Explore NCERT Solutions

Q1:Give five examples of data that you can collect from your day-to-day life.

Solution: 

In our day to day life, we can collect the following data.

1. Number of females per 1000 males in various states of our country.

2. Weights of students of our class.

3. Production of wheat in the last 10 years in our country.

4. Number of plants in our locality.

5. Rainfall in our city in the last 10 years.

Q2: Classify the data in Q.1 above as primary or secondary data.

Solution:

The information which is collected by the investigator himself with a  definite objective in his mind is called as primary data whereas when the information is gathered from a source which already had the information stored, it is called as secondary data. It can be observed that the data in 1, 3, and 5 is secondary data and the data in 2 and 4 is primary data.

                                                        EX - 14.2

Q1 :  The blood groups of 30 students of Class VIII are recoded as follows:

A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O,

A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.

Represent this data in the form of a frequency distribution table. Which is the most common, and which is the rarest, blood group among these students?

Solution: 

It can be observed that 9 students have their blood group as A, 6 as B, 3 as AB, and 12 as O.

Therefore, the blood group of 30 students of the class can be represented as follows.

Blood Group	Numbers of student
A	9
B	6
O	12
AB	3
Total	30

it can be observed clearly that the most common blood group and the rarest blood group among these students is O and AB respectively as 12 (maximum number of students) have their blood group as O, and 3 (minimum number of students) have their blood group as AB.

 

Q2: The distance (in km) of 40 engineers from their residence to their place of work were found as follows:

5 3 10 20 25 11 13 7 12 31 19 10 12 17 18 11 32 17 16 2 7 9 7 8 3 5 12 15 18 3 12 14 2 9 6 15 15 7 6 12

Construct a grouped frequency distribution table with class size 5 for thedata given above taking the first interval as 0 - 5 (5 not included). What main feature do you observe from this tabular representation?

Solution:

It is given that a grouped frequency distribution table of class size 5 has to be constructed. Therefore, the class intervals will be 0 - 5, 5 - 10, 10 - 15, 15 - 20…

Q3:The relative humidity (in %) of a certain city for a month of 30 days was as follows:

98.1 98.6 99.2 90.3 86.5 95.3 92.9 96.3 94.2 95.1

89.2 92.3 97.1 93.5 92.7 95.1 97.2 93.3 95.2 97.3

96.2 92.1 84.9 90.2 95.7 98.3 97.3 96.1 92.1 89

(i) Construct a grouped frequency distribution table with classes 84 - 86, 86 - 88, etc.

(ii) Which month or season do you think this data is about?

(iii) What is the range of this data?

Solution: 

(i) A grouped frequency distribution table of class size 2 has to be constructed.The class intervals will be 84 - 86, 86 - 88, and 88 - 90…

 

Relative humidity (in %)	Number of days (frequency )
84 - 86	1
86 - 88	1
88 - 90	2
90 - 92	2
92 - 94	7
94 - 96	6
96 - 98	7
98 - 100	4
Total	30

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(ii) It can be observed that the relative humidity is high. Therefore, the data is about a month of rainy season.

(iii) Range of data = Maximum value - Minimum value

= 99.2 - 84.9 = 14.3

Q4:The heights of 50 students, measured to the nearest centimeters, have been found to be as follows:

161 150 154 165 168 161 154 162 150 151

162 164 171 165 158 154 156 172 160 170

153 159 161 170 162 165 166 168 165 164

154 152 153 156 158 162 160 161 173 166

161 159 162 167 168 159 158 153 154 159

(i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160 - 165, 165 - 170, etc.

(ii) What can you conclude bout their heights from the table?

Solution: 

(i) A grouped frequency distribution table has to be constructed taking class intervals 160 - 165, 165 - 170, etc. By observing the data given above, the required table can be constructed as follows.

Height (in cm)	Number of students (frequency )
150 - 155	12
155 - 160	9
160 - 165	14
165 - 170	10
170 - 175	5
Total	50

(ii) It can be concluded that more than 50% of the students are shorter than165 cm.

