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Consider the following frequency distribution:

\begin{tabular}{|c|c|}
\hline Class & Frequency \\
\hline [tex]$20-29$[/tex] & 10 \\
\hline [tex]$30-39$[/tex] & 14 \\
\hline [tex]$40-49$[/tex] & 17 \\
\hline [tex]$50-59$[/tex] & 7 \\
\hline [tex]$60-69$[/tex] & 2 \\
\hline
\end{tabular}

Construct a cumulative frequency distribution and a cumulative relative frequency distribution. Round your answers as necessary.

\begin{tabular}{|c|c|c|}
\hline
Class & Cumulative Frequency & Cumulative Relative Frequency \\
\hline
Less than or equal to 29 & [tex]$\square$[/tex] & [tex]$\square$[/tex] \\
\hline
Less than or equal to 39 & [tex]$\square$[/tex] & [tex]$\square$[/tex] \\
\hline
Less than or equal to 49 & [tex]$\square$[/tex] & [tex]$\square$[/tex] \\
\hline
Less than or equal to 59 & [tex]$\square$[/tex] & [tex]$\square$[/tex] \\
\hline
Less than or equal to 69 & [tex]$\square$[/tex] & [tex]$\square$[/tex] \\
\hline
\end{tabular}



Answer :

GinnyAnswer
Let's construct the cumulative frequency distribution and the cumulative relative frequency distribution step-by-step:

### Step 1: Class Intervals and Frequencies
The given class intervals and their frequencies are:

| Class | Frequency |
|--------|-----------|
| 20-29 | 10 |
| 30-39 | 14 |
| 40=49 | 17 |
| 50-59 | 7 |
| 60-69 | 2 |

### Step 2: Cumulative Frequency
To find the cumulative frequency, we sum the frequencies progressively:

- For the interval 20-29: Cumulative frequency is 10.
- For the interval 30-39: Cumulative frequency is [tex]\(10 + 14 = 24\)[/tex].
- For the interval 40=49: Cumulative frequency is [tex]\(24 + 17 = 41\)[/tex].
- For the interval 50-59: Cumulative frequency is [tex]\(41 + 7 = 48\)[/tex].
- For the interval 60-69: Cumulative frequency is [tex]\(48 + 2 = 50\)[/tex].

So, the cumulative frequencies are:

| Class | Cumulative Frequency |
|---------------------- |----------------------|
| Less than or equal to 29 | 10 |
| Less than or equal to 39 | 24 |
| Less than or equal to 49 | 41 |
| Less than or equal to 59 | 48 |
| Less than or equal to 69 | 50 |

### Step 3: Cumulative Relative Frequency
To find the cumulative relative frequency, we divide each cumulative frequency by the total frequency. The total frequency is the sum of all frequencies, which is [tex]\(10 + 14 + 17 + 7 + 2 = 50\)[/tex].

- For the interval 20-29: Cumulative relative frequency is [tex]\(\frac{10}{50} = 0.2\)[/tex].
- For the interval 30-39: Cumulative relative frequency is [tex]\(\frac{24}{50} = 0.48\)[/tex].
- For the interval 40=49: Cumulative relative frequency is [tex]\(\frac{41}{50} = 0.82\)[/tex].
- For the interval 50-59: Cumulative relative frequency is [tex]\(\frac{48}{50} = 0.96\)[/tex].
- For the interval 60-69: Cumulative relative frequency is [tex]\(\frac{50}{50} = 1.0\)[/tex].

So, the cumulative relative frequencies are:

| Class | Cumulative Relative Frequency |
|----------------------- |-------------------------------|
| Less than or equal to 29 | 0.2 |
| Less than or equal to 39 | 0.48 |
| Less than or equal to 49 | 0.82 |
| Less than or equal to 59 | 0.96 |
| Less than or equal to 69 | 1.0 |

Combining both cumulative frequency and cumulative relative frequency distributions:

| Class | Cumulative Frequency | Cumulative Relative Frequency |
|----------------------- |----------------------|-------------------------------|
| Less than or equal to 29 | 10 | 0.2 |
| Less than or equal to 39 | 24 | 0.48 |
| Less than or equal to 49 | 41 | 0.82 |
| Less than or equal to 59 | 48 | 0.96 |
| Less than or equal to 69 | 50 | 1.0 |

These distributions help us understand the accumulation of frequencies and the proportion of the total frequency that falls within or below each class interval.

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