In a histogram, two class intervals were 20-30 and 30-40 with corresponding heights 10 and 20 units. The class intervals were combined to form a single class interval 20-40. What is the height corresponding to this new class interval?

10 units

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15 units

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20 units

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30 units

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Solution

The correct option is B 15 units
In a histogram, the area of
rectangles corresponds to
the frequency of the classes.
Before combining,
$F r e q u e n c y = 10 \times 10 + 10 \times 20 = 300$
The frequency after combining the classes
also will be the same. Suppose 'h' is the
height of the new class interval. Then,
$F r e q u e n c y = 20 \times h = 300 \Rightarrow h = \frac{300}{20} = 15$

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Prepare the frequency distribution table for the given set of scores:

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Take class intervals as (10 -20), (20 − 30), … and answer the following:

(i) What does the frequency corresponding to the third class interval mean?

(ii) What is the size of each class interval? Find the midpoint of the class interval 30- 40.

(iii) What is the range of the given set of scores?

Calculate mean and standard deviation :

$\begin{matrix} Class Interval & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 Frequency & 8 & 13 & 16 & 8 & 5 \end{matrix}$

Question 58

In the class intervals 10-20 and 20-30 respectively, 20 lies in the class___.

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