# 2.15: Chpater 2 Practice

- Page ID
- 51765

## 2.1 Display Data

Figure \(\PageIndex{14}\)**14**.

Construct a frequency polygon for the following:

Pulse rates for women Frequency 60–69 12 70–79 14 80–89 11 90–99 1 100–109 1 110–119 0 120–129 1 Table \(\PageIndex{40}\) Actual speed in a 30 MPH zone Frequency 42–45 25 46–49 14 50–53 7 54–57 3 58–61 1 Table \(\PageIndex{41}\) Tar (mg) in nonfiltered cigarettes Frequency 10–13 1 14–17 0 18–21 15 22–25 7 26–29 2 Table \(\PageIndex{42}\)

**15**.

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

Depth of hunger | Frequency |
---|---|

230–259 | 21 |

260–289 | 13 |

290–319 | 5 |

320–349 | 7 |

350–379 | 1 |

380–409 | 1 |

410–439 | 1 |

**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 – women | Frequency |
---|---|

49–55 | 3 |

56–62 | 3 |

63–69 | 1 |

70–76 | 3 |

77–83 | 8 |

84–90 | 2 |

Life expectancy at birth – men | Frequency |
---|---|

49–55 | 3 |

56–62 | 3 |

63–69 | 1 |

70–76 | 1 |

77–83 | 7 |

84–90 | 5 |

**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 |

- Construct a double time series graph using a common
*x*-axis for both sets of data. - Which variable increased the fastest? Explain.
- 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 player | Batting average | Team batting average | Team standard deviation |
---|---|---|---|

Fredo | 0.158 | 0.166 | 0.012 |

Karl | 0.177 | 0.189 | 0.015 |

- 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.

Grade Frequency 49.5–59.5 2 59.5–69.5 3 69.5–79.5 8 79.5–89.5 12 89.5–99.5 5 Table \(\PageIndex{60}\) Daily low temperature Frequency 49.5–59.5 53 59.5–69.5 32 69.5–79.5 15 79.5–89.5 1 89.5–99.5 0 Table \(\PageIndex{61}\) Points per game Frequency 49.5–59.5 14 59.5–69.5 32 69.5–79.5 15 79.5–89.5 23 89.5–99.5 2 Table \(\PageIndex{62}\)