Question 1:
The following table represents the heights of ten students. Calculate the range of heights.
Answer:
S. No. | Name | Height (in feet) |
1. | Aditi | 4.6 |
2. | Vipul | 4.8 |
3. | Sangam | 4.5 |
4. | Manish | 4.8 |
5. | Sakhshi | 4.1 |
6. | Parul | 4.7 |
7. | Ayushi | 4.9 |
8. | Manoj | 4.8 |
9. | Akash | 5.2 |
10. | Rahul | 5.4 |
Range = Highest height – Lowest height = 5.4 – 4.1 = 1.3 feet.
Question 2:
Organize the following marks in a class test, in a tabular form:
5, 4, 7, 2, 6, 4, 7, 8, 9, 2, 1, 4, 2, 9, 1, 3, 4, 8, 7, 6.
a) Find the number which is the highest.
b) Find the number which is the lowest.
c) Find the range of marks.
d) Find the arithmetic mean.
Answer:
S. No. | Marks | Frequency
(No. of students) |
1. | 1 | 2 |
2. | 2 | 3 |
3. | 3 | 1 |
4. | 4 | 4 |
5. | 5 | 1 |
6. | 6 | 2 |
7. | 7 | 3 |
8. | 8 | 2 |
9. | 9 | 2 |
a) Highest number = 9.
b) Lowest number = 1.
c) Range = 9 – 1 = 8.
d) Arithmetic mean =
Question 3:
Calculate the mean of the first five whole numbers.
Answer:
The first five whole numbers are 0, 1, 2, 3, 4.
Therfore,
Mean = Sum of number/Total numbers = (0 + 1 + 2 + 3 + 4)/5 = 10/5 = 2.
Thus, the mean of first five whole numbers is 5.
Question 4:
A cricketer scores the following runs in eight innings: 58, 56, 89, 69, 76, 78, 44, 90. Calculate the mean score.
Answer:
Number of innings = 8
Mean 0f score = Sum of score/Number of innings = (58 + 56 + 89 + 69 + 76 + 78 + 44 + 90)/8
= 560/8 = 70.
Thus, the mean score is 70.
Question 5:
The score of each player in four games is shown in the following table:
Player | Game 1 | Game 2 | Game 3 | Game 4 |
X | 15 | 25 | 12 | 8 |
Y | 0 | 8 | 4 | 6 |
Z | 9 | 11 | Did not play | 10 |
Now,
a) Calculate the mean to determine X’s average number of points scored per game.
b) To calculate the mean of points per game for Z, we will divide by 3 or 4? Why?
c) Calculate the mean of Y.
d) Who performed the best?
Answer:
a) Mean of player X = Sum of scores by X/No. of games played by X
= (15 + 25 + 12 + 8)/4 = 60/4 = 15
b) We will divide by 3 as player Z played only three games.
c) Mean of player Y = Sum of scores by Y/No. of games played by Y
= (0 + 8 + 4 + 6)/4 = 18/4 = 4.5
d) Mean of player X = 15
Mean of player Y = 4.5
Mean of player Z = Sum of scores by Z/No. of games played by Z
= (9 + 11 + 10)/3 = 30/3 = 10
Player A has the highest mean. Therefore, A performed the best.
Question 6:
A group of students scored 45, 48, 49, 50, 47, 35, 41, 32, 22 and 42 (out of 50) in a science test. Find:
a) the highest and lowest marks obtained by the students.
b) range of the marks obtained.
c) mean marks obtained by the group.
Answer:
a) Highest marks obtained by the student = 50
Lowest marks obtained by the student = 22
b) Range of the marks obtained = 50 – 22 = 28
c) Mean of obtained marks = Sum of marks/Total number of marks
= (45 + 48 + 49 + 50 + 47 + 35 + 41 + 32 + 22 + 42)/10
= 411/10 = 41.1
Thus, the mean mark obtained by the group of student is 41.1.
Question 7:
During the six consecutive years the enrolment in a school was as follows:
1449, 1454, 1419, 2539, 2509, 2630
Find the mean.
Answer:
Mean enrolment = Sum of numbers of enrolment/Total number of enrolment
= (1449 + 1454 + 1419 + 2539 + 2509 + 2630)/6
= 12000/6 = 2000
Therefore, the mean enrolment of the school is 2,000.
Question 8:
The following table shows the rainfall (in mm) in a city of 7 days:
Day | Mon | Tue | Wed | Thurs | Fri | Sat | Sun |
Rainfall (in mm) | 0.0 | 12.3 | 2.5 | 0.0 | 19.5 | 5.5 | 4.5 |
Find:
a) range of the rainfall.
b) mean rainfall for the week
c) on how many days was the rainfall less than the mean rainfall?
Answer:
a) Range of the rainfall = Highest rainfall – Lowest rainfall = 19.5 – 0.0 = 19.5 mm
b) Mean rainfall = Sum of rainfall recorded/Total number of days
= (0.0 + 12.3 + 2.5 + 0.0 + 19.5 + 5.5 + 4.5)/7
= 6.32 mm
c) 5 days, i.e., Monday, Wednesday, Thursday, Saturday, Sunday rainfalls were less than the mean rainfall.
Question 9:
The height of 10 boys (in cm) was as follows:
130, 150, 145, 165, 150, 143, 146, 123, 128, 136
a) Find the height of the tallest boy.
b) Find the height of the shortest boy.
c) Calculate the range of data.
d) Calculate the mean height of the boys.
e) How many boys have heights more than the mean height?
Answer:
a) Height of the tallest boy = 165 cm
b) Height of the shortest boy = 123 cm
c) Range = 165 – 123 = 42 cm
d) Mean height = Sum of the heights of the boys/Total number of boys
= (130 + 150 + 145 + 165 + 150 + 143 + 146 + 123 + 128 + 136)/10
= 1416/10 = 141.6 cm
e) Six boys have heights more than the mean height.