Q.2.65 - Elementary Statistics

Question

Use limit grouping with the first class of $0-4$ and a class width of $5$.

Step-by-Step Solution

Answer

a). The frequency distribution,

$\begin{array}{|cc|}\hline \text{ Limit grouping classes }& \text{ Frequency }\\ 0-4& 5\\ 5-9& 5\\ 10-14& 1\\ 15-19& 4\\ 20-24& 2\\ 25-29& 3\\ \text{ Total }& 20\\ \hline\end{array}$

b). Relative frequency,

$\begin{array}{|ccc|}\hline \text{ Limit grouping classes }& \text{ Frequency }& \text{ Relative Frequency }\\ 0-4& 5& \frac{5}{20}=0.25\\ 5-9& 5& \frac{5}{20}=0.25\\ 10-14& 1& \frac{1}{20}=0.01\\ 15-19& 4& \frac{4}{20}=0.20\\ 20-24& 2& \frac{2}{20}=0.1\\ 25-29& 3& \frac{3}{20}=0.15\\ \text{ Total }& 20& \\ \hline\end{array}$

c). Frequency histogram,

d). Relative frequency histogram,

Part (a) Step 1: Given Information

Given data:

Part (a) Step 2: Explanation

The frequency distribution is calculated as,

$\begin{array}{|cc|}\hline \text{ Limit grouping classes }& \text{ Frequency }\\ 0-4& 5\\ 5-9& 5\\ 10-14& 1\\ 15-19& 4\\ 20-24& 2\\ 25-29& 3\\ \text{ Total }& 20\\ \hline\end{array}$

Part (b) Step 1: Given Information

Given data:

Part (b) Step 2: Explanation

The relative frequency is calculated as follows:

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

$\begin{array}{|ccc|}\hline \text{ Limit grouping classes }& \text{ Frequency }& \text{ Relative Frequency }\\ 0-4& 5& \frac{5}{20}=0.25\\ 5-9& 5& \frac{5}{20}=0.25\\ 10-14& 1& \frac{1}{20}=0.01\\ 15-19& 4& \frac{4}{20}=0.20\\ 20-24& 2& \frac{2}{20}=0.1\\ 25-29& 3& \frac{3}{20}=0.15\\ \text{ Total }& 20& \\ \hline\end{array}$

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) 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.