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Kerala State Syllabus 9th Standard Maths Solutions Chapter 13 Statistics
Statistics Textual Questions and Answers
Textbook Page No. 193
Plus Two Teacher Salary Kerala Question 1.
The weight of 6 players in a volleyball team are all different and the average weight is 60 kilograms.
i. Prove that the team has at least one player weighing more than 60 kilograms.
ii. Prove that the team has at least one player weighing less than 60 kilograms.
Answer:
i. Total weight of 6 players = 60 × 6 = 360 kg
The team contains players having weights 60, less than 60 or greater than 60. If the weights of all the players are less than 60, the average will also be less than 60. This is not possible. Therefore there will be at least one player having weight greater than 60.
ii. If the weight of all the players are greater than 60, the average will also be greater than 60. Therefore there will be at least one player having weight less than 60.
Statistics 9th Class Question 2.
Find two sets of 6 numbers with average 60, satisfying each of the conditions below:
i. 4 of the numbers are less than 60 and 2 of them greater than 60.
ii. 4 of the numbers are greater than 60 and 2 of them less than 60.
Answer:
Total sum = 60 × 6 = 360
i. 20, 30, 40, 50, 100, 120
ii. 5, 15, 70, 80, 90, 100
Other ways are also possible.
Chapter 13 Maths Class 9 Question 3.
The table shows the children in a class, sorted according to the marks they got for a math test.
| Marks | Children |
| 2 | 1 |
| 3 | 2 |
| 4 | 5 |
| 5 | 4 |
| 6 | 6 |
| 7 | 11 |
| 8 | 10 |
| 9 | 4 |
| 10 | 2 |
Calculate the average marks of the class.
Answer:
Total number of children is 45. Repeated addition can be written as multiplication.
Average mark = \(\frac { Total }{ Number }\) = \(\frac { 297 }{ 45 }\) = 6.6
10th Maths Solution Question 4.
The table below shows the days in a month sorted according to the amount of rainfall in a locality
| Rainfall(mm) | Days |
| 54 | 3 |
| 56 | 5 |
| 58 | 6 |
| 55 | 3 |
| 50 | 2 |
| 47 | 4 |
| 44 | 5 |
| 41 | 2 |
What is the average rainfall per day during this month?
Answer:
| Rainfall(mm) | Days | Total |
| 54 | 3 | 54 × 3 = 162 |
| 56 | 5 | 56 ×5 = 280 |
| 58 | 6 | 58 × 6 = 348 |
| 55 | 3 | 55 × 3 = 165 |
| 50 | 2 | 50 × 2=100 |
| 47 | 4 | 47 × 4 =188 |
| 44 | 5 | 44 × 5 = 220 |
| 41 | 2 | 41 × 2 = 82 |
| Total | 30 | 1545 |
The average of the rain fall per day during that month = \(\frac { Total rain fall }{ Number of days }\)
= \(\frac { 1545 }{ 30 }\) = 51.5mm
Solutions Maths Question 5.
The details of rubber sheets a farmer got during a month are given below.
| Rubber (Kg) | Days |
| 9 | 3 |
| 10 | 4 |
| 11 | 3 |
| 12 | 3 |
| 13 | 5 |
| 14 | 6 |
| 16 | 6 |
i. How many kilograms of rubber did he get a day on average in this month?
ii. The price of rubber is 120 rupees per kilogram. What is his average income per day this month from selling rubber?
Answer:
i. Average Quantity of rubber per day = \(\frac { 381 }{ 30 }\) = 12.77kg
ii. . If the price is Rs. 120 per kg, then average incomeperday = 12.7 × 120 = Rs.1524
Textbook Page No. 197
Statistics Class 9 Question 1.
Find different sets of 6 different numbers between 10 and 30 with each number given below as mean:
i. 20
ii. 15
iii. 25
Answer:
i. The mean of 6 numbers is 20.
ie; sum = 6 x 20= 120 (Write 3 pairs with sum 40)
i.e., 15, 25, 18, 22, 19, 21
ii. The mean of 6 numbers is 15
i.e; sum =6 x 15=90
(Write 30 pairs with sum 3)
12, 18, 13, 17, 14, 16
iii. Mean is 25
sum = 25 x 6 = 150
(Write 50 pairs with sum 3)
22, 28, 23, 27, 24, 26
HSSLive Statistics Question 2.
The table below shows the children in a class, sorted according to their heights.
| Height(cm) | Number of children |
| 148 – 152 | 8 |
| 152 – 156 | 10 |
| 156 – 160 | 15 |
| 160 – 164 | 10 |
| 164 – 168 | 7 |
What is the mean height of a child in this class?
Answer:
|
Height (cm) |
No. of children | Mid Value |
Total Height |
| 148 -152 | 8 | 150 | 150 × 8 = 1200 |
| 152 -156 | 10 | 154 | 154 × 10 = 1540 |
| 156 -160 | 15 | 158 | 158 × 15 = 2370 |
| 160 -164 | 10 | 162 | 162 × 10 = 1620 |
| 164 -168 | 7 | 166 | 160 × 7 = 1162 |
| Total | 50 | 7892 |
Mean height = \(\frac { Total height }{ No of children }\)
= \(\frac { 7892 }{ 50 }\) = 157.84 cm
Natural Rubber Sheets Question 3.
The teachers in a university are sorted according to their ages, as shown below.
| Age | Number of Persons |
| 25 – 30 | 6 |
| 30 – 35 | 14 |
| 35 – 40 | 16 |
| 40 – 45 | 22 |
| 45 – 50 | 5 |
| 50 – 55 | 4 |
| 55 – 60 | 3 |
What is the mean age of a teacher in this university?
