Question

histograms practice

1. the numbers below indicate the number of summer olympic medals awarded to athletes from the united states during 18 summer olympic games.

u.s. summer olympic medals
55 56 62 71 74 76 84 90 94 94 96 101 103 103 103 107 108 174
55 - 174
a. construct a histogram of these data.
u.s. medals frequency
50 - 65 3
65 - 80 3
80 - 95 4
95 - 110 7
110 - 125
125 - 140
140 - 155
155 - 170
170 - 185 1
u.s. medals
b. construct a relative - frequency histogram of these data. hint: relative frequencies consist of percentages
u.s. medals frequency rel. freq.

Explanation:

Step1: Find total frequency

The sum of all frequencies is \(3 + 3+4 + 7+0+0+0+0 + 1=18\).

Step2: Calculate relative - frequencies

For the interval \(50 - 65\), relative frequency \(=\frac{3}{18}\approx0.167 = 16.7\%\)
For the interval \(65 - 80\), relative frequency \(=\frac{3}{18}\approx0.167 = 16.7\%\)
For the interval \(80 - 95\), relative frequency \(=\frac{4}{18}\approx0.222 = 22.2\%\)
For the interval \(95 - 110\), relative frequency \(=\frac{7}{18}\approx0.389 = 38.9\%\)
For the interval \(110 - 125\), relative frequency \(=\frac{0}{18}=0 = 0\%\)
For the interval \(125 - 140\), relative frequency \(=\frac{0}{18}=0 = 0\%\)
For the interval \(140 - 155\), relative frequency \(=\frac{0}{18}=0 = 0\%\)
For the interval \(155 - 170\), relative frequency \(=\frac{0}{18}=0 = 0\%\)
For the interval \(170 - 185\), relative frequency \(=\frac{1}{18}\approx0.056 = 5.6\%\)

To construct the histograms:

a. Histogram

On the x - axis, label the intervals \(50 - 65\), \(65 - 80\), \(80 - 95\), \(95 - 110\), \(110 - 125\), \(125 - 140\), \(140 - 155\), \(155 - 170\), \(170 - 185\). On the y - axis, label the frequency. Draw bars with heights corresponding to the frequencies in the frequency - table (\(3\), \(3\), \(4\), \(7\), \(0\), \(0\), \(0\), \(0\), \(1\) respectively).

b. Relative - frequency Histogram

On the x - axis, label the intervals \(50 - 65\), \(65 - 80\), \(80 - 95\), \(95 - 110\), \(110 - 125\), \(125 - 140\), \(140 - 155\), \(155 - 170\), \(170 - 185\). On the y - axis, label the relative frequency (as a percentage). Draw bars with heights corresponding to the relative frequencies calculated above (\(16.7\%\), \(16.7\%\), \(22.2\%\), \(38.9\%\), \(0\%\), \(0\%\), \(0\%\), \(0\%\), \(5.6\%\) respectively)

Answer:

a. Histogram: Bars with heights 3, 3, 4, 7, 0, 0, 0, 0, 1 for intervals \(50 - 65\), \(65 - 80\), \(80 - 95\), \(95 - 110\), \(110 - 125\), \(125 - 140\), \(140 - 155\), \(155 - 170\), \(170 - 185\) respectively.
b. Relative - frequency Histogram: Bars with heights approximately \(16.7\%\), \(16.7\%\), \(22.2\%\), \(38.9\%\), \(0\%\), \(0\%\), \(0\%\), \(0\%\), \(5.6\%\) for intervals \(50 - 65\), \(65 - 80\), \(80 - 95\), \(95 - 110\), \(110 - 125\), \(125 - 140\), \(140 - 155\), \(155 - 170\), \(170 - 185\) respectively.