NCERT Class 9 Solutions: Statistics (Chapter 14) Exercise 14.3-Part 2

Q-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:

Table shows the length of number of leaves
Table shows the length of number of leaves

Length (in mm)

Number of leaves

118-126

3

127-135

5

136-144

9

145-153

12

154-162

5

163-171

4

172-180

2

I. Draw a histogram to represent the given data.

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):

Given frequency distribution is not continuous. So, first convert into frequency distribution.

So, Difference between lower limit of class and upper limit of preceding class: (127126=1)

Hence, h2=12=0.5 added to each upper class limit and subtract from the lower class limits.

Obtain distribution is given as under:

Obtain distribution as per given data
Obtain distribution as per given data

Length (in mm)

Number of leaves

117.5-126.5

3

126.5-135.5

5

135.5-144.5

9

144.5-153.5

12

153.5-162.5

5

162.5-171.5

4

171.5-180.5

2

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Created with Highcharts 4.2.5Length (in mm)Number of leavesLength (in mm) Vs Number of leaves35912542Length (in mm) Vs Number of leaves117.5-126.5126.5-135.5135.5-144.5144.5-153.5153.5-162.5162.5-171.5171.5-180.5051015144.5-153.5Length (in mm) Vs Number of leaves: 12

Solution (II): Other suitable graphical representation of this data is frequency polygon.

Solution (III): No, maximum number of leaves has in between 144.5 mm and 153.5 mm. It is not necessary that all leaves length as 153 mm.

Q-5 The following table gives the life times of 400 neon lamps:

Life times of neon lamps are shown in table
Life times of neon lamps are shown in table

Life time (in hours)

Number of lamps

300-400

14

400-500

56

500-600

60

600-700

86

700-800

74

800-900

62

900-1000

48

I. Represent the given information with the help of a histogram.

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

Solution (I): Life time of x-axis and the number of lamps on y-axis.

Histogram:

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Created with Highcharts 4.2.5Life time (in hours)Number of lampsLife time (in hours) Vs Number of lamps14566086746248Life time (in hours) Vs Number of lamps300-400400-500500-600600-700700-800800-900900-10000255075100700-800Life time (in hours) Vs Number of lamps: 74

Solution (II):

Lifetime more than 700 is the sum of the number of neon lamps having their lifetime as 700800,800900 , and 9001000.

So, neon lamp having more than 700 hour’s lifetime =74+62+48=184lamps

Q-6 The following table gives the distribution of students of two sections according to the mark obtained by them:

Distribution of students according to marks
Distribution of students of two sections according to marks

Section A

Section B

Marks

Frequency

Marks

Frequency

0-10

3

0-10

5

10-20

9

10-20

19

20-30

17

20-30

15

30-40

12

30-40

10

40-50

9

40-50

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.

Solution:

The class marks of the given class intervals by using the formula.

Class interval (Marks) =Upperclasslimit+lowerclasslimit2

Frequency polygons data table of Section A and B
Frequency polygons data table of Section A and B

Section A

Section B

Marks

Class marks

Frequency

Mark

Class marks

Frequency

010

5

3

010

5

5

1020

15

9

1020

15

19

2030

25

17

2030

25

15

3040

35

12

3040

35

10

4050

45

9

4050

45

1

Class marks on x-axis and frequency on y-axis.

Choose appropriate scale.

Below drawn the frequency polygons:

Chart3.txt

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