# EXERCISE –  3.1

Q1. Find the range  of heights of any ten students of your class.

SOLUTION:-

Let us assume heights (in cm) of 10 students of our class.

= 130,132,135,137,139,140,142,143,145,148,.

By observing the above mentioned values , the lowest value is = 130 cm

Then,

Range of heights = highest value – lowest value

= 148 – 130

= 18 cm.

Q2. Organise the following marks in a class assessment in a tabular form.

SOLUTION:-

4,6,,7,3,5,,4,5,2,6,2,5,1,9,6,5,8,4,6,7

(i) Which number is the highest ?

(ii) Which is the numbers is the lowest ?

(iii) What is the range of the data?

(iv) Find the arithmetic mean.

SOLUTION:-

First

we have to arrange the marks in ascending order.

= 1,2,2,3,4,4,4,5,5,5,5,5,6,6,6,6,7,7,8,9

Now, we will draw the frequency table of the given data.

 Marks Tally Marks Frequency 1 I 1 2 II 2 3 I 1 4 III 3 5 5 6 IIII 4 7 II 2 8 I 1 9 I 1

(i) By observing the table clearly the highest number among the given data is 9.

(ii) By observing the table clearly the lowest numbers among the given data is 1.

(iii) We know that range = Highest value – Lowest value

= 9 – 1

= 8

(iv) Now , we have to calculate arithmetic Mean,

Arithmetic Mean = (Sum of all observations) / ( Total numbers of observation)

Then,

Sum of all observation = 1 + 2+2+3+4+4+4+5+5+5+5+5+6+6+6+6+7+7+8+9

= 100

Total numbers of observation = 20

Arithmetic mean = (100/20)

= 5

Q3. Find mean of the first five whole numbers.

SOLUTION:-

The first five whole numbers are 0,1,2,3 and 4.

Mean = ( Sum of first five whole numbers )/(Total numbers of whole numbers)

Then,

Sum of five whole numbers

= 0+1+2+3+4

= 10

Total numbers of whole numbers = 5

Mean = (10/5)

= 2

Mean of first five whole numbers is 2.

Q4. A cricketer scores the following runs in eight innings:

58,76,40,5,46,45,0,100.Find the mean score.

SOLUTION:-

Mean score = (Total runs scored by the cricketer in all innings)/(Total numbers of innings)

Played by the cricketer)

Total runs scored by the cricketer in all innings = 58+76+40+35+46+45+0+100

= 400

Total numbers of innings = 8

Then,

Mean = (400/8)

= 50

Mean score of the cricketer is 50.

Q5. Following table shows the points of each player scored in four games:

 Player Game 1 Game 2 Game 3 Game 4 A 14 16 10 10 B 0 8 6 4 C 8 11 Did not play 13

(i) Find the mean to determine A average number of points scored per game.

(ii) To find the mean numbers of points per game for C, would you divided the total points by 3 or by 4 ? Why ?

(iii) B played in all four games. How would you find the mean?

(iv) Who is the best performer ?

SOLUTION:-

(i) A average number of points scored per game = Total points scored by A in 4 games/

Total numbers of games = (14 + 16 + 10 + 10 + )/4

= 50/4

= 12.5 points

(ii) To find the mean number of points per game for C, we divide the total points by 3. Because C played only 3 games.

(iii) B played in all four games, So we will divide the total points by 4 to find out the mean.

Then,

Mean of B score = Total points scored by B in 4 games/ Total number of games

= ( 0 + 8 + 6 + 4 )/4

= 18/4

= 4.5 points

(iv) Now , we have to find the best perform among 3 players.

So, we have to find the average points of C = ( 8 + 11 + 13 ) /3

= 32/3

= 10.67 POINTS

By observing the average point scored A is 12.5 which is more than B and C.

Clearly, we can say that A is the best performer among three.

Q6. The marks ( out of 100) obtained by a group of students in a science test are 85,76,90,85,39,48,56,95,81, and 75. Find the :

(i) Highest and the lowest marks obtained by the students.

(ii) Range of the marks obtained

(iii) Mean  marks obtained by the group .

SOLUTION:-

First we have to arrange the marks are obtained by a group  of students in a science test in an ascending order,

= 39,48,56,75,76,81,85,85,90,95

(i) The highest marks are obtained by the students = 95

The lowest marks are obtained by the students = 39

(ii) We know that, Range highest marks – lowest marks

= 95 – 39

= 56

(ii) Mean of marks = ( Sum of all marks obtained by the group of students )/(Total numbers of marks)

= ( 39+48+56+75+76+81+85+85+90+95)/10

= 730/10

= 73

Q7. The enrolment in a school during six consecutive years was as follows:

1555,1670,1750,2013,2540,2820

Find the mean enrolment of the school for this period.

SOLUTION:-

Mean enrolment = Sum of all observations/Numbers of observations

= (1555+1670+1750+2013+2540+2820)/6

= (12348/6)

= 2058

The mean enrolment of the school for this given period is 2058.

Q8. The rainfall ( in mm) in a city on 7 days of a certain week was recorded as follows:

 Day Mon Tue Wed Thurs Fri Sat Sun Rainfall (in mm) 0.0 12.2 2.1 0.0 20.5 5.5 1.0

(i) Find the range of the rainfall in the above data.

(ii) Find the mean rainfall for the week.

(iii) On how many days was the rainfall less than the mean rainfall.

SOLUTION:-

(i) Range of rainfall highest rainfall – lowest rainfall

= 20.5 – 0.0

= 20.5 mm

(ii) Mean of rainfall = Sum of all observation / Numbers of observations

= ( 0.0 + 12.2 + 2.1 + 0.0 + 20.5 + 5.5 + 1.0) / 7

= 41.3/7

= 5.9 mm

(iii) We may observes that for 5 days i.e. Monday , Wednesday , Thursday , Saturday and Sunday the rainfall was less than the average rainfall.

Q9. The heights of 10 girls were measured in cm and the results are as follows:

135,150,139,128,151,132,146,149,143,141.

(i) What is the height of the tallest girl ?

(ii) What is the height of the shortest girl?

(iii) What is the mean heights of the girls?

(iv) What is the mean height of the girls?

(v) How many girls have heights more than the mean heights .

SOLUTION:-

First we have to arrange the given data in an ascending order,

= 128,132,135,139,141,143,146,149,150,151

(i) The height of the tallest girl is 151 cm

(ii) The height of the shortest girl is 128 cm

(iii) Range of given data = tallest height – shortest height

= 151 – 128

= 23 cm

(iv) Mean height of the girls = Sum of height of all the girls/ Numbers of girls

= ( 128 + 132 + 135 + 139 + 141 + 143 + 146 + 149 + 150 + 151 )/10

= 1414/10

= 141.4 cm

(v) 5 girls have height more than the mean height (i.e. 141.4 cm ) .