NCERT Solutions Class 9 Maths Chapter 14- Statistics

Exercise 14.1

Question 1.

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

Solution

Here are five real-life examples:

• Our class has a certain number of students.
• Our school has a large number of fans.
• Our household’s electricity bills for the past two years.
• The results of the election were received through television or newspapers.
• Figures from the Educational Survey on literacy rates

Question 2.

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

Solution:

Primary data is gained when the material was gathered by the investigator herself or himself with a specific goal in mind.

I, (ii), and (iii) primary data

Secondary data is gained when information is gathered from a source that already has the information stored.

(IV) and secondary data (v)

Exercise 14.2

Question 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?

Solution:

Frequency is the number of students having the same blood group. The frequency is represented in the table or the frequency distribution table:

The most common Blood Group is the blood group with highest frequency: O

The rarest Blood Group is the blood group with lowest frequency: AB

Question 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?

Solution:

Since the given data is very large, we construct a grouped frequency distribution table of class size 5. ∴, class interval will be 0-5, 5-10, 10-15, 15-20 and so on. The data is represented in the grouped frequency distribution table as:

The classes in the table do not overlap. We also discovered that 36 of the 40 engineers’ homes are less than 20 kilometers apart.

Question 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?

Solution:

(i) Due to the high amount of data, we create a grouped frequency distribution table with a class size of 2. 84-86, 86-88, 88-90, 90-92, and so on will be the class intervals. In the grouped frequency distribution table, the data is displayed as follows:
Relative humidity(in percentage)

(ii) The humidity in the data is really high. So because humidity is higher during the rainy season, the data must be from that time period.

(iii) A data’s range is defined as the difference between the data’s highest and minimum values.
= 99.2−84.9
= 14.3

Question 4.

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 about their heights from the table?

Solution:

(i) A grouped frequency distribution table can be used to depict the data in the question, using class intervals of 160 – 165, 165 – 170, and so on, as follows:

(ii) Based on the information provided in the table, 35 students, or more than half of the total, are under the height of 165 cm.

Question 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?

Solution:

(i) Below is a grouped frequency distribution table for the data in the question, with class intervals ranging from 0.00 to 0.04, 0.04 to 0.08, and so on.

(ii) The number of days in which the concentration of Sulphur dioxide was more than 0.11 parts per million = 2+4+ 2 = 8

Question 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.

Solution:

The frequency distribution table for the data given in the question is given below:

Question 7.

The value of π up to 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?

Solution:

(i) The frequency distribution of the digits from 0 to 9 after the decimal point is given in the table below:

(ii) The digit with the lowest frequency appears the fewest times. The least commonly occurring digit is 0. It occurs only twice and has a frequency of 2. The digit with the highest frequency appears the most frequently. The most often occurring digits are 3 and 9. They occur eight times and have a frequency of 8.

Question 8.

Thirty children were asked about the number of hours they watched TV programmers 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?

Solutions:

(i) The grouped frequency distribution table for the data given in the question, taking class width 5 and one of the class intervals as 5-10 is given below:

(ii) We can deduce from the table that two children watched television for 15 hours or more every week.

Question 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

Solution:

The grouped frequency distribution table for the data given in the table, using class intervals of size 0.5 starting from the interval 2 – 2.5, is given below.

Exercise 14.3

Question 1.
A survey conducted by an organization for the cause of illness and death among the women between the ages 15 – 44 (in years) worldwide, found the following figures (in %):

(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) The information given in the question is represented below graphically.

(ii) The graph shows that reproductive health issues are the leading cause of women’s illness and mortality worldwide.

(iii) There are two variables that contribute to the causation of (ii):
Insufficient attention and understanding.
Medical services are scarce.

Question 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.

(i) Represent the information above by a bar graph.

(ii) In the classroom discuss what conclusions can be arrived at from the graph.

Solution:

(i) The information given in the question is represented below graphically.

(ii) We can deduce from the graph above that the region ST has the highest number of girls per thousand guys. We may also see that girls per thousand boys are higher in backward districts and rural areas than in non-backward districts and metropolitan areas.

Question 3.

Given below are the seats won by different political parties in the polling outcome of a state assembly elections

(i) Draw a bar graph to represent the polling results.

(ii) Which political party won the maximum number of seats?

Solution:

(i) The bar graph representing the polling results is given below:

(ii) From the bar graph it is clear that Party A won the maximum number of seats.

Question 4.

The length of 40 leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table:

(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?

