Q.2.69 - Elementary Statistics

Question

Use cutpoint grouping with a first class of $40$ -under $46$.

Step-by-Step Solution

Answer

a). The frequency distribution,

$\begin{array}{|cc|}\hline \text{ Cut-point grouping classes }& \text{ Frequency }\\ 40-\text{ under }46& 3\\ 46\text{-under }52& 6\\ \text{ 52-under }58& 10\\ 58-\text{ under }64& 0\\ \text{ 64-under }70& 1\\ \text{ Total }& 20\\ \hline\end{array}$

b). Relative distribution,

$\begin{array}{|ccc|}\hline \text{ Cut-point grouping classes }& \text{ Frequency }& \text{ Relative Frequency }\\ 40\text{-under }46& 3& \frac{3}{20}=0.15\\ \text{ 46-under }52& 6& \frac{6}{20}=0.3\\ \text{ 52-under }58& 10& \frac{10}{20}=0.5\\ \text{ 58-under64 }& 0& \frac{0}{20}=0\\ \text{ 64-under }70& 1& \frac{1}{20}=0.05\\ \text{ Total }& 20& 1\\ \hline\end{array}$

c). The frequency histogram,

d). Relative frequency histogram,

Part (a) Step 1: Given Information

Given data:

Part (a) Step 2: Explanation

The frequency distribution is computed as,

$\begin{array}{|cc|}\hline \text{ Cut-point grouping classes }& \text{ Frequency }\\ 40-\text{ under }46& 3\\ 46\text{-under }52& 6\\ \text{ 52-under }58& 10\\ 58-\text{ under }64& 0\\ \text{ 64-under }70& 1\\ \text{ Total }& 20\\ \hline\end{array}$

Part (b) Step 1: Given Information

Given data:

Part (b) Step 2: Explanation

The relative frequency is calculated as follows:   
$\text{ Relative Frequency }=\frac{\text{ Frequency }}{\text{ Number of observations }}$

$\begin{array}{|ccc|}\hline \text{ Cut-point grouping classes }& \text{ Frequency }& \text{ Relative Frequency }\\ 40\text{-under }46& 3& \frac{3}{20}=0.15\\ \text{ 46-under }52& 6& \frac{6}{20}=0.3\\ \text{ 52-under }58& 10& \frac{10}{20}=0.5\\ \text{ 58-under64 }& 0& \frac{0}{20}=0\\ \text{ 64-under }70& 1& \frac{1}{20}=0.05\\ \text{ Total }& 20& 1\\ \hline\end{array}$

Part (c) Step 1: Given Information

Given data:

Part (c) Step 2: Explanation

MINITAB is used to generate the frequency histogram.

The following is the technique for obtaining a frequency histogram:

• Navigate to Graph>Histogram.
• Click OK after selecting Simple.
• Click OK after entering the matching column of DATA in Graph variables.

The output of MINITAB is displayed below.

Part (d) Step 1: Given Information

Given data:

Part (d) Step 2: Explanation

MINITAB is used to generate the relative frequency histogram.

The following is the technique for obtaining a frequency histogram:

• Navigate to Graph>Histogram.
• Click OK after selecting Simple.
• In the Graph variables section, enter the corresponding DATA column.
• Go to Vertical Axis and select TYPE TAB.
• Choose Percentage
• Click OK

The output of MINITAB is displayed below.