Chapter 14: Statistics and Probability

Q1Written answer

The following are the marks (out of 100) of 60 students in mathematics.

16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35, 72, 55, 75,

31, 52, 28,72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55, 26, 95, 31, 7, 78, 92, 62,

52, 56, 15, 63,25, 36, 54, 44, 47, 27, 72, 17, 4, 30.

Construct a grouped frequency distribution table with width 10 of each class starting from 0 – 9.

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Worked solution

Arranging the given data in ascending order

4, 5, 7, 7,13,15,16,16,17,17,19, 24, 25, 26, 27, 28, 30, 31,31,34, 34, 35, 35, 36, 36, 36, 42, 44, 45, 47, 48, 51, 52, 52, 54, 55, 55, 56, 56, 61,62, 62, 63, 68, 70, 72, 72, 72, 74, 75, 75, 78, 80, 81,85, 86, 86, 92, 95, 97.

Then arrange the given data into groups with 10 as class width in each case.

The Frequency Distribution Table of the given data can be represented as follows:

NCERT Exemplar Solutions Class 9 Maths Chapter 14 Ex.14.4-1

Q2Written answer

Refer to Q1 above. Construct a grouped frequency distribution table with width 10 of each class, in such a way that one of the classes is 10 – 20 (20 not included).

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Worked solution

The grouped frequency distribution table with width 10 of each class, in such a way that one of the classes is 10 – 20 (20 not included) is represented below:

Q3Written answer

Draw a histogram of the following distribution:

NCERT Exemplar Solutions Class 9 Maths Chapter 14 Ex.14.4-3

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Worked solution

Q4Written answer

Draw a histogram to represent the following grouped frequency distribution:

NCERT Exemplar Solutions Class 9 Maths Chapter 14 Ex.14.4-5

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Worked solution

The frequency distribution table is in inclusive form. First we must convert it to exclusive form.

Consider the class 20-24, 25-29.

Lower limit of 25-29 is 25

Upper limit of 20-24 is 24

Half of the difference = (25-24)/2 = 1/2 = 0.5

We should subtract 0.5 from each lower limit and add 0.5 to each upper limit.

Let us first make the data continuous:

Ages	Number of teachers
19.5 – 24.5	10
24.5 – 29.5	28
29.5 – 34.5	32
34.5 – 39.5	48
39.5 – 44.5	50
44.5 – 49.5	35
49.5 – 54.5	12

Hence, the histogram can be represented as:

Q5Written answer

The lengths of 62 leaves of a plant are measured in millimetres and the data is represented in the following table:

NCERT Exemplar Solutions Class 9 Maths Chapter 14 Ex.14.4-7

Draw a histogram to represent the data above.

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Worked solution

The frequency distribution table is in inclusive form. First we must convert it to exclusive form.

Half of the difference = (127-126)/2 = 1/2 = 0.5

We should subtract 0.5 from each lower limit and add 0.5 to each upper limit.

Let us first make the data continuous:

Length (in mm)	Number of Leaves
117.5 – 126.5	8
126.5 – 135.5	10
135.5 – 144.5	12
144.5 – 153.5	17
153.5 – 162.5	7
162.5 – 171.5	5
171.5 – 180.5	3

Hence, the histogram can be represented as:

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Exercise 14.4