Answer:
| Age | No.of persons | Midvalue | Total |
| 25 – 30 | 6 | 27.5 | 165 |
| 30 – 35 | 14 | 32.5 | 455 |
| 35 – 40 | 16 | 37.5 | 600 |
| 40 – 45 | 22 | ‘42.5 | 935 |
| 45 – 50 | 5 | 47.5 | 237.5 |
| 50 – 55 | 4 | 52.5 | 210 |
| 55 – 60 | 3 | 57.5 | 172.5 |
| Total | 70 | 2775 |
Mean age = \(\frac { Total age }{ No of persons }\)
= \(\frac { 2775 }{ 70 }\) = 39.64
HSSlive Maths Question 4.
The table below shows children in a class sorted according to their weights.
| Weight (kg) | Number of children |
| 21 – 23 | 4 |
| 23 – 25 | — |
| 25 – 27 | 7 |
| 27 – 29 | 6 |
| 29 – 31 | 3 |
| 31 – 33 | 1 |
The mean weight is calculated as 26 kilograms. How many children have weights between 23 and 25 kilograms?
Answer:
Let’s prepare the table for finding the mean by considering the number of children in the group 23 to 25, as ‘x’.
|
Weight (kg) |
No.of children | Mid value |
Total weight |
| 21 – 23 | 4 | 22 | 22 × 4 = 88 |
| 23 – 25 | X | 24 | 24 × x = 24x |
| 25 – 27 | 7 | 26 | 26 × 7 = 182 |
| 27 – 29 | 6 | 28 | 28 × 6 = 168 |
| 29 – 31 | 3 | 30 | 30 × 3 = 90 |
| 31 – 33 | 1 | 32 | 32 × 1 = 32 |
| Total | 21 + x | 560 + 24x |
Mean weight = 26 kg
i.e; the number of children having weight between 23 to 25 is 7.
Statistics Exam oriented Questions and Answers
Question 1.
The details of rubber sheets got for a month by a farmer are given in the table.
| Rubber (kg) | No. of days |
| 7 | 3 |
| 8 | 4 |
| 9 | 5 |
| 10 | 6 |
| 11 | ? |
| 12 | 4 |
| 13 | 3 |
During this month he got an average of 10 sheets per day. If so in how many days did he get 11kg per day ?
Answer:
| Rubber (kg) | Days | Total weights (kg) |
| 7 | 3 | 7 × 3 = 21 |
| 8 | 4 | 8 × 4= 32 |
| 9 | 5 | 9 × 5 = 45 |
| 10 | 6 | 10 × 6 = 60 |
| 11 | X | 11 × x= 11x |
| 12 | 4 | 12 × 4 = 48 |
| 13 | 3 | 13 × 3 = 39 |
| Total | 25 + x | 245 + 11x |
Let ‘x’ be the number of days in which he got 11 kg rubber sheet.
∴ He got 11 kgs of sheets for 5 days.
Question 2.
In a factory, there are workers belonging to four categories. The average income and the number of workers in each category are given. What is the mean income when all the workers in the four categories are combined?
| Class | No.of workers | Average income (Rs) |
| I | 12 | 6000 |
| II | 16 | 8000 |
| III | 8 | 9500 |
| IV | 4 | 11000 |
Answer:
Mean income = \(\frac { 320000 }{ 40 }\)
= Rs. 8000
Question 3.
The daily wages of 10 workers in a factory are given below.
400, 350, 450, 500, 400, 500, 350, 500, 350, 450
If one more person is joined, the mean becomes Rs. 450. What is the daily wage of the new person?
Answer:
Total wages of 10 workers = 4250 Total wages of 11 workers= 11 × 450 = Rs. 4950
Wage of the 11th person = 4950 – 4250
Question 4.
Find 10 different numbers between 10 and 30 whose mean is 20.
Answer:
Given mean is 20
Sum 20 × 10 = 200.
We have to find 10 different numbers whose sum is 200 (for this find 5 pairs of sum 40)
(15, 25) (16, 24) (17, 23) (18, 22) (19, 21)
The numbers are 15, 16, 17, 18, 19, 21, 22, 23, 24, 25
Question 5.
A table categorizing the workers in an office on the basis of their salary is given below.
| Salary (Rs) | Number of workers |
| 15000 -18000 | 1 |
| 18000 – 21000 | 3 |
| 21000 – 24000 | 5 |
| 24000 – 27000 | 4 |
| 27000 – 30000 | 1 |
| 30000 – 33000 | 1 |
Find the mean of salary.
Answer:
Mean income = \(\frac { 349500 }{ 15 }\)
= R.s 23300
Question 6.
i. Find the mean of natural numbers from 1 to 100.
ii. What is the mean of even numbers from 1 to 100? What is the mean of odd numbers?
iii. What is the difference between the means of the first 100 even numbers and odd numbers?
iv. What is the difference between the means of the first 200 even numbers and 200 odd numbers?
Answer:
Sum of the natrural numbers from 1 to n = \(\frac n{ n + 1 }{ 2 }\)
Sum of the first 100 odd numbers
= 1002 = 100 × 100
In general, the difference between the means of n even numbers and n odd numbers is always 1.
Question 7.
A table tabulating the players in a cricket team on the basis of their age is given below.
| Age | Number of players |
| 21 | 1 |
| 22 | 2 |
| 25 | 3 |
| 26 | 3 |
| 29 | 2 |
| 30 | 1 |
Calculate the mean age of the players?
Answer:
Mean age of players = 306/12 = 25.5