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Page No 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:

(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.

Page No 263:

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:

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

Page No 263:

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:

Daily wages in the ascending order:

130, 130, 150, 150, 150, 150, 180, 180, 180, 180, 180, 180, 200, 200, 200

Frequency table:

Page No 263:

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:

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:

Page No 263:

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:

(i) numerical
(ii) original
(iii) array
(iv) frequency
(v) tabulation

Page No 263:

Question 6:

Find the mean of first five natural numbers.

Answer:

First five natural numbers are 1, 2, 3, 4 and 5.

Mean of the first five natural numbers =Sum of the given observationsNumber of given observations 

         =1+2+3+4+55=155=3
Hence, mean of the first five natural numbers is 3.

Page No 263:

Question 7:

Find the mean of first six odd natural numbers.

Answer:

First six odd natural numbers are 1, 3, 5, 7, 9 and 11.

Mean of the first six natural numbers = Sum of the given observations Number of the given observations 

                                                = 1+3+5+7+9+116=366=6

Mean of the first six odd natural numbers is 6.

Page No 263:

Question 8:

Find the mean of first seven even natural numbers.

Answer:

First seven even natural numbers are 2, 4, 6, 8, 10, 12 and 14.

Mean of the first seven even natural numbers =Sum of the given observations Number of the given observations 

                                                              =2+4+6+8+10+12+147=567=8

Mean of the first seven even natural numbers is 8.

Page No 263:

Question 9:

Find the mean of first five prime numbers.

Answer:

First five prime numbers are 2, 3, 5, 7 and 11.

Mean of the first five prime numbers =Sum of the given observations Number of the given observations 

                                                       =2+3+5+7+115=285=5.6
Mean of the first five prime numbers is 5.6.

Page No 263:

Question 10:

Find the mean of first six multiples of 5.

Answer:

First six multiples of 5 are 5, 10, 15, 20, 25 and 30.

Mean of the first six multiples of 5 =Sum of the given observations Number of the given observations 

                                                   5+10+15+20+25+306=1056=17.5

Page No 263:

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:


Mean weight =Σ(fi×xi)Σfi=97515=65 kg

Page No 263:

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:


Mean daily wages =Σ(fi×xi)Σfi=954060=Rs 159

Page No 263:

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:


Mean height =Σ(fi×xi)Σfi=563490=62.6 cm

Page No 263:

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:


Mean age =Σ(fi×xi)Σfi=77050=15.4 years



Page No 264:

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:


Mean height =Σ(fi×xi)Σfi=693040=173.25 cm



Page No 266:

Question 1:

Find the median of:

(i) 3, 11, 7, 2, 5, 9, 9, 2, 10
(ii) 9,25, 18, 15, 6, 16, 8, 22, 21
(iii) 21, 15, 6, 25, 18, 13, 20, 9, 16, 8, 22

Answer:

We have to find the median of the following data.

(i)  3, 11, 7, 2, 5, 9, 9, 2 and 10

Arranging them in ascending order:

 2, 2, 3, 5, 7, 9, 9, 10, 11

Number of terms, N= 9
It is an odd number.

Median =N+12th observation

Median=9+12th observation

Median = 5th observation

Median=7

(ii) 9, 25, 18, 15, 6, 16, 8, 22, 21

Arranging them in ascending order,

6, 8, 9, 15, 16, 18, 21, 22, 25

Number of terms, N=9
It is an odd number.

Median =N+12th observation

Median =9+12th observation
Median = 5th observation

Median=16

(iii) 21, 15, 6, 25, 18, 13, 20, 9, 16, 8, 22

Arranging them in ascending order:

6, 8, 9, 13, 15, 16, 18, 20, 21, 22, 25

Number of terms, N = 11
It is an odd number.

Median =N+12th observation

Median =11+12th observation

Median = 6th observation

Median=16

Page No 266:

Question 2:

Find the median of:

(i) 10, 32, 17, 19, 21, 22, 9, 35
(ii) 55, 60, 35, 51, 29, 63, 72, 91, 85, 82

Answer:

We have to find the median of the following data.

(i) 10, 32, 17, 19, 21, 22, 9, 35

Arranging them in ascending  order:

9, 10, 17, 19, 21, 22, 32, 35

Number of terms, N = 8

 Median =12N2th observation+N2+1th observation

Median =124th observation+5th observation

Median =1219+21=20

∴ Median= 20

(ii) 55, 60, 35, 51, 29, 63, 72, 91, 85, 82

Arranging them in ascending order:

29, 35, 51, 55, 60, 63, 72, 82, 85, 91

Number of terms, N =10

Median =12N2th observation+N2+1th observation

Median = 125th observation +6th observationMedian =1260+63 Median=61.5

Page No 266:

Question 3:

Find the median of first 15 odd numbers.

Answer:

First 15 odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27 and 29.

Number of terms, N = 15
It is an odd number.

Median =N+12th observation

Median =15+12th observationMedian =15

Page No 266:

Question 4:

Find the median of first 10 even numbers.

Answer:

First 10 even numbers are 2, 4, 6, 8, 10, 12, 14, 16, 18 and 20.

Number of terms, N=10

Median =12N2th observation+N2+1th observation

Median =125th observation+6th observationMedian =1210+12=11

Page No 266:

Question 5:

Find the median of first 50 whole numbers.

Answer:

First 50 whole numbers are 0, 1, 2, 3, 4 ... and 49.

Number of terms, N= 50
It is an even number.