Solution:

(i) The data in the question is presented as a discrete class interval. As a result, we must create it in a continuous class interval. Because the difference is 1, we deduct 1/2 = 0.5 from the lower limit and add 0.5 to the upper limit. The table then becomes:

(ii) Frequency polygons can be used to depict the data in the question.

(iii) No, we cannot deduce that the maximum number of leaves is 153 mm long because the greatest number of leaves is between 144.5 and 153.5 mm long.

Question 5.

The following table gives the life times of 400 neon lamps:

(i) Represent the given information with the help of a histogram.

(ii) How many lamps have a life time of more than 700 hours?

Solution:

(i) The histogram representation of the given data is given below.

(II) How many lamps have a life time of more than 700 hours?

The number of lamps having a life time of more than 700 hours = 74+62+48 = 184.

Question 6.

The following table gives the distribution of students of two sections according to the marks obtained by them:

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.

Solution:

For Section A

For Section B

Now, representing these data on a graph using two frequency Polygon we get,

From the graph, we can conclude that the students of Section A performed better than Section B.

Question 7.

The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:

Represent the data of both the teams on the same graph by frequency polygons. [Hint: First make the class intervals continuous.]

Solution:

The data in the question is shown as a discontinuous class interval. As a result, we must construct it in a continuous class interval. We deduct 1/2 = 0.5 = 0.5 from the lower limit and add 0.5 to the upper limit because the difference equals 1. The following is the table:

The data of both the teams are represented on the graph below by frequency polygons.

Question 8.

A random survey of the number of children of various age groups playing in a park was found as follows:

Draw a histogram to represent the data above.

Solution:

The width of the class intervals in the given data is varying.

We know that,

The area of rectangle is proportional to the frequencies in the histogram.

Thus, the proportion of the children per year can be calculated as given in the table below.

Let x-axis = the age of children

Y-axis = proportion of children per 1 year interval

Question 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:

(i) Draw a histogram to depict the given information.

(ii) Write the class interval in which the maximum number of surnames lie.

Solution:

(i) In the given data, the width of the class intervals varies. We’re aware of this.

The area of the rectangle is proportional to the histogram’s frequencies.

As a result, the proportion of surnames per two-letter interval can be computed, as shown in the table below.

(ii) Here, 6-8 is the class interval in which the maximum number of surnames lie.

Exercise 14.4

Question 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.

Solution:

Median,

To find the median, we first arrange the data in ascending order.

0, 1, 2, 3, 3, 3, 3, 4, 4, 5

Here,

Number of observations (n) = 10

Since the number of observations are even, the median can be calculated as:

Mode,

To find the mode, we first arrange the data in ascending order.

0, 1, 2, 3, 3, 3, 3, 4, 4, 5.

Here,

We find that 3 occurs most frequently (4 times)

∴ Mode = 3

Question 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.

Solution:

Median,

To find the median, we first arrange the data in ascending order.

39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

Here,

Number of observations (n) = 15

Since the number of observations are odd, the median can be calculated as:

Mode,

To find the mode, we first arrange the data in ascending order.

39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

Here,

We find that 52 occurs most frequently (3 times)

∴ Mode = 52

Question 3.

The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.

29, 32, 48, 50, x, x+2, 72, 78, 84, 95

Solution:

Number of observations (n) = 10

Given that Median = 63

Since the number of observations are even, the median can be calculated as:

Question 4.

Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.

Solution:

Mode,

To find the mode, we first arrange the given data in ascending order.

14,14,14,14,17,18,18,18,22,23,25,28

Here,

Here we find that 14 occurs most frequently (4 times)

∴ Mode = 14

Question 5.

Find the mean salary of 60 workers of a factory from the following table:

Solution:

Hence, the mean salary is 5083.33 Rupees.

Question 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.

Solution:

Mean marks obtained in the examination
Runs scored by Mahendra Singh Dhoni in 7 matches are,
39, 51, 56, 102, 83, 48, 91
Here,
Mean\ =\frac{39+51+56+102+83+48+91}{7} =\frac{470}{7} =\ 67.1.
Median,
Arranging in ascending order we get 39, 48 51, 56, 83, 91, 102
n = 7
Median\ =\ \left[\frac{n+1}{2}\right]^{th}observation =\ \left(\frac{7+1}{2}\right)^{th}\ observation =\ \left(\frac{8}{2}\right)^{th}\ observation =\ 4^{th}\ observation =\ 56