# The Measurement of Adolescents

## CONTENTS OF CURRICULUM UNIT 85.08.02

## An Introduction to Elementary Statistics

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## Prices of Television Sets

$219 | $399 | $400 | $359 | $318 |

$360 | $200 | $480 | $247 | $430 |

$475 | $250 | $260 | $278 | $397 |

$499 | $480 | $427 | $387 | $435 |

$314 | $425 | $450 | $287 | $498 |

Solution: Establish six intervals of $50 each. Tally the number of items in each interval.

*(figure available in print form)*

(25 + 1) $dv$ 2 = 26 $dv$ 2 = 13

The l3th item of the set is the median price. The l3th item is the fourth item in the interval $350 $399. The items in this interval are: $359, $360, $387, $397, $399. The median price is $397.

The range may be determined as follows:

Range = $498 $200 = $298.

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Exercises
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: Solve the following problems.

- 1.) Ask your classmates which of the following flavors of ice cream they prefer-vanilla, chocolate, butter pecan, or chocolate chip. Construct a frequency table to display the results of your survey.
- ____ a.) How many people are included in this survey?
- ____ b.) What percent of the people surveyed prefer chocolate ice cream?
- ____ c.) What is the most popular flavor of ice cream among this group of people?
- ____ d.) What is the least popular flavor of ice cream among this group of people?
- ____ e.) What is the ratio of people who prefer butter pecan ice cream to those who prefer chocolate chip ice cream?
- ____ f.) If the number of people who prefer vanilla ice cream were increased by 8, what would the percent of increase be?
- 2.) The high temperatures in twenty-five cities on June 29 were as follows:

69 | 64 | 61 | 87 | 87 | |

58 | 71 | 58 | 87 | 72 | |

70 | 52 | 82 | 107 | 112 | |

73 | 68 | 78 | 87 | 68 | |

71 | 73 | 90 | 96 | 83 |

- ____ a.) Arrange the temperatures in intervals and make a frequency table for the set of data.
- ____ b.) What is the range of the temperatures?
- ____ c.) What is the mode of the temperatures?
- ____ d.) What is the median temperature?
- ____ e.) What is the mean temperature?
- 3.) The salaries of thirty people are listed below.

$12,500 | $23,900 | $18,750 | $24,000 | $14,000 | |

$18,750 | $11,570 | $25,000 | $9,200 | $15,000 | |

$24,000 | $22,000 | $20,500 | $12,500 | $17,300 | |

$10,980 | $15,550 | $18,750 | $18,000 | $16,200 | |

$32,000 | $13,000 | $22,000 | $35,000 | $21,000 |

- ____ a.) Arrange the salaries in intervals and make a frequency table for the set of data.
- ____ b.) What is the range of the salaries?
- ____ c.) What is the median salary?
- ____ d.) What is the mean salary?

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*
Histogram
*

The frequency of a set of numbers can be represented graphically on a histogram. A
*histogram*is a bar graph on which the bars are adjacent to each other with no space between them. To construct a histogram, arrange the data in equal intervals. Represent each interval on the horizontal axis of the graph. Represent the frequency of items in the interval on the vertical axis of the graph.

- Example: The number of students in twenty-five classes of a high school are as follows: 15, 27, 22, 18, 10, 25, 27, 12, 19, 26, 14, 12, 22, 20 21, 17, 21, 20, 13, 12, 22, 27, 21, 17, 27. Arrange the class sizes in intervals and construct a histogram depicting the number of classes in each interval.

*(figure available in print form)*

*(figure available in print form)*

Exercises: A test was scored on the basis of 1 to 20 points. The scores obtained by thirty students are as follows: 20, 12, 18, 11, 20, 8, 1, 5, 10, 12, 15, 15, 18, 13, 19, 20, 18, 15, 16, 18, 17, 14, 20, 19, 13, 16, 12, 18, 20, 8.

- 1.) Arrange the scores in intervals and construct a histogram depicting the number of students who scored in each interval.
- 2.) In which interval do most test scores lie?
- 3.) Which interval contains the least number of test scores?
- 4.) What is the average number of points scored?
- 5.) What is the range of test scores?
- 6.) What is the median test score?
- 7.) What percent of all scores lie in an interval from eleven to fifteen inclusive?
- 8.) What is the mode of the test scores?
- 9.) How many students received a grade of 75% or better?
- 10.) If 60% of the total possible points represents a passing grade, how many students passed the test?
- 11.) How many more students scored in the interval 16 to 20 than in the interval 11 to 15?
- 12.) Did any student receive the median score?
- 13.) How many students scored higher than the mean?
- 14.) How many students scored below the median?
- 15.) What percent of the students failed the test?

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*
Frequency
*
*
Polygon
*

A frequency
*polygon*is a line graph which can be used to represent the frequency of a set of numbers. It is formed by connecting a series of points. The abscissa of each point is the midpoint of the interval in which the point lies. The ordinate of each point is the frequency for the interval. The polygon is closed at each end by drawing a line from the endpoints to the horizontal axis at the midpoint of the next interval.

Example: The number of students in twenty-five classes of a high school are as follows: 15, 27, 22, 18, 10, 25, 27, 12, 19, 26, 14, 12, 22, 20, 21, 17, 21, 20, 13, 12, 22, 27, 21, 17, 27. Arrange the class sizes in intervals and construct a frequency polygon depicting the number of classes in each interval.

*(figure available in print form)*

*(figure available in print form)*

Exercises: The students in a certain class received the following marks on a test:

94 | 96 | 72 | 90 | 87 | 84 |

72 | 90 | 60 | 68 | 93 | 78 |

68 | 80 | 94 | 75 | 87 | 90 |

87 | 78 | 81 | 85 | 70 | 87 |

- 1.) Group the data in intervals and construct a frequency polygon to show the number of students in each interval.
- 2.) What is the mode?
- 3.) What is the mean score?
- 4.) What is the range?