Andhra Pradesh SCERT Class 7 Maths Data Handling Question and Answers Solutions
Andhra Pradesh SCERT 7th Class Maths Solutions Chapter 3 Data Handling Question and answers. Students who are searching for Andhra Pradesh Class 7 Maths Chapter 3 can find here Solution of this chapter.
Board |
Andhra Pradesh (AP Board) |
Class |
7th |
Subject |
Maths |
Topic |
Solution |
1.) Find the range of heights of any ten students of your class.
ANSWER:
Here we have to find range of heights of any ten students of my class.
We know,
The difference between the highest and the lowest observation is called Range.
Let, heights of students of my class in cm are
145, 156,167,175,165,146,178,169,140 and 181 cm
Range = highest Height – lowest Height
Range = 181 – 140
Range = 41
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
1st we have to arrange data in tabular form.
Marks |
Tally Marks |
Frequency |
1 |
I |
1 |
2 |
II | 2 |
3 | I |
1 |
4 |
III | 3 |
5 |
5 |
|
6 |
IIII | 4 |
7 | II |
2 |
8 |
I | 1 |
9 | I |
1 |
(i) Which number is the highest?
ANSWER:
9 number is the highest.
(ii) Which number is the lowest?
ANSWER:
1 number is the lowest.
(iii) What is the range of the data?
ANSWER:
We know,
Range = highest mark – lowest mark
Range = 9 – 1
Range = 8
(iv) Find the arithmetic mean.
ANSWER:
We know,
The most common representative value of a group of data is the arithmetic mean or the mean.
Arithmetic mean = Sum of all marks / Number of marks
Arithmetic mean = 1 + 2 + 3 + 4 + 5+ 6 + 7 + 8 + 9 / 9
Arithmetic mean = 45/9
Arithmetic mean = 5
3.) Find the mean of the first five whole numbers.
ANSWER:
We have to find mean of the first five whole numbers.
First five whole numbers are 0,1,2,3 and 4
Arithmetic mean = Sum of first five whole numbers / number of whole numbers
Arithmetic mean = 0 + 1 + 2 + 3 + 4 / 5
Arithmetic mean = 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.
ANSWER:
Here we have to find mean of cricketer scores.
Arithmetic mean = Sum of cricketer scores / number of innings
Arithmetic mean = 58 + 76 + 40 + 35 + 46 + 45 + 0 + 100 / 8
Arithmetic mean = 400 / 8
Arithmetic mean = 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.
ANSWER:
We have to find mean of player A score.
Arithmetic mean = Sum of points scored per game by player A / number of games
Arithmetic mean = 14 + 16 + 10 + 10 / 4
Arithmetic mean = 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?
ANSWER:
To find the mean number of points per game for C we divide total points by 3 because player C not play game 3.
(iii) B played in all the four games. How would you find the mean?
ANSWER:
We have to find mean of player B.
Arithmetic mean = Sum of points scored per game by player B / number of games
Arithmetic mean = 0 + 8 + 6 + 4 / 4
Arithmetic mean = 18 / 4 = 4.5
(iv) Who is the best performer?
ANSWER:
Player A score 50 points.
Player B score 18 points.
Player C score 32 points.
Player A 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.
ANSWER:
Given marks (out of 100) obtained by a group of students in a science test.
Highest mark obtained by the student is 95.
Lowest mark obtained by the students is 39.
(ii) Range of the marks obtained.
ANSWER:
We know,
Range = Highest mark – Lowest mark
Range = 95 – 39
Range = 56
(iii) Mean marks obtained by the group.
ANSWER:
We have to find Mean marks obtained by the group.
Arithmetic mean = Sum of marks obtained by the group / Number of students
Arithmetic mean = 85 + 76 + 90 + 85 + 39 + 48 + 56 + 95 + 81 + 75 / 10
Arithmetic mean = 730/10
Arithmetic mean = 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.
ANSWER:
Here we have to find mean enrolment of the school for this period.
Arithmetic mean = Sum of all enrolment / Number of years
Arithmetic mean = 1555 + 1670 + 1750 + 2013 + 2540 + 2820 / 6
Arithmetic mean = 2058
8.) The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:
Day | Mon | Tue | Wed | Thurs | Fri | Sat | Sun |
Rainfall (in 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.
ANSWER:
We know,
Range = Highest rainfall – Lowest rainfall
Range = 20.5 – 0.0
Range = 20.5
(ii) Find the mean rainfall for the week.
ANSWER:
Arithmetic mean = Sum of all rainfall for the week / Number of days
Arithmetic mean = 0 + 12.2 + 2.1 + 0 + 20.5 + 5.5 + 1 / 7
Arithmetic mean = 5.9
(iii) On how many days was the rainfall less than the mean rainfall.
ANSWER:
The mean rainfall is 5.9
On 5 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?
ANSWER:
Given, heights of 10 girls were measured in cm
Height of the tallest girl is 151 cm.
(ii) What is the height of the shortest girl?
ANSWER:
Height of the shortest girl is 128 cm.
(iii) What is the range of the data?
ANSWER:
We know,
Range = Highest height – Lowest height
Range = 151 – 128
Range = 23
(iv) What is the mean height of the girls?
ANSWER:
We have to find mean height of the girls.
Arithmetic mean = Sum of all heights / Number of students
Arithmetic mean = 135 + 150 + 139 + 128 + 151 + 132 + 146 + 149 + 143 + 141 /10
Arithmetic mean = 1414 / 10
Arithmetic mean = 141.4 cm
(v) How many girls have heights more than the mean height.
ANSWER:
Mean height of 10 girls are 141.4 cm
There are 5 girls have heights more than the mean height.