Q5: A study was conducted to find out the concentration of Sulphur dioxide in the air in parts per million (p pm) of a certain city. The data obtained for 30 days is as follows:

0.03 0.08 0.08 0.09 0.04 0.17 0.16 0.05 0.02 0.06 0.18 0.20 0.11 0.08 0.12 0.13 0.22 0.07 0.08 0.01 0.10 0.06 0.09 0.18 0.11 0.07 0.05 0.07 0.01 0.04

(i) Make a grouped frequency distribution table for this data with classintervals as 0.00 - 0.04, 0.04 - 0.08, and so on.

(ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?

Solution: 

Taking class intervals as 0.00, - 0.04, 0.04, - 0.08, and so on, a grouped frequency table can be constructed as follows.

Concentration of SO2 (in p pm)	Number of days (frequency )
0.00 - 0.04	4
0.04 - 0.08	9
0.08 - 0.12	9
0.12 - 0.16	2
0.16 - 0.20	4
0.20 - 0.24	2
Total	30

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The number of days for which the concentration of SO₂ is more than 0.11 is the number of days for which the concentration is in between

0.12 - 0.16, 0.16 - 0.20, 0.20 - 0.24.

Required number of days = 2 + 4 + 2 = 8

Therefore, for 8 days, the concentration of SO₂ is more than 0.11 ppm

Q6:  Three coins were tossed 30 times simultaneously. Each time the   number of heads occurring was noted down as follows:

0 1 2 2 1 2 3 1 3 0 1 3 1 1 2 2 0 1 2 1 3 0 0 1 1 2 3 2 2 0

Prepare a frequency distribution table for the data given above.

Solution: 

Frequncy distribution table as below: 

Number of heads	Number of times (frequency)
0	6
1	10
2	9
3	5
Total	30

 

 

 

 

 

 

 

 

 

 

Q7: The value of π up to50 decimal places is given below:

3.14159265358979323846264338327950288419716939937510

(i) Make a frequency distribution of the digits from 0 to 9 after the decimal point.

(ii) What are the most and the least frequently occurring digits?

Solution: 

 (i) By observation of the digits after decimal point, the required table can be

constructed as follows.

Digit	Frequency
0	2
1	5
2	5
3	8
4	4
5	5
6	4
7	4
8	5
9	8
Total	50

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(ii) It can be observed from the above table that the least frequency is 2 of digit 0, and the maximum frequency is 8 of digit 3 and 9. Therefore, the most frequently occurring digits are 3 and 9 and the least frequently occurring digit is 0.

 Q8: Thirty children were asked about the number of hours they watched TV Programs in the previous week. The results were found as follows:

1 6 2 3 5 12 5 8 4 8 10 3 4 12 2 8 15 1 17 6 3 2 8 5 9 6 8 7 14 12

(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 - 10.

(ii) How many children watched television for 15 or more hours a week?

Solution:  

(i) Our class intervals will be 0 - 5, 5 - 10, 10 - 15…..

The grouped frequency distribution table can be constructed as follows.

Hours	Number of children
0 - 5	10
5 - 10	13
10 - 15	5
15 - 20	2
Total	30

(ii) The number of children who watched TV for 15 or more hours a week is 2 (i.e., the number of children in class interval 15 - 20).

Q9: A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:

2.6 3.0 3.7 3.2 2.2 4.1 3.5 4.5 3.5 2.3 3.2 3.4 3.8 3.2 4.6 3.7 2.5 4.4 3.4 3.3 2.9 3.0 4.3 2.8 3.5 3.2 3.9 3.2 3.2 3.1 3.7 3.4 4.6 3.8 3.2 2.6 3.5 4.2 2.9 3.6

Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the intervals 2 - 2.5.

Solution: 

A grouped frequency table of class size 0.5 has to be constructed, starting from class interval 2 - 2.5.

