Question 1

1. Find the range of heights of any ten students of your class. 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. 3. Find the mean of the first five whole numbers. 4. A cricketer scores the following runs in eight innings: 58, 76, 40, 35, 46, 45, 0, 100. Find the mean score. 5. Following table shows the points of each player scored in four games: Player A: Game 1 = 14, Game 2 = 16, Game 3 = 10, Game 4 = 10; Player B: Game 1 = 0, Game 2 = 8, Game 3 = 6, Game 4 = 4; Player C: Game 1 = 8, Game 2 = 11, Game 3 = Did not Play, Game 4 = 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? 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. 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. 8. The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows: Mon 0.0, Tue 12.2, Wed 2.1, Thurs 0.0, Fri 20.5, Sat 5.5, Sun 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. 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.

Accepted Answer

1. Answers will vary according to the ten students measured. Arrange the ten heights, then range

$=$

greatest height

$-$

least height.
2. Frequency table: mark 1 occurs 1 time, 2 occurs 2 times, 3 occurs 1 time, 4 occurs 3 times, 5 occurs 5 times, 6 occurs 4 times, 7 occurs 2 times, 8 occurs 1 time and 9 occurs 1 time. (i) Highest mark

$=9$

(ii) Lowest mark

$=1$

(iii) Range

$=9-1=8$

(iv) Arithmetic mean

=\frac{101}{20}=5.05

.
3. Mean of

$0,1,2,3,4$

is

\frac{0+1+2+3+4}{5}=2

.
4. Mean score

=\frac{58+76+40+35+46+45+0+100}{8}=50

.
5. (i) A's average

=\frac{14+16+10+10}{4}=12.5

(ii) Divide by 3, because C played only 3 games (iii) B's mean

=\frac{0+8+6+4}{4}=\frac{18}{4}=4.5

(iv) A is the best performer.
6. (i) Highest marks

$=95$

, lowest marks

$=39$

(ii) Range

$=95-39=56$

(iii) Mean

=\frac{85+76+90+85+39+48+56+95+81+75}{10}=73

.
7. Mean enrolment

=\frac{1555+1670+1750+2013+2540+2820}{6}=2058

.
8. (i) Range

$=20.5-0.0=20.5$

mm (ii) Mean rainfall

=\frac{0.0+12.2+2.1+0.0+20.5+5.5+1.0}{7}=5.9

mm (iii) Rainfall was less than the mean on 5 days.
9. (i) Tallest height

$=151$

cm (ii) Shortest height

$=128$

cm (iii) Range

$=151-128=23$

cm (iv) Mean height

=\frac{1414}{10}=141.4

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

Question 2

1. 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? 2. 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? 3. 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? 4. Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14. 5. Tell whether the statement is true or false: (i) The mode is always one of the numbers in a data. (ii) The mean is one of the numbers in a data. (iii) The median is always one of the numbers in a data. (iv) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.

Accepted Answer

1. Arranged data: 5, 9, 10, 12, 15, 16, 19, 20, 20, 20, 20, 23, 24, 25, 25. Mode

$=20$

, median

$=20$

; yes, they are the same.
2. Sum

$=429$

, so mean

=\frac{429}{11}=39

. Arranged data: 6, 8, 10, 10, 15, 15, 15, 50, 80, 100, 120. Mode

$=15$

, median

$=15$

; no, the three are not the same.
3. Arranged data: 32, 35, 36, 37, 38, 38, 38, 40, 42, 43, 43, 43, 45, 47, 50. (i) Modes

$=38$

kg and

$43$

kg; median

$=40$

kg (ii) Yes, there are two modes.
4. Arranged data: 12, 12, 13, 13, 14, 14, 14, 16, 19. Mode

$=14$

, median

$=14$

.
5. (i) True (ii) False (iii) True (iv) False.

Question 3

1. Use the bar graph (Fig 3.3) to answer the following questions. In Fig 3.3, the bar graph titled "Pets owned by students of class seven" has pet animals Dogs, Cats, Rabbits, Hamsters and Others on the horizontal axis and number of students on the vertical axis; the bar heights are Dogs 8, Cats 10, Rabbits 2, Hamsters 5 and Others 3. (a) Which is the most popular pet? (b) How many students have dog as a pet? 2. 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: In Fig 3.4, the scale is 1 unit = 100 books; the approximate bar heights are 1989 = 180 books, 1990 = 475 books, 1991 = 300 books, 1992 = 225 books and 1993 = 600 books. (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? (iv) Can you explain how you would estimate the number of books sold in 1989? 3. Number of children in six different classes are given below. Represent the data on a bar graph. Class: Fifth, Sixth, Seventh, Eighth, Ninth, Tenth. Number of Children: 135, 120, 95, 100, 90, 80. (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. 4. The performance of a student in 1st Term and 2nd Term is given. Draw a double bar graph choosing appropriate scale and answer the following: Subject English, Hindi, Maths, Science, S. Science; 1st Term (M.M. 100): 67, 72, 88, 81, 73; 2nd Term (M.M. 100): 70, 65, 95, 85, 75. (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? 5. Consider this data collected from a survey of a colony. Favourite Sport: Cricket, Basket Ball, Swimming, Hockey, Athletics. Watching: 1240, 470, 510, 430, 250. Participating: 620, 320, 320, 250, 105. (i) Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph? (ii) Which sport is most popular? (iii) Which is more preferred, watching or participating in sports? 6. Take the data giving the minimum and the maximum temperature of various cities given in the beginning of this Chapter (Table 3.1). Plot a double bar graph using the data and answer the following: Table 3.1 records maximum/minimum temperature (in degree Celsius) as Ahmedabad 38/29, Amritsar 37/26, Bangalore 28/21, Chennai 36/27, Delhi 38/28, Jaipur 39/29, Jammu 41/26 and Mumbai 32/27. (i) Which city has the largest difference in the minimum and maximum temperature on the given date? (ii) Which is the hottest city and which is the coldest city? (iii) Name two cities where maximum temperature of one was less than the minimum temperature of the other. (iv) Name the city which has the least difference between its minimum and the maximum temperature.

Accepted Answer

1. (a) Cats are the most popular pet (b) 8 students have dog as a pet.
2. (i) About 180 books in 1989, about 475 books in 1990 and about 225 books in 1992 (ii) About 475 books were sold in 1990; about 225 books were sold in 1992 (iii) Fewer than 250 books were sold in 1989 and 1992 (iv) The 1989 bar lies between 100 and 200, close to 200, so it is estimated as about 180 books.
3. (a) One convenient scale is 1 unit = 10 children (b) (i) Class Fifth has the maximum number of children and class Tenth has the minimum (ii) Ratio of class sixth to class eighth

$=120:100=6:5$

.
4. (i) Maths (ii) S. Science (iii) Yes, the performance has gone down in Hindi.
5. (i) The graph shows that watching is preferred to participating for every sport (ii) Cricket is the most popular sport (iii) Watching is more preferred.
6. (i) Jammu has the largest difference (ii) Jammu is the hottest city and Bangalore is the coldest city (iii) For example, the maximum temperature of Bangalore is less than the minimum temperature of Ahmedabad; it is also less than the minimum temperature of Jaipur (iv) Mumbai has the least difference.