3. Data Handling

Solutions to Ex. 3.1:

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

Ans:

(i) Highest marks is 9.

(ii) Lowest marks is 1.

(iii) Range = Highest marks – lowest marks

                  = 9 – 1 = 8

(iv) Total marks = 4 + 6 + 7 + 5 + 3 + 5 + 4 + 5 + 2 + 6 +2 + 5 + 1 + 9 + 6 + 5 + 8 + 4 + 6 +7 = 100

       Total students = 20

       Arithmetic mean = Total marks / Total students

                          = 100 / 20 = 5

Q3. Find the mean of the first five whole numbers.

Ans:

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

Sum of the digits is = 0 + 1 + 2 + 3 + 4 = 10

Total digits = 5

Mean = Total sum / total digits = 10 /2 = 5

Q4. A cricketer scores the following runs in eight innings: 58, 76, 40, 35, 46, 45, 0, 100. Find the mean score.

Ans:

Total runs scored = 58 + 76 + 40 + 35 + 46 + 45 + 0 + 100 = 400

Total innings = 8

Mean score = Total runs scored / Total innings

 = 400 / 8 = 50

Q5. Following table shows the points of each player scored in four games. Now answer the following questions:

Ans:

(i) Total points of A = 14 + 16 + 10 + 10 = 50

    Total games = 4

    Mean = total points / total games

     = 50 / 4 = 12.5

(ii) For C, divide the total points by 3 as C did not play 1 game. Hence total games played by C = 3.

(iii) Total points of B = 0 + 8 + 6 + 4 = 18

Total games = 4

Mean = total points / total games

= 18 / 4 = 4.5

(iv) A is the best performer.

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:

Ans:

(i) Highest marks obtained is 95

    Lowest marks obtained is 39

(ii) Range = highest marks – lowest marks

 = 95 – 39 = 56

(iii) Total marks = 85 + 76 + 90 + 85 + 39 + 48 + 56 + 95 + 81 + 75 = 730

       Total students = 10

       Mean = total marks / total students

        = 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.

Ans:

Total enrollment = 1555 + 1670 + 1750 + 2013 + 2540 + 2820 = 12348

Total years = 6

Mean = total enrollment / total years

 = 12348 / 6 = 2058

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

Ans:

(i) Highest rain = 20.5mm

  Lowest rain = 0

  Range = highest rain – lowest rain

    = 20.5 – 0 = 20.5mm

(ii) Total rainfall = 0 + 12.2 + 2.1 + 0 + 20.5 + 5.5 + 1 = 41.3

    Total days = 7

    Mean = total rainfall / total days

     = 41.3 / 7 = 5.9

(iii)  5 days the rainfall is less than the mean 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.

Ans:

(i) Height of the tallest girl = 151cm

(ii) Height of the shortest girl = 128cm

(iii) Range = height of tallest girl – height of the shortest girl

= 151 -128 = 23cm

(iv) Total height = 1414 cm

       Total girls = 10

       Mean = Total height / total girls

        = 1414 / 10 = 141.4cm

(v) 5 girls have height more than the mean height.

Solutions to ex. 3.2:

Q1. The scores in mathematics test (out of 25) of 15 students is as follows: 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20. Find the mode and median of this data. Are they same?

Ans:

Arranging the data: 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25

Mode = 20

Median is 20

Yes, mode & median are same.

Q2. The runs scored in a cricket match by 11 players is as follows: 6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15 Find the mean, mode and median of this data. Are the three same?

Ans:

Mean = Sum of score / no. of players

          = 6 + 15 + 120 + 50 + 100 + 80 + 10 + 15 + 8 + 10 + 15 / 11

          = 429 / 11 = 39

Arranging the data: 6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120

Mode = 15

Median is 15.

No, the three are not same.

Q3. The weights (in kg.) of 15 students of a class are: 38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47.
      (i) Find the mode and median of this data.
      (ii) Is there more than one mode?

Ans:

Arranging data: 32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50

Mode is 38 & 43.

Median is 40.

Yes, there is more than 1 mode.

Q4. Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14.

Ans:

Arranging data: 12, 12, 13, 13, 14, 14, 14, 16, 19

Mode is 14.

Median is 14.

Q5. Tell whether the statement is true or false:

Ans:

(i) The mode is always one of the numbers in a data. - True
(ii) The mean is one of the numbers in a data. - False
(iii) The median is always one of the numbers in a data. - True
(iv) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9. - False

Solutions to Ex. 3.3

Q1. Use the bar graph (Fig 3.3) to answer the following questions.

(a) Which is the most popular pet? 

(b) How many students have dog as a pet?

Ans:

(a) Cat is the most popular pet.

(b) 8 students have dog as a pet.

Q2. Read the bar graph (Fig 3.4) which shows the number of books sold by a bookstore during five consecutive years and answer the following questions:

(i) About how many books were sold in 1989? 1990? 1992?
(ii) In which year were about 475 books sold? About 225 books sold?
(iii) In which years were fewer than 250 books sold?

Ans:

(i)    175 books in 1989, 475 books in 1990 & 225 books in 1992 were sold.

(ii)  In the year 1990, 475 books & year 1992, 225 books were sold.

(iii) In the year 1992.

Q3. Number of children in six different classes are given below. 

(a) How would you choose a scale?
(b) Answer the following questions:
(i) Which class has the maximum number of children? And the minimum?
(ii) Find the ratio of students of class sixth to the students of class eight.

Ans:

(a) Scale will be 1 unit = 10 children.

(b) (i) Maximum number of children are in fifth class.

          Minimum children are in tenth class.

      (ii) Ratio = 120 / 100 = 6:5

Q4. The performance of a student in 1st Term and 2nd Term is given. Answer the following questions:

(i) In which subject, has the child improved his performance the most?
(ii) In which subject is the improvement the least?
(iii) Has the performance gone down in any subject?

Ans:

(i) Maths

(ii) S. Science

(iii) Hindi

Q5. Consider this data collected from a survey of a colony. Answer the following questions:

(i) What do you infer from the bar graph?
(ii) Which sport is most popular?
(iii) Which is more preferred, watching or participating in sports?

Ans:

(i) Watching the game is more preferred than participating.

(ii) Cricket

(iii) Watching

Q6. Answer the questions:

Ans:

(i) Jammu

(ii) Jammu & Bangalore

(iii) Bangalore & Jaipur or Bangalore & Ahmedabad

(iv) Mumbai