Statistics
Class 9th Mathematics Part 2 Kerala Board Solution
- The weight of 6 players in a volley ball team are all different and the average weight…
- Find two sets of 6 numbers with average 60, satisfying each of the conditions below: i)…
- The table shows the children in a class, sorted according to the marks they got for a…
- The table below shows the days in a month sorted according to the amount of rainfall in…
- The details of rubber sheets a farmer got during a month are given below. |c|c| & 9&3…
- 20 Find different sets of 6 different numbers between 10 and 30 with each number given…
- 15 Find different sets of 6 different numbers between 10 and 30 with each number given…
- 25 Find different sets of 6 different numbers between 10 and 30 with each number given…
- The table below shows the children in a class, sorted according to their heights. |c|c|…
- The teachers in a university are sorted according to their ages, as shown below. What…
- The table below shows children in a class sorted according to their weights. The mean…
Questions Pg-221
Question 1.The weight of 6 players in a volley ball 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) Given: number of players = 6
Their average weight = 60Kg
If all the players will have weight more than 60 then average weight will be more than 60. Hence, to have average weight to be 60 atleast one of the player must have his weight less than 60.
(ii) Given: number of players = 6
Their average weight = 60Kg
If all the players will have weight less than 60 then average weight will be less than 60. Hence, to have average weight to be 60 atleast one of the player must have his weight more than 60.
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:
(i) Given: 6 numbers and their average is 60.
As the given average is 60 and numbers = 6
Hence, the sum of numbers must be = 60 × 6 = 360
So, Set having 4 of the numbers are less than 60 and 2 of them greater than 60 = {56, 57, 58, 59, 62, 68}
Average =(56+57+58+59+62+68)/6
= 360/6
= 60
Which is true as per given condition.
Hence, the required set is {56, 57, 58, 59, 62, 68}.
(ii) Given: 6 numbers and their average is 60.
As the given average is 60 and numbers = 6
Hence, the sum of numbers must be = 60 × 6 = 360
Set having 4 of the numbers are greater than 60 and 2 of them less than 60 = {61, 62, 63, 64, 58, 52}
Average =(61+62+63+64+58+52)/6
= 360/6
= 60
Which is true as per given condition.
Hence, the required set is {61, 62, 63, 64, 58, 52}.
Question 3.
The table shows the children in a class, sorted according to the marks they got for a math test.
Calculate the average marks of the class.
Answer:
Average marks = Total marks/ total number of students
Average marks obtained by each student = 6.6
Question 4.
The table below shows the days in a month sorted according to the amount of rainfall in a locality.
What is the average rainfall per day during this month?
Answer:
Average Rainfall = Total rainfall/ total number of days
Average rainfall each day = 51.5cm
Question 5.
The details of rubber sheets a farmer got during a month are given below.
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 Rubber each day = Total rubber/ total number of days
Average Rubber each day = 12.7Kg
(ii) Price of rubber per kilogram = 120 rupees
Price of Average Rubber of 12.7Kg = 12.7 × 120
= 1524 rupees
Questions Pg-225
Question 1.Find different sets of 6 different numbers between 10 and 30 with each number given below as mean:
20
Answer:
Given: 6 numbers and their average is 20 between 10 and 30.
As the given average is 20 and numbers = 6
Hence, the sum of numbers must be = 20 × 6 = 120
So, Set having different numbers between 10 and 30 = {12, 13, 15, 25, 27, 28}
Average =(12+13+15+25+27+28)/6
= 120/6
= 20
Which is true as per given condition.
Hence, the required set is {12, 13, 15, 25, 27, 28}.
Question 2.
Find different sets of 6 different numbers between 10 and 30 with each number given below as mean:
15
Answer:
Given: 6 numbers and their average is 15 between 10 and 30.
As the given average is 15 and numbers = 6
Hence, the sum of numbers must be = 15 × 6 = 90
So, Set having different numbers between 10 and 30 = {11, 12, 13, 14, 15, 25}
Average =(11+12+13+14+15+25)/6
= 90/6
= 15
Which is true as per given condition.
Hence, the required set is {11, 12, 13, 14, 15, 25}.
Question 3.
Find different sets of 6 different numbers between 10 and 30 with each number given below as mean:
25
Answer:
Given: 6 numbers and their average is 25 between 10 and 30.
As the given average is 25 and numbers = 6
Hence, the sum of numbers must be = 25 × 6 = 150
So, Set having different numbers between 10 and 30 = {22, 23, 24, 26, 27, 28}
Average =(22+23+24+26+27+28)/6
= 150/6
= 25
Which is true as per given condition.
Hence, the required set is {22, 23, 24, 26, 27, 28}.
Question 4.
The table below shows the children in a class, sorted according to their heights.
What is the mean height of a child in this class?
Answer:
Mean height of child = Total height/ total number of children
Mean height of a child in this class = 157.84
Question 5.
The teachers in a university are sorted according to their ages, as shown below.
What is the mean age of a teacher in this university?
Answer:
Mean age of child = Total age/ total number of children
Mean age of a child in this class = 39.64
Question 6.
The table below shows children in a class sorted according to their weights.
The mean weight is calculated as 26 kilograms. How many children have weights between 23 and 25 kilograms?
Answer:
Given: mean weight = 26 Kg
Let the unknown weight is x.
Mean age of child = Total age/ total number of children
⇒ 560 + 24x = 26(21 + x)
⇒ 560 + 24x = 546 + 26x
⇒ 560 - 546 = 26x – 24x
⇒ 14 = 2x
⇒ x = 7
children have weights between 23 and 25 kilograms = 7
Total number of questions = 12
How much each question will cost?