**Data Handling**

**Exercise 3.1**

1). Find the range of heights of any ten students of your class.

The heights of any ten students of the class are 134, 132, 132, 135, 124, 130, 128, 141, 125, 137.

Highest height = 141

Lowest height = 124

Range = highest height – lowest height

= 140 – 124

= 17

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.

Marks in the ascending order are 1, 2, 2, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6,

6, 6, 6, 7, 7, 8, 9

(i) highest marks = 9

(ii) lowest marks = 1

(iii) range = highest marks – lowest marks

= 9 – 1

= 8

(iv) Arithmetic Mean = __Sum of total marks__

Number of students

= __(1+2+2+ 3+4+4+4+5+5+5+5+5+6+6+6+6+7+7+8+9)__

20

= __100__

20

= 5

3). Find the mean of the first five whole numbers.

First five whole numbers are 0, 1, 2, 3, 4

Arithmetic Mean = __sum of the first five whole numbers__

Number of whole numbers

= __0+1+2+3+4__

5

= __10__

5

= 2

4). A cricketer scores the following runs in eight innings: 58, 76, 40, 35, 46, 45, 0, 100. Find the mean score.

Scores of the cricketer is 58, 76, 40, 35, 46, 45, 0, 100

Sum of the scores = 58+76+40+35+46+45+0+100 = 400

Number of innings = 8

Mean = __sum of the scores__

No. of innings

= __400__

8

= 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:

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

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

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

(iv) Who is the best performer?

Solution:

(i) sum of the points scored = 14+16+10+10 = 50

Number of games = 4

Mean of A = __Sum of the points scored__

No. of games

= __50__

4

= 12.5

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

To find the mean number of points per game for C, we would divide the total points by 3 because C played only 3 games.

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

B played in all the four games so to find the mean we divide by 4

sum of the points scored = 0+8+6+4 = 18

Number of games = 4

Mean of B = __Sum of the points scored__

No. of games

= __18__

4

= 4.5

(iv) Who is the best performer?

To tell who is the best performe we have to find the mean points scored by player C

sum of the points scored = 8+11+13 = 32

Number of games = 3

Mean of B = __Sum of the points scored__

No. of games

= __32__

3

= 10.67

Player A is best performer among the three.

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:

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

(ii) Range of the marks obtained.

(iii) Mean marks obtained by the group.

The marks in the ascending order are 39, 48, 56, 75, 76, 81, 85, 85, 90, 95

(i) Highest marks obtained = 95

Lowest marks obtained = 39

(ii) Range = highest marks – lowest marks

= 95 – 39

= 56

(iii) sum of all the marks = 39+48+56+75+76+81+85+85+90+95

= 730

Total students = 10

Mean = __Sum of the marks obtained by the students__

No of students

= __730__

10

= 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.

Mean = __sum of the enrolment__

No. of years

= __1555+ 1670+ 1750+2013+2540+2820__

6

= __12348__

6

= 2058

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

Day | Mon | Tues | Wed | Thurs | Fri | Sat | Sun |

Rainfall (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?

(i) range of the rainfall = highest rainfall – lowest rainfall

= 20.5 – 0.0

= 20.5

(ii) Mean of the rainfall = __sum of the rainfall on all days__

No. of days

= __0.0+12.2+2.1+0.0+20.5+5.5+1.0__

7

= __41.3__

7

= 5.9

(iii) on five days the rainfall was less than mean rainfall.

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.

Solution:

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

The height of the tallest girl = 151 cm

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

the height of the shortest girl = 128 cm

(iii) What is the range of the data?

Range = the height of the tallest girl – the height of the shortest girl

= 151 – 128

= 23

iv) What is the mean height of the girls?

Mean height = __sum of the heights of all the girls__

No. of girls

= __135+150+139+128+151+132+146+149+143+141__

10

= __1414__

10

= 141.4

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

Five many girls have heights more than the mean height.

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