Mean Value – Word problems   

In this lesson we will learn about mean.

We will also learn how to find mean of given data and solve word problems on mean.

How to calculate mean

Example: (1)What is the mean of  1, 2, 5, and 4.

Solution :

Mean = Sum of observations/Number of observations

the numbers are 1, 2, 5, and 4, and total numbers are 4. so, 

                               mean =  (1 + 2 + 5 + 4)/4   
                                                                                                     mean  = 12/4                              

mean  = 3

The mean = 3

or

There are two steps to calculate mean 

Step 1: Add all numbers.

Step 2: Divide by how many numbers are there.

Example: (2) What is the mean of  1, 4, 5, 3, and 7.

Solution :

 1.  Step 

 Add all numbers 

1 + 4 + 5 + 3 + 7 

= 20

2.  Step 

Divide by how many numbers are there.

There are total numbers are 5 so, 20 divide by 5

values put in the formula

      Mean = Sum of observations/Number of observations

                    mean   = 20/5

                     mean  = 5 . 

                                       ,The mean is 5. 


Example:(3) The age of 10 students in years in a class are 

15, 23, 17, 20, 22, 18, 16, 25, 24 and 20.

(i) What is the age of youngest student.
(ii) What is the age of oldest student.
(iii) What is the range of the age of the students.
(iv) What is the mean age of the students.

Solution : Arranging the ages in ascending order we get,

15, 16, 17, 18, 20, 20, 22, 23, 24, 25.

From above data we observe that the

 (i)Age of youngest student is 15 years.

(ii) Age of oldest student is 25 years.

(iii)Range of the age of the students is 

              25 – 15 = 10 years

(iv) What is the mean age of the students.

Mean =  
Mean age of the students/Number of students

= (15+16+17+18+20+20+22+23+24+25)/10 

= 200/10

= 20 years
Therefore, mean age of student = 20 years.

Example:(4) Find the mean of first five natural numbers.

Solution : First five natural numbers are

                         1, 2, 3, 4, and 5

             Mean = Sum of observations/Number of observations

                  = (1 + 2 + 3 + 4 + 5)/5

                   = 15/5

           mean = 3
                           Mean = 3

 Example:(5) The marks (out of 200) obtained by 10 girls in a physics test are as follows,

150, 180, 170, 175, 182, 128. 177, 153, 155, 190.

Give the answers of below questions.

(i) Highest marks obtained by girl.
(ii) Lowest marks obtained by girl.
(iii) What is the range of marks.

(iv) What is the mean marks obtained by girls.
(v) How many girls obtained more than mean marks.

  Solution : Arranging the marks in ascending order we get,

128, 150, 153, 155, 170, 175, 177, 180, 182 190.

From above data we observe that the

 (i) Highest marks is 190 obtained by girl.

(ii) Lowest marks is 128 obtained by girl.

(iii) Range of the marks is 

              190 – 128 = 62 marks

(iv) mean marks obtained by girls.

Mean =  
 marks obtained by girls/Number of girls

= (128+150+153+155+170+175+177+180+182+190)/10 

= 1660/10

= 166 marks
Therefore, mean = 166 marks.

(v) Six girls obtained more than mean marks, the marks are 170, 175, 177, 180, 182 and 190.