Convert the given frequency distribution into a continuous grouped frequency distribution:
Class Interval Frequency
150-153 7
154-157 7
158-161 15
162-165 10
166-169 5
170-173 6
In which intervals would 153.5 and 157.5 be included?

Solution:

Given, the table represents the frequency distribution

We have to find in which interval 153.5 and 157.5 be included.

The given frequency distribution is in the inclusive form.

On converting to exclusive form,

Now, consider the classes 150 - 153 and 154 - 157

The lower limit of 154 - 157 is 154.

The upper limit of 150 - 153 is 153.

Half the difference between lower and upper limit = (154 - 153)/2

= 0.5

Thus, we subtract 0.5 from each lower limit and add 0.5 to each upper limit.

The table for continuous grouped frequency distribution becomes,

From the above table,

We observe that 153.5 and 157.5 lies in the intervals 153.5 - 157.5 and 157.5 - 161.5

✦ Try This: Convert the given frequency distribution into a continuous grouped frequency distribution:

In which intervals would 161.5 and 165.5 be included?

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14

NCERT Exemplar Class 9 Maths Exercise 14.3 Problem 5

Convert the given frequency distribution into a continuous grouped frequency distribution: Class Interval Frequency 150-153 7 154-157 7 158-161 15 162-165 10 166-169 5 170-173 6. In which intervals would 153.5 and 157.5 be included?

Summary:

The given frequency distribution is converted into a continuous grouped frequency distribution. 153.5 and 157.5 be included in the intervals 153.5 - 157.5 and 157.5 - 161.5 respectively

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