Questions: Construct a cumulative frequency distribution using 6 classes. Cumulative frequency Less than 53.5 Less than 63.5 Less than 73.5 Less than 83.5 Less than 93.5 Less than 103.5 Less than 113.5

Construct a cumulative frequency distribution using 6 classes.
Cumulative frequency
Less than 53.5
Less than 63.5
Less than 73.5
Less than 83.5
Less than 93.5
Less than 103.5

Less than 113.5

Transcript text: Construct a cumulative frequency distribution using 6 classes. Cumulative frequency Less than 53.5 Less than 63.5 Less than 73.5 Less than 83.5 Less than 93.5 Less than 103.5 $\square$ $\square$ Less than 113.5 $\square$

Solution

Solution Steps

Step 1: Identify the Class Boundaries

The given table provides class boundaries and frequencies. The class boundaries are:

$73.5-83.5$ with frequency 5,
$83.5-93.5$ with frequency 5,
$93.5-103.5$ with frequency 2,
$103.5-113.5$ with frequency 2.

Step 2: Calculate Cumulative Frequencies

To construct the cumulative frequency distribution, we sum the frequencies up to each class boundary:

Less than $53.5$: 0 (no data below this boundary),
Less than $63.5$: 0 (no data below this boundary),
Less than $73.5$: 0 (no data below this boundary),
Less than $83.5$: 5 (frequency of the first class),
Less than $93.5$: $5 + 5 = 10$ (sum of the first two classes),
Less than $103.5$: $10 + 2 = 12$ (sum of the first three classes),
Less than $113.5$: $12 + 2 = 14$ (sum of all classes).

Step 3: Fill in the Cumulative Frequency Table

The cumulative frequency distribution is as follows:

Less than $53.5$: $\square$ 0,
Less than $63.5$: $\square$ 0,
Less than $73.5$: $\square$ 0,
Less than $83.5$: $\square$ 5,
Less than $93.5$: $\square$ 10,
Less than $103.5$: $\square$ 12,
Less than $113.5$: $\square$ 14.

Final Answer

Less than $53.5$: $\boxed{0}$
Less than $63.5$: $\boxed{0}$
Less than $73.5$: $\boxed{0}$
Less than $83.5$: $\boxed{5}$
Less than $93.5$: $\boxed{10}$
Less than $103.5$: $\boxed{12}$
Less than $113.5$: $\boxed{14}$

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