RS Aggarwal 2019,2020 solution class 7 chapter 21 Collection and Organisation of Data(Mean, Median and Mode) Exercise 21A

Exercise 21A

Paper-263

Question 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 =$\frac{\mathrm{Sum} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{observations}}{\mathrm{Number} \mathrm{of} \mathrm{given} \mathrm{observations} }$

         =$\frac{1+2+3+4+5}{5}=\frac{15}{5}=3$
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 = $\frac{\mathrm{Sum} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{observations} }{\mathrm{Number} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{observations} }$

                                                = $\frac{1+3+5+7+9+11}{6}=\frac{36}{6}=6$

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 =$\frac{\mathrm{Sum} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{observations} }{\mathrm{Number} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{observations} }$

                                                              =$\frac{2+4+6+8+10+12+14}{7}=\frac{56}{7}=8$

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 =$\frac{\mathrm{Sum} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{observations} }{\mathrm{Number} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{observations} }$

                                                       =$\frac{2+3+5+7+11}{5}=\frac{28}{5}=5.6$
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 =$\frac{\mathrm{Sum} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{observations} }{\mathrm{Number} \mathrm{of} \mathrm{the} \mathrm{given} \mathrm{observations} }$

                                                   $\frac{5+10+15+20+25+30}{6}=\frac{105}{6}=17.5$

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 =$\frac{\Sigma (f_i\times x_i)}{\Sigma f_i}=\frac{975}{15}=65 \mathrm{kg}$

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 =$\frac{\Sigma (f_i\times x_i)}{\Sigma f_i}=\frac{9540}{60}=\mathrm{Rs} 159$

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 =$\frac{\Sigma (f_i\times x_i)}{\Sigma f_i}=\frac{5634}{90}=62.6 \mathrm{cm}$

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 =$\frac{\Sigma (f_i\times x_i)}{\Sigma f_i}=\frac{770}{50}=15.4 \mathrm{years}$

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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 =$\frac{\Sigma (f_i\times x_i)}{\Sigma f_i}=\frac{6930}{40}=173.25 \mathrm{cm}$