Q.2.64 - Elementary Statistics

Question

Use limit grouping with the first class of $0-9$ and a class width of $10$.

Step-by-Step Solution

Answer

a). The frequency distribution,

$\begin{array}{|cc|}\hline \text{ Limit grouping classes }& \text{ Frequency }\\ 0-9& 3\\ 10-19& 3\\ 20-29& 5\\ 30-39& 8\\ 40-49& 1\\ \text{ Total }& 20\\ \hline\end{array}$

b). Relative frequency distribution,$\begin{array}{|ccc|}\hline \text{ Limit grouping classes }& \text{ Frequency }& \text{ Relative Frequency }\\ 0-9& 3& \frac{3}{20}=0.5\\ 10-19& 3& \frac{3}{20}=0.5\\ 20-29& 5& \frac{5}{20}=0.25\\ 30-39& 8& \frac{8}{20}=0.40\\ 40-49& 1& \frac{1}{20}=0.05\\ \text{ Total }& 20& \\ \hline\end{array}$

c). Frequency histogram,

d). Relative frequency histogram,

Part (a) Step 1: Given Information

Given data:

Part (a) Step 2; Explanation

Frequency distribution is calculated as,

$\begin{array}{|cc|}\hline \text{ Limit grouping classes }& \text{ Frequency }\\ 0-9& 3\\ 10-19& 3\\ 20-29& 5\\ 30-39& 8\\ 40-49& 1\\ \text{ Total }& 20\\ \hline\end{array}$

Part (b) Step 1: Given Information

Given data:

Part (b) Step 2: Explanation

The relative frequency distribution is computed as follows: 

$\text{ Relative Frequency }=\frac{\text{ Frequency }}{\text{ Number of observations }}$

$\begin{array}{|ccc|}\hline \text{ Limit grouping classes }& \text{ Frequency }& \text{ Relative Frequency }\\ 0-9& 3& \frac{3}{20}=0.5\\ 10-19& 3& \frac{3}{20}=0.5\\ 20-29& 5& \frac{5}{20}=0.25\\ 30-39& 8& \frac{8}{20}=0.40\\ 40-49& 1& \frac{1}{20}=0.05\\ \text{ Total }& 20& \\ \hline\end{array}$

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): 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.