NCERT Class 9 Solutions: Statistics (Chapter 14) Exercise 14.3Part 2
Q4 The length of 40 leaves of a plant are measured correct to one millimeter, and the obtained data is represented in the following table:
Length (in mm)  Number of leaves 
118126  3 
127135  5 
136144  9 
145153  12 
154162  5 
163171  4 
172180  2 

Draw a histogram to represent the given data.

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

Is it correct to conclude that the maximum number of leaves is 153 mm long?
Why?
Solution (I):

The length of leaves is represented in a discontinuous class interval of 1 in between them.

So add, to each upper class limit

And subtract 0.5 from the lower class limits
Length (in mm)  Number of leaves 
117.5126.5  3 
126.5135.5  5 
135.5144.5  9 
144.5153.5  12 
153.5162.5  5 
162.5171.5  4 
171.5180.5  2 
Solution (II):

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

No, all we know is the frequency distribution between specific ranges. We cannot draw conclusion about a particular values. We can say that maximum number of leaves were found to have lengths between 144.5 mm and 153.5 mm. We cannot say that for a particular value in this range (say 153 mm)
Q5 The following table gives the life times of neon lamps:
Length (in hours)  Number of lamps 
300400  14 
400500  56 
500600  60 
600700  86 
700800  74 
800900  62 
9001000  48 
Title: Neon lamps
Description: The life times of neon lamps, also give length (in hours) and number of lamps.

Represent the given information with the help of a histogram.

How many lamps have a lifetime of more than 700 hours?
Solution (I):

With neon lamps on xaxis and the number of lamps on yaxis

The intervals are continuous so we don’t need to change them

The histogram of the given information can be draw below:
Solution (II):

It can be concluded that the number of neon lamps having their 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 lifetime more than 700 hours is (74 + 62 + 48 = 184).
Q6 The following table gives the distribution of students of two sections according to the mark obtained by them:
Section A  Section B  
Marks  Frequency  Marks  Frequency 
010  3  010  5 
1020  9  1020  19 
2030  17  2030  15 
3040  12  3040  10 
4050  9  4050  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 students in the two sections.
Solution:
The class marks of the given class intervals are calculated by using the formula.
Class mark = . For example, for the range 010 class mark would be . Therefore we can put the class marks in the above table and redraw it as:
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 
We draw the graph with following properties:

On xaxis we put the class marks and on yaxis put the frequency.

Scale is kept so that 1 mark on frequency is given 1 unit on yaxis.

We get following frequency polygon.
Chart3.txt