Question

(c) plot a histogram from the data shown in the table. time (hours) frequency frequency density $0 < h \leq 4$ 3 $4 < h \leq 8$ 5 $8 < h \leq 16$ 22 $16 < h \leq 22$ 15 $22 < h \leq 25$ 6

Explanation:

Step1: Calculate class width

For \(0 < h\leq4\), width \(=4 - 0=4\).
For \(4 < h\leq8\), width \(=8 - 4 = 4\).
For \(8 < h\leq16\), width \(=16 - 8=8\).
For \(16 < h\leq22\), width \(=22 - 16 = 6\).
For \(22 < h\leq25\), width \(=25 - 22=3\).

Step2: Calculate frequency density

Frequency density formula: \(FD=\frac{\text{Frequency}}{\text{Class Width}}\)
For \(0 < h\leq4\): \(FD=\frac{3}{4}=0.75\)
For \(4 < h\leq8\): \(FD=\frac{5}{4}=1.25\)
For \(8 < h\leq16\): \(FD=\frac{22}{8}=2.75\)
For \(16 < h\leq22\): \(FD=\frac{15}{6}=2.5\)
For \(22 < h\leq25\): \(FD=\frac{6}{3}=2\)

Step3: Plot the histogram

On the \(x -\)axis, mark the class intervals (\(0 - 4\), \(4 - 8\), \(8 - 16\), \(16 - 22\), \(22 - 25\)). On the \(y -\)axis, mark the frequency density values (\(0.75\), \(1.25\), \(2.75\), \(2.5\), \(2\)). Draw bars with bases as class intervals and heights as corresponding frequency densities.

Answer:

The frequency densities are \(0.75\), \(1.25\), \(2.75\), \(2.5\), \(2\) for the class intervals \(0 < h\leq4\), \(4 < h\leq8\), \(8 < h\leq16\), \(16 < h\leq22\), \(22 < h\leq25\) respectively. Plot the histogram using these values.