Therefore, the class intervals will be 2 - 2.5, 2.5 - 3, 3 - 3.5…

By observing the data given above, the required grouped frequency distribution table can be constructed as follows.

Lives of batteries (in years)	Number of batteries
2 - 2.5	2
2.5 - 3.0	6
3.0 - 3.5	14
3.5 - 4.0	11
4.0 - 4.5	4
4.5 - 5.0	3
Total	40

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

EXERCISE 14.3

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Q1. A survey conducted by an organisation for the cause of illness and death among the women between the ages 15 - 44 (in years) worldwide, found the following figures (in %):

S.No.	Causes	Female fatality rate (%)
1.  2.  3.  4.  5.  6.	Reproductive health conditions  Neuropsychiatric conditions  Injuries  Cardiovascular conditions  Respiratory conditions  Other causes	31.8  25.4   12.4   4.3   4.1   22.0

(i) Represent the information given above graphically.
(ii) Which condition is the major cause of women’s ill health and death worldwide?
(iii) Try to find out, with the help of your teacher, any two factors which play a major role in the cause in (ii) above being the major cause.

Solution: 

(i) These data can be represented graphically using bar-graph. By representing cause on x-axis family fatality rate on y-axis. 

 

Q2. The following data on the number of girls (to the nearest ten) per thousand boys in different sections of Indian society is given below

Section	Number of girls per thousand boys
Scheduled Caste (SC)  Scheduled Tribe (ST)  Non SC/ST  Backward districts  Non-backward districts  Rural  Urban	940  970  920  950  920  930  910

(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusions can be arrived at from the graph.

 

Important-Questions

 

Q1.  Find the value of x if median of Data is 49.

        32, 42, 45, x, x + 2, 53, 54, 56

Q2.  Find the mode of the following data:
        5, 7, 6, 5, 9, 8, 6, 7, 11, 10, 5, 7, 6, 8, 6, 9, 10.

Q3.  If the arithmetic mean of 25, 30, 32, x, 43 is 34, then find the value of x.

Q4. The points scored by a basket-ball team in a series of matches are as follows:
       17, 2, 7, 27, 25, 5, 14, 18 , 10, 24, 10, 8, 7, 10
        Find mean, median and mode for the data.

Q5. Find  the Mode of following data;

2, 3, 4, 5, 0, 1, 3, 3, 4, 3 

Q6. The followings data are written in ascending orders. If the median of data is 14.5then find the value of x.

      11, 12, 13, 7x, 7x + 1, 16, 16, 18, 20

Q7.  Find the median of 34, 32, x, x-1, 19, 15, 11 where x is the mean of data
10, 20, 30, 40, 50.

Q8.  If the mean of 10, 12, 18, 11, p and 19 is 15 then find the value of p and
also find the median.

        

      

Q10. What is the range for the given data 
         31, 32.5, 20.3, 27.9, 28, 19.7, 31.7.

Q11. Find the mode for the data given below 
         14, 25, 14, 28, 18, 17, 14, 23, 22, 14, 18.

Q12. If the mean of 6, 8, 5, 7, x and 4 is 7 then find the value of x.

Q13.  Find the mean for 
          4, 3, 7, 0, 0, 6, 8.

Q14.  Find the mode for the following :-
          7, 9, 12, 13, 7, 12, 15, 7, 12, 7, 25, 18, 7.

Q15.  If means of 1 x , 2 x is 6 and mean of 1 x , 2 x and 3 x is 7 then find 3 x .

Q16.  If 3 is the mean for x, 3, 4, 5 then find the value of x.

Q17.  What is the range of 40, 42, 80, 69, 56, 47?

Q18.  The class marks are given below 
          47, 52, 57, 62, 67, 72, 77, 82
          What is the class size?

Q19.  Find the median :-
          36, 39, 42, 48, 52, 68, 69, 71, 72, 78.

Q20.  One student has scored the marks in five subject as below
          70, 64, 56, 54, 51.
          find the mean.