Questions: Construct the cumulative frequency distribution for the given data Age (years) of Best Actress when award was won Frequency 20-29 28 30-39 33 40-49 15 50-59 3 60-69 6 70-79 2 80-89 1

Construct the cumulative frequency distribution for the given data

Age (years) of Best Actress when award was won Frequency
20-29 28
30-39 33
40-49 15
50-59 3
60-69 6
70-79 2
80-89 1

Transcript text: Construct the cumulative frequency distribution for the given data \begin{tabular}{|c|c|} \hline Age (years) of Best Actress when award was won & Frequency \\ \hline $20-29$ & 28 \\ \hline $30-39$ & 33 \\ \hline $40-49$ & 15 \\ \hline 50.59 & 3 \\ \hline $60-69$ & 6 \\ \hline $70-79$ & 2 \\ \hline $80-89$ & 1 \\ \hline \end{tabular}

Solution

Solution Steps

To construct the cumulative frequency distribution, we need to calculate the cumulative frequency for each age group. This involves adding the frequency of the current age group to the cumulative frequency of the previous age groups.

Step 1: Understand the Problem

We are given a frequency distribution of ages at which actresses won an award. Our task is to construct the cumulative frequency distribution, which involves calculating the cumulative frequency for each age group.

Step 2: Calculate Cumulative Frequencies

To find the cumulative frequency for each age group, we add the frequency of the current age group to the cumulative frequency of all previous age groups. Mathematically, if $ f_i $ is the frequency of the $ i $-th age group, then the cumulative frequency $ CF_i $ is given by: \[ CF_i = \sum_{j=1}^{i} f_j \]

Step 3: Apply the Formula

Using the given frequencies:

For the age group $ 20-29 $, $ CF_1 = 28 $
For the age group $ 30-39 $, $ CF_2 = 28 + 33 = 61 $
For the age group $ 40-49 $, $ CF_3 = 61 + 15 = 76 $
For the age group $ 50-59 $, $ CF_4 = 76 + 3 = 79 $
For the age group $ 60-69 $, $ CF_5 = 79 + 6 = 85 $
For the age group $ 70-79 $, $ CF_6 = 85 + 2 = 87 $
For the age group $ 80-89 $, $ CF_7 = 87 + 1 = 88 $

Final Answer

The cumulative frequency distribution is:

Age group $ 20-29 $: Cumulative Frequency $ 28 $
Age group $ 30-39 $: Cumulative Frequency $ 61 $
Age group $ 40-49 $: Cumulative Frequency $ 76 $
Age group $ 50-59 $: Cumulative Frequency $ 79 $
Age group $ 60-69 $: Cumulative Frequency $ 85 $
Age group $ 70-79 $: Cumulative Frequency $ 87 $
Age group $ 80-89 $: Cumulative Frequency $ 88 $

\[ \boxed{ \begin{array}{|c|c|} \hline \text{Age Group} & \text{Cumulative Frequency} \\ \hline 20-29 & 28 \\ 30-39 & 61 \\ 40-49 & 76 \\ 50-59 & 79 \\ 60-69 & 85 \\ 70-79 & 87 \\ 80-89 & 88 \\ \hline \end{array} } \]

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