EXERCISE 3.2
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?
ANSWER:
We have to find mode and median of given data.
We know,
The mode of a set of observations is the observation that occurs most often.
The mode of 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20 =
Observations 20 occurs most often hence mode is 20.
Now,
We know,
When we arrange given data in ascending or descending order, the median gives us the middle observation.
Ascending order of given data are,
5,9,10,12,15,16,19,20,20,20,20,23,23,25,25.
Total 15 observations. The middle observation is 8
The median is 20.
The mean and the median are 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?
ANSWER:
Here runs scored in a cricket match by 11 players are given.
We have to find mean, mode and median of this data.
Arithmetic mean = Sum of all runs / Number of players
Arithmetic mean = 6 + 15 + 120 + 50 + 100 + 80 + 10 + 15 + 8 + 10 + 15/11
Arithmetic mean = 39
Now,
We know,
The mode of a set of observations is the observation that occurs most often.
The mode of 6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15 =
Observations 15 occurs most often hence mode is 15.
Now,
We know,
When we arrange given data in ascending or descending order, the median gives us the middle observation.
Ascending order of given data are,
6,8,10,10,15,15,15,50,80,100,129
Total 11 observations. The middle observation is 6
The median is 15.
Mean, mode and median are not 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.
ANSWER:
Given weights (in kg.) of 15 students of a class
We have to find mode and median of this data.
We know,
The mode of a set of observations is the observation that occurs most often.
The mode of 38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47 =
Observations 38 and 43 occurs most often hence mode are 38 and 43.
Now,
We know,
When we arrange given data in ascending or descending order, the median gives us the middle observation.
Ascending order of given data are,
32,35,36,37,38,38,38,40,42,43,43,43,45,47,50
Total 15 observations. The middle observation is 8
The median is 40.
(ii) Is there more than one mode?
ANSWER:
Yes, there are 2 modes of given data.
4.) Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14
ANSWER:
We have to find mode and median of this data.
We know,
The mode of a set of observations is the observation that occurs most often.
The mode of 13, 16, 12, 14, 19, 12, 14, 13, 14 =
Observations 14 occurs most often hence mode is 14.
Now,
We know,
When we arrange given data in ascending or descending order, the median gives us the middle observation.
Ascending order of given data are,
12, 12, 13,13,14,14,14,16,19
Total 9 observations. The middle observation is 5
The median is 14.
5.) Tell whether the statement is true or false:
(i) The mode is always one of the numbers in a data.
ANSWER:
True.
(ii) The mean is one of the numbers in a data.
ANSWER:
False.
(iii) The median is always one of the numbers in a data.
ANSWER:
True.
(iv) The data 6, 4, 3, 8, 9, 12, 13, 9 has mean 9.
ANSWER:
False.
EXERCISE 3.3
1.) Use the bar graph (Fig 3.3) to answer the following questions.
(a) Which is the most popular pet?
ANSWER:
From graph,
Cat is the most popular pet.
(b) How many students have dog as a pet?
ANSWER:
From graph,
There are 8 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:
(i) About how many books were sold in 1989? 1990? 1992?
ANSWER:
Given, graph of the number of books sold by a bookstore during five consecutive years.
We have to find books were sold in 1989, 1990 and 1992.
Books sold in 1989 = 175
Books sold in 1990 = 475
Books sold in 1992 = 225
(ii) In which year were about 475 books sold? About 225 books sold?
ANSWER:
In 1990 about 475 books sold and In 1992 About 225 books sold.
(iii) In which years were fewer than 250 books sold?
ANSWER:
In 1989 and 1992 were fewer than 250 books sold.
(iv) Can you explain how you would estimate the number of books sold in 1989?
ANSWER:
Yes, we explain the number of books sold in 1989.
Given scale is 1 unit = 100 books sold.
In 1989 there are 1 complete unit and 0.75 more hence total 175 books sold.
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 |
No. Of Children | 135 | 120 | 95 | 100 | 90 | 80 |
We have to represent given data on bar graph.
(a) How would you choose a scale?
ANSWER:
Scale is 1 unit = 20 students
(b) Answer the following questions:
(i) Which class has the maximum number of children? And the minimum?
ANSWER:
Class 5 has the maximum number of children.
Class 10 has the minimum number of children.
(ii) Find the ratio of students of class sixth to the students of class eight.
ANSWER:
Students of class sixth = 120
Students of class Eighth = 100
Ratio of students of class sixth to the students of class eight = 120: 100
Ratio of students of class sixth to the students of class eight = 6:5
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 (MM 100) | 67 | 72 | 88 | 81 | 73 |
2nd Term Term (MM 100) | 70 | 65 | 95 | 85 | 75 |
We have to draw double bar graph of the performance of a student in 1st Term and 2nd Term.
(i) In which subject, has the child improved his performance the most?
ANSWER:
In math subject, the child has improved his performance the most.
(ii) In which subject is the improvement the least?
ANSWER:
In Social science subject is the improvement the least.
(iii) Has the performance gone down in any subject?
ANSWER:
In Hindi the performance gone down.
5.) Consider this data collected from a survey of a colony.
Favorite Sport | Cricket | Basket Ball | Swimming | Hocky | Athmetics |
Watching | 1240 | 470 | 510 | 430 | 250 |
Participate | 620 | 320 | 320 | 250 | 105 |
(i) Draw a double bar graph choosing an appropriate scale.
ANSWER:
(ii) Which sport is most popular?
ANSWER:
Cricket is most popular sport.
(iii) Which is more preferred, watching or participating in sports?
ANSWER:
Watching is more preferred in sports