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Statistics and Probability — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsStatistics and Probability4 Marks
Question
Convert the given frequency distribution into a continuous grouped frequency distribution:
Class interval
Frequency
$150-153$
$154-157$
$158-161$
$162-165$
$166-169$
$170-173$
$7$
$7$
$15$
$40$
$5$
$6$
In which intervals would $153.5$ and $157.5$ be included?
✓

Answer

It is clear that, the given table is in inclusive (discontinuous) form.
So, we first convert it into exclusive form.
Now, consider the classes $150 - 153, 154 - 157$
Lower limit of $154 - 157 = 154$ and upper limit of $150-153 = 153$
Required difference $= 154 - 153 = 1$
So, half the difference $=\frac{1}{2}=0.5$
So, we subtract $0.5$ from each lower limit and add $0.5$ to each upper limit.
The table for continuous grouped frequency distribution is given below:
Class interval
Frequency
$149.5-153.5$
$153.5-157.5$
$157.5-161.5$
$161.5-165.5$
$165.5-169.5$
$169.5-173.5$
$7$
$7$
$15$
$10$
$5$
$6$
Thus, $153.5$ and $157.5$ would use in the class intervals $153.5-157.5$ and $157.5-161.5$, respectively.

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