Exercise 21A
Paper-263Question 1:
Define the terms:
(i) Data
(ii) Raw data
(iii) Array
(iv) Tabulation of data
(v) Observations
(vi) Frequency of an observation
(vii) Statistics
Answer 1:
(i) Data: Information in the form of numerical figures is known as data.
(ii) Raw data: Data that is obtained in the original form is known as raw data.
(iii) Array: When the raw data is obtained in ascending or descending order of magnitude, it is known as array.
(iv) Tabulation of data: Arranging the data in a systematic way in the form of a table is known as the tabulation of the data.
(v) Observations: Each numerical figure in a data is known as an observation.
(vi) Frequency of an observation: Number of times an observation occurs in the data is known as the frequency of an observation.
(vii) Statistics: The subject that deals with the collection, presentation, analysis and interpretation of the numerical data is known as statistics.
Question 2:
A die was thrown 20 times and the following outcomes were recorded:
5, 2, 1, 3, 4, 4, 5, 6, 2, 2, 4, 5, 5, 6, 2, 2,4, 5, 5, 1.
Arrange the above data in ascending order and prepare the frequency table.
Answer 2:
Data in the ascending order:
1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6
Question 3:
The daily wages (in Rs) of 15 workers in a factory are given below.
200, 180, 150, 150, 130, 180, 180, 200, 150, 130, 180, 180, 200, 150, 180.
Arrange the above data in ascending order and prepare the frequency table.
Answer 3:
Daily wages in the ascending order:
130, 130, 150, 150, 150, 150, 180, 180, 180, 180, 180, 180, 200, 200, 200
Frequency table:
Question 4:
Write the data given below in ascending order and prepare the frequency table.
7, 8, 7, 10, 6, 8, 9, 7, 10, 5, 7, 6, 8, 5, 6, 7, 8, 9, 7, 6, 7, 8.
Answer 4:
Data in ascending order:
5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 10, 10
Frequency table:
Question 5:
Fill in the blanks:
(i) Data means information in the form of ...... figures.
(ii) Data obtained in the ..... form is called raw data.
(iii) Arranging the numerical figures in ascending of descending order is called an ...... .
(iv) The number of times a particular observation occurs is called its ...... of data.
(v) Arranging the data in the form of a table is called ...... of data.
Answer 5:
(i) numerical
(ii) original
(iii) array
(iv) frequency
(v) tabulation
Question 6:
Find the mean of first five natural numbers.
Answer 6:
First five natural numbers are 1, 2, 3, 4 and 5.
Mean of the first five natural numbers =
=
Hence, mean of the first five natural numbers is 3.
Question 7:
Find the mean of first six odd natural numbers.
Answer 7:
First six odd natural numbers are 1, 3, 5, 7, 9 and 11.
Mean of the first six natural numbers =
=
Mean of the first six odd natural numbers is 6.
Question 8:
Find the mean of first seven even natural numbers.
Answer 8:
First seven even natural numbers are 2, 4, 6, 8, 10, 12 and 14.
Mean of the first seven even natural numbers =
=
Mean of the first seven even natural numbers is 8.
Question 9:
Find the mean of first five prime numbers.
Answer 9:
First five prime numbers are 2, 3, 5, 7 and 11.
Mean of the first five prime numbers =
=
Mean of the first five prime numbers is 5.6.
Question 10:
Find the mean of first six multiples of 5.
Answer 10:
First six multiples of 5 are 5, 10, 15, 20, 25 and 30.
Mean of the first six multiples of 5 =
Question 11:
The following table shows the weights (in kg) of 15 workers in a factory:
Weight (in kg) | 60 | 63 | 66 | 72 | 75 |
Number of workers | 4 | 5 | 3 | 1 | 2 |
Calculate the mean weight.
Answer 11:
Mean weight =
Question 12:
The daily wages (in rupees) of 60 workers in a factory are given below:
Daily wages (in Rs) | 140 | 150 | 160 | 180 | 190 |
Number of workers | 14 | 16 | 15 | 7 | 8 |
Find the mean daily wages.
Answer 12:
Mean daily wages =
Question 13:
The heights (in cm) of 90 plants in a garden are given below:
Height (in cm) | 58 | 60 | 62 | 64 | 66 | 74 |
Number of plants | 20 | 25 | 15 | 8 | 12 | 10 |
Find the mean height.
Answer 13:
Mean height =
Question 14:
The ages (in years) of 50 players of a school are given below:
Age (in years) | 14 | 15 | 16 | 17 | 18 |
Number of players | 15 | 14 | 10 | 8 | 3 |
Find the mean age.
Answer 14:
Mean age =
Question 15:
The heights (in cm ) of 40 boys were measured and recorded and under:
Height (in cm) | 165 | 170 | 175 | 180 |
Number of boys | 9 | 8 | 11 | 12 |
Find the mean height.
Answer 15:
Mean height =
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