= 4+11+3+5+10+15+40 ÷ 7
= 88 ÷ 7
= 12.57(approx)

Example 3:

In the annual board exams in mathematics, 5 students scored 80 marks, 8 students scored 75 marks, 10 students scored 65 marks and 2 students scored 55 marks. Find the mean of their score.

Solution:

Given that,
Number of students scored 80 marks  =  5
Number of students scored 75 marks  =  8
Number of students scored 65 marks  =  10
Number of students scored 55 marks  =  2
Mean = [5(80) + 8(75) + 10(65) + 2(55)] / (5 + 8 + 10 + 2)
= 1760 / 25
= 70.4

Example 4:

The mean weight of five complete computer stations is 167.2 pounds. The weights of four of the computer stations are 158.4 pounds, 162.8 pounds, 165 pounds, and 178.2 pounds respectively. What is the weight of the fifth computer station?

Solution:

Given Mean weight of five computer stations = 167.2 pounds
To find the weight of the fifth computer station, use the mean formula
Let the fifth weight of computer stations be x.
Mean = Sum of weights / Number of weights
167.2 = 158.4+162.8+165+178.2+x / 5
167.2*5 = 664.4 + x
664.4 + x = 836
x = 836 – 664.4
x = 171.6 pounds
Hence, the weight of the fifth computer station is 171.6 pounds.

Example 5:

The mean height of 4 members of a family is 5.5. Three of them have heights of 5.6, 6.0, and 5.2. Find the height of the fourth member.

Solution:

Given heights of family members are 5.6, 6.0, 5.2
Mean height of 4 members of a family = 5.5
Let the fourth member height would be x
To find the fourth height x, apply the mean formula
Mean = sum of observations / number of observations
5.5 = 5.6+6.0+5.2+x / 4
5.5 * 4 = 16.8+x
16.8 + x = 22
x = 22-16.8
x = 5.2
Hence, the height of the fourth member is 5.2

Example 6:

20 25 30 25 40 45 50 55

Solution:

Given data is 20 25 30 25 40 45 50 55
Mean = Sum of data / Total number of data
= 20+25+30+35+40+45+50+55 / 8
= 300/8
= 37.5

Example 7:

In a week, the temperature of a certain place is measured during winter are as follows 24ºC, 28ºC, 22ºC, 18ºC, 30ºC, 26ºC, 22ºC. Find the mean temperature of the week.

Solution:

Given temperatures are 24ºC, 28ºC, 22ºC, 18ºC, 30ºC, 26ºC, 22ºC
Mean temperature = Sum of all temperature / Number of terms
= 24ºC+28ºC+22ºC+18ºC+30ºC+26ºC+22ºC / 7
= 170 / 7
= 24.28 (approx)