Q.2.66 - Elementary Statistics

Question

Use limit grouping with the first class of $30-36$ and a class width of $7$.

Step-by-Step Solution

Answer

a). The frequency distribution,

$\begin{array}{|cc|}\hline \text{ Limit grouping classes }& \text{ Frequency }\\ 30-36& 7\\ 37-43& 2\\ 44-50& 5\\ 51-57& 2\\ 58-64& 2\\ 65-71& 25\\ 72-78& 3\\ \text{ Total }& 2\\ \hline\end{array}$

b). Relative frequency distribution,

$\begin{array}{|ccc|}\hline \text{ Limit grouping classes }& \text{ Frequency }& \text{ Relative Frequency }\\ 30-36& 7& \frac{7}{25}=0.28\\ 37-43& 2& \frac{2}{25}=0.08\\ 44-50& 5& \frac{5}{25}=0.20\\ 51-57& 4& \frac{4}{25}=0.16\\ 58-64& 3& \frac{3}{25}=0.12\\ 65-71& 2& \frac{2}{25}=0.08\\ 72-78& 2& \frac{2}{25}=0.08\\ \text{ Total }& 25& 1\\ \hline\end{array}$

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,

$\begin{array}{|cc|}\hline \text{ Limit grouping classes }& \text{ Frequency }\\ 30-36& 7\\ 37-43& 2\\ 44-50& 5\\ 51-57& 2\\ 58-64& 2\\ 65-71& 25\\ 72-78& 3\\ \text{ Total }& 2\\ \hline\end{array}$

Part (b) Step 1: Given Information

Given data:

Part (b) Step 2: Explanation

The relative frequency is calculated as follows: 

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

$\begin{array}{|ccc|}\hline \text{ Limit grouping classes }& \text{ Frequency }& \text{ Relative Frequency }\\ 30-36& 7& \frac{7}{25}=0.28\\ 37-43& 2& \frac{2}{25}=0.08\\ 44-50& 5& \frac{5}{25}=0.20\\ 51-57& 4& \frac{4}{25}=0.16\\ 58-64& 3& \frac{3}{25}=0.12\\ 65-71& 2& \frac{2}{25}=0.08\\ 72-78& 2& \frac{2}{25}=0.08\\ \text{ Total }& 25& 1\\ \hline\end{array}$

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.