Exercise 3.1
1. Find the range of heights of any ten students of your class.
Solution:
Let us assume the heights (in cm) of 10 students of our class as :
120, 122, 125, 137, 139, 150, 142, 133, 145, 158
By observing the above-mentioned values, the highest value is =
By observing the above-mentioned values, the lowest value is =
The range is the difference between the highest value and the lowest value of the data. It helps in knowing the spread of the data.
Then,
Range of Heights = Highest value – Lowest value
= 158 – 120 =
Que
2.Organise the following marks in a class assessment, in a tabular form.4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7.
(i) Which number is the highest?
(ii) Which number is the lowest?
(iii) What is the range of the data?
(iv) Find the arithmetic mean
Sol
Solution:
As per the question, we use the basic definition of parameters of statistics like mean and range to solve the problem.
The given data is as follows,
4, 6, 7, 5, 3, 5, 4, 5, 2, 6, 2, 5, 1, 9, 6, 5, 8, 4, 6, 7
Let's tabulate the data as shown below.
| Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
|---|---|---|---|---|---|---|---|---|---|
| Frequency | 1 | 2 | 1 | 3 | 5 | 4 | 2 | 1 | 1 |
(i)The highest number is
(ii)The lowest number is
(iii) We know that, Range = Highest marks – Lowest marks.
The range of the data = Highest number – Lowest number
= 9 - 1 =
(iv) Arithmetic mean = Sum of all the marks / Total number of observations.
=
=
3. Find the mean of the first five whole numbers
Solution:
The first five whole numbers are 0, 1, 2, 3 and 4.
Therefore, the mean of first five whole numbers
=
=
Thus, the mean of first five whole numbers is 2.
4. A cricketer scores the following runs in eight innings: 58, 76, 40, 35, 46, 45, 0, 100.
Find the mean score
Solution:
We use the basic formula of mean or average to solve the problem given.
Total number of innings =
Scores of cricketer in 8 innings = 58, 76, 40, 35, 46, 45, 0, 100
Mean of the score =
=
Thus, the mean score of the cricketer in 8 innings is 50.
5. 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 |
Now answer the following questions:
a
(i) Find the mean to determine A’s average number of points scored per game.
Solution:
We will use the basic formula of mean in statistics to solve the questions given.
Total number of games played by A = 4
Scores obtained by A = 14, 16, 10, 10
Mean score of A =
=
=
b
(ii) To find the mean number of points per game for C, would you divide the total points by 3 or by 4? Why?
Solution:
We should divide the total points by
c
(iii) B played in all the four games. How would you find the mean?
Solution:
Total number of games played by B =
Scores obtained by B = 0, 8, 6,
Mean score of B = Sum of scores obtained by B / Number of games played by B
=
=
=
d
(iv) Who is the best performer?
Solution:
To find the best performer, we should find the mean of all players.
Mean of player A =
Mean of player B =
Mean of player C = Sum of scores obtained by C / Number of games played by C
=
=
=
Therefore, by comparing the average scores of all players, we see that A is the best performer as it has the highest mean.
Que
6.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 given below.
(i) Highest marks obtained by the student
(ii) Range of the marks obtained
(iii) Mean marks obtained by the group.
Sol
Solution:
We use the basic formulae of statistics such as mean and range to solve the given questions.
Mean marks =
Marks obtained by the group of students = 85, 76, 90, 85, 39, 48, 56, 95, 81, 75
(i) Highest marks obtained by the student
= 95, Lowest marks obtained by the student =
(ii) Range of the marks obtained
= Highest marks – Lowest marks
= 95 – 39 =
(iii) Mean marks obtained by the group.
=
=
Thus, the mean marks obtained by the group of the students are 73.
7. 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:
The enrolment in a school for six consecutive years are 1555, 1670, 1750, 2013, 2540, 2820.
Total number of years = 6
Mean enrolment = Sum of all the enrollments / Total numbers of years
=
=
=
Hence, the mean enrolment of the school for this period is 2058.
8.The rainfall (in mm) in a city on 7 days of a certain week as recorded as follows:
| Day | Mon | Tue | Wed | Thurs | Fri | Sat | Sun |
|---|---|---|---|---|---|---|---|
| Rainfall | 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
Highest of the rainfall (in mm) = 20.5, Lowest of the rainfall (in mm) = 0.0
Range of the rainfall = Highest rainfall – Lowest rainfall
= 20.5 – 0.0
=
(ii) Find the mean rainfall for the week.
Total number of days =
Record of the rainfall (in mm) = 0.0, 12.2, 2.1, 0.0, 20.5, 5.5, 1.0
Mean of the rainfall (in mm) = Sum of rainfalls (in mm) / Number of days
=
=
(iii) On how many days was the rainfall less than the mean rainfall.
On
Que
9. 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 range of the data?
(iv) What is the mean height of the girls?
(v) How many girls have heights more than the mean height.
Sol
Solution:
We use the basic formulae of statistics such as mean and range to solve the given problems.
The given data about the heights of 10 girls measured in cm are as follows: 135, 150, 139, 128, 151, 132, 146, 149, 143, 141
(i) What is the height of the tallest girl?
The height of the tallest girl =
(ii) What is the height of the shortest girl?
The height of the shortest girl =
(iii) What is the range of the data?
Range of the data = Height of tallest girl – Height of the shortest girl
= 151 – 128 =
(iv) What is the mean height of the girls?
Mean height of the girls =
Total number of girls =
Measurement of the heights of 10 girls = 135, 150, 139, 128, 151, 132, 146, 149, 143, 141.
=
=
(v) How many girls have heights more than the mean height.
Five girls have heights more than the mean height i.e.,