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1.   Set up equations and solve them to find the unknown numbers in the following cases:
(a) Add 4 to eight times a number; you get 60.
(b) One-fifth of a number minus 4 gives 3.
(c) If I take three-fourths of a number and add 3 to it, I get 21.
(d) When I subtracted 11 from twice a number, the result was 15.
(e) Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.
(f) Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.
(g) Anwar thinks of a number. If he takes away 7 from 5/2  of the number, the result is 23.

Let the number in each case be n. (a)  According to question:            or                                                              or                                                                  (b) We have :                                                      or                                        or                                          (c)  The equation is :                ...

3.  A coin is flipped to decide which team starts the game. What is the probability that your team will start?

We know, a coin has two faces : Head and Tail One can choose either Head or Tail. Therefore, number of favourable outcome = 1 We know, Probability of any outcome

2. There are 6 marbles in a box with numbers from 1 to 6 marked on each of them.
(i) What is the probability of drawing a marble with number 2?
(ii) What is the probability of drawing a marble with number 5?

There are 6 marbles in the box numbered from 1 to 6 (i) Number of marble with number 2 on it = 1  Probability of getting a marble with number 2 (ii) Number of marble with number 5 on it = 1  Probability of getting a marble with number 5

1. Tell whether the following is certain to happen, impossible, can happen but not certain.
(i) You are older today than yesterday. (ii) A tossed coin will land heads up.
(iii) A die when tossed shall land up with 8 on top.
(iv) The next traffic light seen will be green. (v) Tomorrow will be a cloudy day.

(i) You are older today than yesterday. -This event is certain to happen. (ii) A tossed coin will land heads up. - This event can happen but not certain.      (iii) A die when tossed shall land up with 8 on top. - This event is impossible. A die can only show one of the numbers (1,2,3,4,5,6) (iv) The next traffic light seen will be green. - This event can happen but not certain.  (v) Tomorrow...

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:
(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.

Table 3.1 is  The double bar graph is : (i) From the graph, Jammu has the largest difference between the maximum and minimum temperature bars.  Jammu is the city with the largest difference in its maximum temperature and minimum temperatures on the given date.   (ii) The city with the maximum temperature would be the hottest. And the city with the least temperature will be the...

5. Consider this data collected from a survey of a colony. (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?

(i)   The double bar graph represents the number of people who like watching and participating in various sports. We observe that, The maximum number of people like either watching or participating in cricket. The minimum number of people like either watching or participating in athletics. (ii) According to the graph, the tallest bar is of cricket. Hence, cricket is the most popular...

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: (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?

(i) According to the graph, Maths had the maximum increase in marks. Hence, The child improved his performance the most in Maths.   (ii)  According to the graph, S.Science had the least increase in marks. Hence, The child improved his performance the least in S.Science.   (iii) According to the graph, Hindi's marks went down in the second term Hence, The child’s performance has gone down in Hindi.

3. Number of children in six different classes are given below. Represent the data on a bar graph. (a) How would you choose a scale?
(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.

(a) The scale : 1 unit = 10 children. (b) (i) Class fifth has the maximum number of children.  Whereas, class tenth has the minimum number of children (ii) Number of students in class sixth = 120 Number of students in class eight = 100 Therefore, the required ratio =  Required ratio is

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:
(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? (i) Observing the graph, Number of books sold in 1989 = 180 Number of books sold in 1992 = 220 Number of books sold in 1990 = 480 (ii)  475 books were sold in the year 1990 225 books were sold in the year 1992 (iii)  The years in which the total number of books sold was less than 250 are 1989 and 1992. (iv) Around 175 books were sold in the year 1989. By drawing a line from the top of 1989 bar...

1. 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? (a) The bar graph represents the pets owned by the students of class seven. And, The bar of the cat is the tallest Hence, cat is the most popular pet. (b) The bar of the dog is reaches the value 8 8 students have dog as pet.

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.

(i) True. Mode is the observation which occurs maximum number of times. Hence, Mode will always be the one of the numbers in a data. (ii) False. (iii) False. For even number of observations, the median is the mean of the  and values. (iv) Mean =  Hence, the statement is False.

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

Given,  Arranging in ascending order =  We know, The mode is observation which occurs a maximum number of times. Median is the middle observation when that data is arranged in ascending or descending order. Now, Clearly,  occurs thrice. So,  is the mode of the data. Now, there are 9 values, so the median is the  Hence,  is the median value.

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?

Given, weights of 15 students (in kg)=  Arranging the data in ascending order =  (i) Clearly, 38 and 43 both occur thrice. So, they both are the mode of the data. Now, there are 15 values, so the median is the  Hence, 40 is the median value. (ii) Yes, there are two modes of the data given.

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?

Runs scored in the match =  Arranging in ascending order =  Here, 15 occurs the maximum number of times. Hence, 15 is the mode of the data Now,     Therefore the mean score is  Now, the median is the middle observation of the data. There are 11 terms. Therefore the middle observation is  Therefore, 15 is the median of the data. No, they are not the same.

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?

Scores of 15 students are :  Arranging the data in ascending order =  We know, Mode: The number which occurs most frequently.  Median: Median is the mid-value of the set of numbers.  Here, 20 occurs 4 times, therefore 20 is the mode of the data. Also, the middle value is 20. Therefore, the median of the data is 20. Yes, the median and mode of this data are the same.

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.

Given, Heights of 10 girls (in cm) =   Arranging the above data in ascending order =  (i) Height of the tallest girl =  (ii) Height of the shortest girl =  (iii) Range of the data =  (iv)  We know, Arithmetic mean =  Therefore, mean height of the girls is  (iv) Here, mean height =  And,  are more than  Therefore, 5  girls have height more than the average height.

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

Given, (i) Range = Maximum rainfall - Minimum rainfall (ii)  We know, Arithmetic mean =  Therefore, mean rainfall is  (iii) Here, mean =  Mon(0.0), Wed(2.1), Thu(0.0), Sat(5.5), Sun(1.0) are less than the mean Therefore, on 5 days, rainfall was less than the mean.

8. 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.

Given, Enrolment during 6 consecutive years =   We know, Arithmetic mean Therefore, mean enrolment per year is

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.

Given, Marks obtained the students =  Arranging in ascending order =  (i) Highest marks obtained =  Lowest marks obtained =  (ii) Range of marks = Highest marks - Lowest marks (iii) We know, Arithmetic mean   Therefore, mean marks =

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