# 2.15: Chpater 2 Practice

## 2.1 Display Data Figure $$\PageIndex{14}$$14.

Construct a frequency polygon for the following:

1. Pulse rates for womenFrequency
60–6912
70–7914
80–8911
90–991
100–1091
110–1190
120–1291
Table $$\PageIndex{40}$$
2. Actual speed in a 30 MPH zoneFrequency
42–4525
46–4914
50–537
54–573
58–611
Table $$\PageIndex{41}$$
3. Tar (mg) in nonfiltered cigarettesFrequency
10–131
14–170
18–2115
22–257
26–292
Table $$\PageIndex{42}$$
15.

Construct a frequency polygon from the frequency distribution for the 50 highest ranked countries for depth of hunger.

Depth of hungerFrequency
230–25921
260–28913
290–3195
320–3497
350–3791
380–4091
410–4391
Table $$\PageIndex{43}$$
16.

Use the two frequency tables to compare the life expectancy of men and women from 20 randomly selected countries. Include an overlayed frequency polygon and discuss the shapes of the distributions, the center, the spread, and any outliers. What can we conclude about the life expectancy of women compared to men?

Life expectancy at birth – womenFrequency
49–553
56–623
63–691
70–763
77–838
84–902
Table $$\PageIndex{44}$$
Life expectancy at birth – menFrequency
49–553
56–623
63–691
70–761
77–837
84–905
Table $$\PageIndex{45}$$
17.

Construct a times series graph for (a) the number of male births, (b) the number of female births, and (c) the total number of births.

 Sex/Year 1855 1856 1857 1858 1859 1860 1861 Female 45,545 49,582 50,257 50,324 51,915 51,220 52,403 Male 47,804 52,239 53,158 53,694 54,628 54,409 54,606 Total 93,349 101,821 103,415 104,018 106,543 105,629 107,009
 Sex/Year 1862 1863 1864 1865 1866 1867 1868 1869 Female 51,812 53,115 54,959 54,850 55,307 55,527 56,292 55,033 Male 55,257 56,226 57,374 58,220 58,360 58,517 59,222 58,321 Total 107,069 109,341 112,333 113,070 113,667 114,044 115,514 113,354
 Sex/Year 1870 1871 1872 1873 1874 1875 Female 56,431 56,099 57,472 58,233 60,109 60,146 Male 58,959 60,029 61,293 61,467 63,602 63,432 Total 115,390 116,128 118,765 119,700 123,711 123,578
18.

The following data sets list full time police per 100,000 citizens along with homicides per 100,000 citizens for the city of Detroit, Michigan during the period from 1961 to 1973.

 Year 1961 1962 1963 1964 1965 1966 1967 Police 260.35 269.8 272.04 272.96 272.51 261.34 268.89 Homicides 8.6 8.9 8.52 8.89 13.07 14.57 21.36
 Year 1968 1969 1970 1971 1972 1973 Police 295.99 319.87 341.43 356.59 376.69 390.19 Homicides 28.03 31.49 37.39 46.26 47.24 52.33
1. Construct a double time series graph using a common x-axis for both sets of data.
2. Which variable increased the fastest? Explain.
3. Did Detroit’s increase in police officers have an impact on the murder rate? Explain.

## 2.2 Measures of the Location of the Data

19.

Listed are 29 ages for Academy Award winning best actors in order from smallest to largest.Figure $$\PageIndex{15}$$66.

Describe the relationship between the mode and the median of this distribution. Figure $$\PageIndex{16}$$67.

Describe the relationship between the mean and the median of this distribution. Figure $$\PageIndex{17}$$68.

Describe the shape of this distribution. Figure $$\PageIndex{18}$$69.

Describe the relationship between the mode and the median of this distribution. Figure $$\PageIndex{19}$$70.

Are the mean and the median the exact same in this distribution? Why or why not? Figure $$\PageIndex{20}$$71.

Describe the shape of this distribution. Figure $$\PageIndex{21}$$72.

Describe the relationship between the mode and the median of this distribution. Figure $$\PageIndex{22}$$73.

Describe the relationship between the mean and the median of this distribution. Figure $$\PageIndex{23}$$74.

The mean and median for the data are the same.

3; 4; 5; 5; 6; 6; 6; 6; 7; 7; 7; 7; 7; 7; 7

Is the data perfectly symmetrical? Why or why not?

75.

Which is the greatest, the mean, the mode, or the median of the data set?

11; 11; 12; 12; 12; 12; 13; 15; 17; 22; 22; 22

76.

Which is the least, the mean, the mode, and the median of the data set?

56; 56; 56; 58; 59; 60; 62; 64; 64; 65; 67

77.

Of the three measures, which tends to reflect skewing the most, the mean, the mode, or the median? Why?

78.

In a perfectly symmetrical distribution, when would the mode be different from the mean and median?

## 2.7 Measures of the Spread of the Data

Use the following information to answer the next two exercises: The following data are the distances between 20 retail stores and a large distribution center. The distances are in miles.
29; 37; 38; 40; 58; 67; 68; 69; 76; 86; 87; 95; 96; 96; 99; 106; 112; 127; 145; 150

79.

Use a graphing calculator or computer to find the standard deviation and round to the nearest tenth.

80.

Find the value that is one standard deviation below the mean.

81.

Two baseball players, Fredo and Karl, on different teams wanted to find out who had the higher batting average when compared to his team. Which baseball player had the higher batting average when compared to his team?

Baseball playerBatting averageTeam batting averageTeam standard deviation
Fredo0.1580.1660.012
Karl0.1770.1890.015
Table 2:59 to find the value that is three standard deviations:
• above the mean
• below the mean

Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83/84.

83.

Find the standard deviation for the following frequency tables using the formula. Check the calculations with the TI 83/84.

49.5–59.52
59.5–69.53
69.5–79.58
79.5–89.512
89.5–99.55
Table $$\PageIndex{60}$$
2. Daily low temperatureFrequency
49.5–59.553
59.5–69.532
69.5–79.515
79.5–89.51
89.5–99.50
Table $$\PageIndex{61}$$
3. Points per gameFrequency
49.5–59.514
59.5–69.532
69.5–79.515
79.5–89.523
89.5–99.52
Table $$\PageIndex{62}$$