Median =12N2th observation+N2+1th observation              =1225th observation +26th observation              =1224+25              = 24.5

Page No 266:

Question 6:

The marks of 15 students (out of 50) in an examination are
20, 22, 26, 31, 40, 19, 17, 19, 25, 29, 23, 17, 24, 21, 35

Find the median marks.

Answer:

Marks of the students (out of 50) in an examination are given below:

20, 22, 26, 31, 40, 19, 17, 19, 25, 29, 23, 17, 24, 21, 35

Arranging the marks in ascending order:

17, 17, 19, 19, 20, 21, 22, 23, 24, 25, 26, 29, 31, 35, 40

Number of terms, N=15
This is an odd number.

Median = N+12th observationMedian=15+12th observationMedian =8th observationMedian = 23

Hence, the median marks are 23.

Page No 266:

Question 7:

The ages (in years) of 10 teachers in a school are
34, 37, 53, 46, 52, 43, 31, 36, 40, 50.

Find the median age.

Answer:

Ages (in years) of 10 teachers in a school are given below:

34, 37, 53, 46, 52, 43, 31, 36, 40, 50

Arranging them in ascending order:

31, 34, 36, 37, 40, 43, 46, 50, 52, 53

Number of terms, N=10
It is an even number.

Median=12N2th observation+N2+1th observationMedian =125th observation +6th observationMedian =1240+43Median =41.5

Hence, the median age is 41.5 years.



Page No 267:

Question 8:

Find the median weight for the following data:
 

Weight (in kg) 45 46 48 50 52 54 55
Number of boys 8 5 6 9 7 4 2

Answer:

Cumulative frequency table:

 

Number of terms, N = 41
It is an odd number.

Median =N+12th observation               =41+12th observation               =21th observation               =50  kg         

Hence, the median weight is 50 kg.

Page No 267:

Question 9:

Calculate the median for the following data:
 

Marks 17 20 22 15 30 25
Number of students 5 9 4 3 10 6

Answer:

Arranging the terms in ascending order, we have:



Cumulative frequency table:


Number of terms, N = 37

Median = N+12th observation               =37+12th observation               =19th observation               =22

Hence, the median is 22.

Page No 267:

Question 10:

The heights (in cm) of 50 students of a class are given below:
 

Height (in cm) 156 154 155 151 157 152 153
Number of students 8 4 10 6 7 3 12

Find the median height.

Answer:

Arranging the terms in ascending order:



Cumulative frequency table:



Number of terms, N = 50

Median =12N2th observation+N2+1th observation               =1225th observation+26th observation               =12154+155

Median =154.5



Page No 269:

Question 1:

Find the mode of the data:

(i) 10, 8, 4, 7, 8, 11, 15, 8, 6, 8
(ii) 27, 23, 39, 18, 27, 21, 27, 27, 40, 36, 27

Answer:

We have to find the mode of the given data.

Mode - It is that value of the variables that occurs most frequently.

(i) 10, 8, 4, 7, 8, 11, 15, 8, 6, 8

Here, 8 occurs most frequently. Hence, the mode of the data is 8.

(ii) 27, 23, 39, 18, 27, 21, 27, 27, 40, 36, 27

Here, 27 occurs most frequently. Hence, the mode of the data is 27.

Page No 269:

Question 2:

The ages (in years) of 11 cricket players are given below:
28, 34, 32, 41, 36, 32, 32, 38, 32, 40, 31.

Find the mode of the ages.

Answer:

Following are the ages (in years) of 11 cricket players:

28, 34, 32, 41, 36, 32, 32, 38, 32, 40, 31

Mode is the value of the variable that occurs most frequently.

Here, 32 occurs maximum number of times.

Hence, 32 is the mode of the ages.

Page No 269:

Question 3:

Daily wages of 45 workers in a factory are given below:
 

Daily wages (in Rs) 100 125 150 175 200
Number of workers 6 8 9 12 10

Find the median and the mean.
Using empirical formula, calculate its mode.

Answer:


Here, N is 45, which is odd.Median =N+12th observation               =45+12observation               =23 th observationMedian =150Mean =(fi×xi)fi=705045=156.67Mode=3(Median)-2(Mean)          =3150-2(156.67)          =450-313.34          =136.6

Hence, the median is 150, the mean is 156.67 and the mode is 136.6.

Page No 269:

Question 4:

The following table shows the marks obtained by 41 students of a class.

Marks obtained 15 17 20 22 25 30
Number of students 2 5 10 12 8 4

Find the median and mean marks.
Using empirical formula, calculate its mode.

Answer:


Number of terms (N) is 41, which is odd.Median =N+12th observation              =21th observation              =22Median =22Mean =(fi×xi)fi            =89941Mean =21.92Using empirical formula:Mode = 3(Median)-2(Mean)            = 66-43.84Mode=22.16

Hence, the median is 22, the mean is 21.92 and the mode is 22.16.

Page No 269:

Question 5:

The following table shows the weight of 12 players:
 

Weight (in kg) 48 50 52 54 58
Number of players 4 3 2 2 1

Find the median and mean weights.
Using empirical formula, calculate its mode.

Answer:

We will prepare the table given below:



Number of terms (N) is 12, which is an even number.Median =12N2th observation+N2+1th observation               =6th observation+7th observation               =1250+50Median  =50Mean =(fi×xi)fi            =61212Mean = 51Using empirical formula:Mode = 3(Median)-2(Mean)            = 150-102Mode=48 

Hence, the median is 50, the mean is 51 and the mode is 48.



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