14. Statistics
NCERT
14. Statistics
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Important Note :
1. When the information was collected by the investigator herself or himself with a definite objective in her or his mind, the data obtained is called primary data.
2. When the information was gathered from a source which already had the information stored, the data obtained is called secondary data.
3. The difference of the highest and the lowest values in the data is called the range of the data.
i.e., the range 
highest values – lowest values .
4. Class size (class width) Upper class limit – Lower class limit .
5. Class mark 
6. Mean 
7. The median is that value of the given number of observations, which divides it into exactly two parts.
(i) When the number of observations (
) is odd, then the median 
observation.
(ii) When the number of observations (
) is even, then the median 
observations.
9. Mode : The mode is the most frequently occurring observation.
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EXERCISE 14.1
1. Give five example of data that you can collect from your day-to-day life .
2. Classify the data in Q.1 above as primary or secondary data .
EXERCISE 14.2
1. The blood groups of 30 students of Class VIII are recorded 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?
2. 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 the data given above taking the first interval as 0-5 (5 not included). What main features do you observe from this tabular representation?
3. 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?
4. The heights of 50 students, measured to the nearest centimetres, 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 about their heights from the table?
5. A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) 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 class intervals 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?
6. 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.
7. The value of π upto 50 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?
8. Thirty children were asked about the number of hours they watched TV programmes 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?
9. 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 interval 2 - 2.5.
EXERCISE 14.3
1. 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.
2. 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.
3. Given below are the seats won by different political parties in the polling outcome of a state assembly elections:
|
Political Party |
A |
B |
C |
D |
E |
F |
|
Seats Won |
75 |
55 |
37 |
29 |
10 |
37 |
(i) Draw a bar graph to represent the polling results.
(ii) Which political party won the maximum number of seats?
4. The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:
|
Length (in mm) |
Number of leaves |
|
118 – 126 127 – 135 136 – 144 145 – 153 154 – 162 163 – 171 172 – 180 |
3 5 9 12 5 4 2 |
(i) Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]
(ii) Is there any other suitable graphical representation for the same data?
(iii) Is it correct to conclude that the maximum number of leaves are 153 mm long ? Why?
5. The following table gives the life times of 400 neon lamps:
|
Life time (in hours) |
Number of lamps |
|
300 – 400 400 – 500 500 – 600 600 – 700 700 – 800 800 – 900 900 – 1000 |
14 56 60 86 74 62 48 |
(i) Represent the given information with the help of a histogram.
(ii) How many lamps have a life time of more than 700 hours?
6. The following table gives the distribution of students of two sections according to the marks obtained by them:
|
Section A |
Section B |
||
|
Marks |
Frequency |
Marks |
Frequency |
|
0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 |
3 9 17 12 9 |
0 – 10 10 – 20 20 – 30 30 – 40 40 – 50 |
5 19 15 10 1 |
Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.
7. The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:
|
Number of balls |
Team A |
Team B |
|
1 – 6 7 – 12 13 – 18 19 – 24 25 – 30 31 – 36 37 – 42 43 – 48 49 – 54 55 – 60 |
2 1 8 9 4 5 6 10 6 2 |
5 6 2 10 5 6 3 4 8 10 |
Represent the data of both the teams on the same graph by frequency polygons. [Hint : First make the class intervals continuous.]
8. A random survey of the number of children of various age groups playing in a park was found as follows:
|
Age (in years) |
Number of children |
|
1 – 2 2 – 3 3 – 5 5 – 7 7 – 10 10 – 15 15 – 17 |
5 3 6 12 9 10 4 |
Draw a histogram to represent the data above.
9. 100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
|
Number of letters |
Number of surnames |
|
1 – 4 4 – 6 6 – 8 8 – 12 12 – 20 |
6 30 44 16 4 |
(i) Draw a histogram to depict the given information.
(ii) Write the class interval in which the maximum number of surnames lie.
EXERCISE 14.4
1. The following number of goals were scored by a team in a series of 10 matches:
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Find the mean, median and mode of these scores.
2. In a mathematics test given to 15 students, the following marks (out of 100) are recorded: 41 , 39 , 48 , 52 , 46 , 62 , 54 , 40 , 96 , 52 , 98 , 40 , 42 , 52 , 60
Find the mean, median and mode of this data.
3. The following observations have been arranged in ascending order. If the median of the data is 63, find the value of 
.
29 , 32 , 48 , 50 , , 
, 72 , 78 , 84 , 95
4. Find the mode of 14 , 25 , 14 , 28 , 18 , 17 , 18 , 14 , 23 , 22 , 14 , 18.
5. Find the mean salary of 60 workers of a factory from the following table:
|
Salary (in Rs) |
Number of workers |
|
3000 4000 5000 6000 7000 8000 9000 10000 |
16 12 10 8 6 4 3 1 |
|
Total 60 |
|
6. Give one example of a situation in which
(i) the mean is an appropriate measure of central tendency.
(ii) the mean is not an appropriate measure of central tendency but the median is an appropriate measure of central tendency.
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