Q.2.68 - Elementary Statistics

Question

Use cutpoint grouping with a first class of $10$ -under $15$.

Step-by-Step Solution

Answer

a). The frequency distribution,

$\begin{array}{|cc|}\hline \text{ Cut-point grouping classes }& \text{ Frequency }\\ \text{ 10-under 15 }& 4\\ \text{ 15-under }20& 5\\ \text{ 20-under }25& 7\\ \text{ 25-under }30& 3\\ 30-\text{ under }35& 0\\ 35-\text{ under }40& 1\\ \text{ Total }& 20\\ \hline\end{array}$

b). The relative frequency,

$\begin{array}{|ccc|}\hline \text{ Cut-point grouping classes }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ 10-under }15& 4& \frac{4}{20}=0.20\\ 15\text{-under }20& 5& \frac{5}{20}=0.25\\ \text{ 20-under }25& 7& \frac{7}{20}=0.35\\ 25\text{-under }30& 3& \frac{3}{20}=0.15\\ 30\text{-under }35& 0& \frac{0}{20}=0\\ 35\text{-under }40& 1& \frac{1}{20}=0.05\\ \text{ Total }& 20& 1\\ \hline\end{array}$

c). Frequency histogram,

d). Relative frequency histogram,

Part (a) Step 1: Given Information

Given data:

Part (a) Step 2: Explanation

The frequency distribution is computed as,

$\begin{array}{|cc|}\hline \text{ Cut-point grouping classes }& \text{ Frequency }\\ \text{ 10-under 15 }& 4\\ \text{ 15-under }20& 5\\ \text{ 20-under }25& 7\\ \text{ 25-under }30& 3\\ 30-\text{ under }35& 0\\ 35-\text{ under }40& 1\\ \text{ Total }& 20\\ \hline\end{array}$

Part (b) Step 1: Given Information

Given data:

Part (b) Step 2: Explanation

The relative frequency is calculated as follows:  

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

$\begin{array}{|ccc|}\hline \text{ Cut-point grouping classes }& \text{ Frequency }& \text{ Relative Frequency }\\ \text{ 10-under }15& 4& \frac{4}{20}=0.20\\ 15\text{-under }20& 5& \frac{5}{20}=0.25\\ \text{ 20-under }25& 7& \frac{7}{20}=0.35\\ 25\text{-under }30& 3& \frac{3}{20}=0.15\\ 30\text{-under }35& 0& \frac{0}{20}=0\\ 35\text{-under }40& 1& \frac{1}{20}=0.05\\ \text{ Total }& 20& 1\\ \hline\end{array}$

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)b 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.