NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.1 - Statistics

Q1 (i) 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 $^{o}/_{o}$ ):

Represent the information given above graphically

Answer:

The graphical representation of the given data is as follows:

Q1 (ii) 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 $^{o}/_{o}$ ) :

Which condition is the major cause of women’s ill health and death worldwide?

Answer:

Records from the graph demonstrate that reproductive health conditions represent the biggest factor which leads to worldwide women's deaths and illnesses. Reproductive health conditions cause fatality in 31.8% of women throughout the world.

Q1 (iii) 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 $^{o}/_{o}$ ):

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

Answer:

Women experience major illnesses and deaths throughout the globe because of inadequate healthcare coverage, coupled with their economically struggling situations.

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

Represent the information above by a bar graph.

Answer:

The graphical representation of the given information is as follows:

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

In the classroom discuss what conclusions can be arrived at from the graph

Answer:

The graph reveals that urban society has the fewest number of girls per thousand boys, yet the Scheduled Tribes have the most girls per thousand boys: 910 in the case of urban society and 970 in that of the Scheduled Tribes.

Q3 (i) Given below are the seats won by different political parties in the polling outcome of a state assembly elections:

Draw a bar graph to represent the polling results.

Answer:

The representation of the given data in the form of a bar graph is as follows:

Q3 (ii) Given below are the seats won by different political parties in the polling outcome of state assembly elections:

Which political party won the maximum number of seats?

Answer:

From the data, we can clearly see that Party A has a maximum number of seats, that is 75.

Q4 (i) The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:

Draw a histogram to represent the given data. [Hint: First make the class intervals continuous]

Answer:

Both upper and lower class limits must be modified by dividing their difference by 2 since the data has a 1-unit difference between its values( e.g 127 - 135 would become 126.5 - 235.5)
Therefore, the modified table is as follows:

The representation of the above data through a histogram is as follows:

Q4 (ii) The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:

Is there any other suitable graphical representation for the same data?

Answer:

Yes, the same data would be appropriately displayed by a frequency polygon.

Q4 (iii) The length of 40 leaves of a plant are measured correct to one millimetre, and the obtained data is represented in the following table:

Is it correct to conclude that the maximum number of leaves are 153 mm long? Why?

Answer:

No, as the information provided does not establish 153 mm as the precise length for the maximum number of leaves. The data provides information only about the possible length range for the leaves. The available evidence supports the conclusion that 12 leaves have measurements contained within 145-153.

Q5 (i) The following table gives the life times of 400 neon lamps:

Represent the given information with the help of a histogram.

Answer:

The representation of the given information in the form of a histogram is as follows:

Q5 (ii) The following table gives the life times of 400 neon lamps:

How many lamps have a lifetime of more than 700 hours?

Answer:

Lamps having lifetime in the range 700 - 800 = 74

Lamps having lifetime in the range 800 - 900 = 62

Lamps having lifetime in the range 900 - 1000 = 48

Lamps having a lifetime of more than 700 hours = 74 + 62 + 48 = 184.

Q6 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

Answer:

To make the frequency polygon, we first modify the table by using the following formula:

$\\Class\ marks= \frac{Upper\ limit\ of\ class\ interval+Lower\ limit\ of\ class\ interval}{2}$

The frequency polygon requires markings which depict marks on the x-axis and student frequencies on the y-axis. A frequency polygon represents the given information in this manner:

From the frequency polygon, we can see that the performance of section A is better.

Q7 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.]

Answer:

To make the frequency polygon, we first modify the table by using the following formula:

$\\Class\ marks= \frac{Upper\ limit\ of\ class\ interval+Lower\ limit\ of\ class\ interval}{2}$

The frequency polygon requires markings which depict a number of balls on the x-axis and runs scored on the y-axis. A frequency polygon represents the given information in this manner:

Q8 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.

Answer:

The calculation of weighted frequencies must be performed for each rectangle because different class sizes were used to construct the histogram.

$\\Weighted\ frequency=\frac{Minimum\ class\ size}{Class\ size\ of\ the\ interval}\times Frequency$

$Length\ of\ the\ rectangle=\frac{Minimum\ width}{Width\ of\ the\ rectangle}\times Frequency$

Minimum class size = 2 - 1 = 1
The modified table showing the weighted frequency as per the size of the class intervals is as follows:

The histogram representing the information given in the above table is as follows:

Q9 (i) 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:

Answer:

The calculation of weighted frequencies must be performed for each rectangle because different class sizes were used to construct the histogram.

$\\Weighted\ frequency=\frac{Minimum\ class\ size}{Class\ size\ of\ the\ interval}\times Frequency$

$Length\ of\ the\ rectangle=\frac{Minimum\ width}{Width\ of\ the\ rectangle}\times Frequency$

Minimum class size = 6 - 4 = 2
The modified table showing the weighted frequency as per the size of the class intervals is as follows:

The histogram representing the information given in the above table is as follows:

Q9 (ii) 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:

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

Answer:

The largest number of surnames lies in the class interval of 6 - 8. This class interval's weighted frequency is 44 (assuming a minimum class size of 2).