Question

(b)
plot a histogram from the data shown in
the table.
speed (mph) frequency frequency density
0 < s ≤ 10 5
10 < s ≤ 35 30
35 < s ≤ 50 24
50 < s ≤ 70 16

Explanation:

Step1: Calculate class widths

For \(0 < s\leq10\), width \(w_1=10 - 0=10\).
For \(10 < s\leq35\), width \(w_2=35 - 10 = 25\).
For \(35 < s\leq50\), width \(w_3=50 - 35=15\).
For \(50 < s\leq70\), width \(w_4=70 - 50 = 20\).

Step2: Calculate frequency densities

Frequency density formula: \(fd=\frac{\text{Frequency}}{\text{Class width}}\)
For \(0 < s\leq10\): \(fd_1=\frac{5}{10}=0.5\)
For \(10 < s\leq35\): \(fd_2=\frac{30}{25}=1.2\)
For \(35 < s\leq50\): \(fd_3=\frac{24}{15}=1.6\)
For \(50 < s\leq70\): \(fd_4=\frac{16}{20}=0.8\)

Step3: Plot the histogram

On the \(x -\)axis, mark the class intervals (\(0 - 10\), \(10 - 35\), \(35 - 50\), \(50 - 70\)). On the \(y -\)axis, mark the frequency densities (\(0.5\), \(1.2\), \(1.6\), \(0.8\)). Draw bars with bases as the class intervals and heights as the frequency densities.

Answer:

The completed table with frequency densities:

Speed (mph)	Frequency	Frequency Density
\(10 < s\leq35\)	\(30\)	\(1.2\)
\(35 < s\leq50\)	\(24\)	\(1.6\)
\(50 < s\leq70\)	\(16\)	\(0.8\)

The histogram is plotted with \(x -\)axis as speed (mph) and \(y -\)axis as frequency density, with bars for each class interval having heights \(0.5\), \(1.2\), \(1.6\), \(0.8\) respectively.