Gujarat Board Textbook Solutions Class 9 Maths Chapter 14 Statistics

 Gujarat Board Textbook Solutions Class 9 Maths Chapter 14 Statistics

GSEB Solutions Class 9 Maths Chapter 14 Statistics

Ex 14.1

Question 1.
Give five examples of data that you can collect from your day-to-day life.
Solution:

1. A number of students in our class.
2. A number of fans in our school.
3. Electricity bills of our house for the last two years.
4. Election results obtained from television or newspaper.
5. Literary rate figure obtained from the educational survey.

Question 2.
Classify the data in Q. 1 above as primary or secondary data
Solution:
(i), (ii) and (iii) are primary data, (iv) and (v) are secondary data.

Primary data:
When the information is collected by the investigator herself or himself with a definite
objective is called primary data. These types of data are original and collected for the first time.

Secondary data:
When the information is gathered from a source (like newspaper, TV, or some records) that already had the information stored, the data is called secondary data. Such data has been collected by someone else.

Ex 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? [NCERT Exemplar]
Solution:

O is the most common and AB is the rarest blood group among these students.

Question 2.
The distance (in km) of 40 engineers from their residence to their place of work was found as follows:

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:

We observe the following features from this tabular representation:

1. The distance (in km) from their residence to their work of the maximum number of engineers are less than 20 km.
2. Very few engineers have their residence 20 km or far away from their workplace.

Question 3.
The relative humidity (in %) of a certain city for a month of 30 days was as follows:

(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?
(ii) What is the range of this data?
Solution:

(ii) This data appears to be taken in the rainy reason as the relative humidity is high.
(iii) Range = Highest value – Lowest value.
= 99.2 – 84.9 = 14.3 (in %).

Question 4.
The heights of 50 students, measured to the nearest centimetres, have been found to be as follows:

(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:

(ii) The heights of the maximum number of students are in the group 160-165 and the heights of the minimum number of students are in the group 170-175. More than 50% of students are shorter than 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:

(i) Make a grouped frequency distribution table for this data with class intervals as 0.00-0.04, 0.04-0.08, as so on.
(ii) For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million?
Solution:
(i)

(ii) The concentration of sulphur dioxide was more than 0.11 parts per million for 2 + 4 + 2 = 8 days.

Question 6.
Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows:

Prepare a frequency distribution table for the data given above.
Solution:

Question 7.
The value of it up to 50 decimal places is given below:
3.1415926535897932384626433832795028841 9716939937510.
(i) Make a frequency distribution of the digits from O to 9 after the decimal point.
(ii) What are the most and the least frequency occurring digits?
Solution:
(i)

(ii) The most frequently occurring digits are 3 and 9. The least frequently occurring digit is O.

Question 8
Thirty children were asked about the number of hours they watched TV programmes in the previous week. The result was found as follows:

(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)

(ii) Children watched television for 15 or more hours a week.

Question 9.
A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows:

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

Ex 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 %).

Represent the information given above graphically.
Which condition is the major cause of women’s ill health and death worldwide?
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)

(ii) Reproductive health conditions is the major cause of women’s health and death worldwide.
(iii) Lack of proper diet, lack of advised exercises.

Question 2.
The following data on the number of girls (to the nearest ten) per thousand boys in different sections of the Indian society is given below:

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

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

(ii) The two conclusions we can arrive at from the graph are as follows:
(a) The number of girls to the nearest ten per thousand boys is maximum in the scheduled tribe section of the society and minimum in the urban section of the society.
(b) The number of girls to the nearest ten per thousand boys is the same for ‘Non-SC/ST’ and ‘Non-backward districts’ sections of the society.

Question 3.
Given below are the seats won by different political parties in the polling outcome of 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)

(ii) Political party A won the maximum number of seats

Question 4.
The length of 40 leaves of a plant is measured correct to one millimeter, and the obtained data is represented in the following table:

(i) Draw a histogram to represent the given data correct to one millimeter, and the obtained data is in the following represented table:
(ii) Is there any other suitable graphical representation for the same data?
(iii) Is it correct to conclude that the maximum number of leaves is 153 mm long? Why?
Solution:
(i) Modified continuous distribution is as follows

(ii) Frequency polygon.
(iii) No, because the maximum number of leaves have their lengths lying in the interval 145-153. ‘

Question 5.
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:
Modified tables:
For Section A:

For Section B:


From the graph, it can be observed that students. The performance of section A is better than section B in terms of good marks.

Question 6.
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 interval continuous).
Solution:
Modified table:

Question 7.
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:
Modified table
(Minimum class size = 1)

Question 8.
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 lies.
Solution:
(i) Modified table:
(Minimum class size = 2)


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

Ex 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:

3. Mode:
Arranging the given data in ascending order, we have
0,1,2,3,3,3,3,4,4, 5.
Here, 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:
1. Mean:

2. Median:
Arranging the given data in ascendin order, we have
39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98.
Number of observations (n) = 15, which is odd.

3. Mode:
Arranging the given data in descending or der, we have
98, 96, 62, 60, 54, 52, 52, 52, 48, 46, 42, 41, 40, 40, 39.
Here, 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, which is even.
∴ Median

According to the questions,
x + 1 = 63 ⇒ x = 63 – 1 ⇒ x = 62
Hence, the value of x is 62.

Question 4
Find the mode of 14, 25, 14, 28, 18, 17, 18, 14, 23, 22, 14, 18.
Solution:
Arranging the given data in ascending order, we have
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28
Here 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.

Question 6.
Give one example of a situation in which:

1. the mean is an appropriate measure of central tendency.
2. the mean is hot an appropriate measure of central tendency but the median is an appropriate measure of central tendency.

Solution:

1. mean marks in a test in mathematics.
2. average beauty.