Identify sampling methods and recognize biased samples

Transcription

1 9-1 Samples and Surveys Identify sampling methods and recognize biased samples Vocabulary population (p. 462) sample (p. 462) biased sample (p. 463) random sample (p. 462) systematic sample (p. 462) stratified sample (p. 462) convenience sample (p. 462) voluntary-response sample (p. 462) Additional Eamples Eample 1 Identify the sampling method used. A. In a county survey, Democratic Party members whose names begin with the letter D are chosen. The is to survey members whose names begin with D. B. A telephone company randomly chooses customers to survey about its service. Customers are chosen by. 181 Holt Mathematics

2 9-1 CONTINUED Eample 2 Identify the population and the sample. Give a reason why the sample could be biased. A. A record store manager asks customers who make a purchase how many hours of music they listen to each day. Population Sample Possible Bias Customers who make a purchase might be more in music than others in the store. Try This 1. Identify the sampling method used. In a county survey, families with 3 or more children are chosen. 2. Identify the population and the sample. Give a reason why the sample could be biased. People attending a baseball game were asked if they support the construction of a new stadium in the city. Population Sample Possible Bias People that attend a baseball game are more likely to the construction of a new stadium. 182 Holt Mathematics

3 9-2 Organizing Data Organize data in tables and stem-and-leaf plots Vocabulary stem-and-leaf plot (p. 467) back-to-back stem-and-leaf plot (p. 468) line plot (p. 467) Venn diagram (p. 468) Additional Eamples Eample 1 Use a line plot to organize the math eam scores. Student Test Scores Find the least value,, and the greatest value,, in the data set. Then draw a number line from to. Place an above each number on the number line for each time it appears in the data set There are and numbers in the data set s above the number line. 183 Holt Mathematics

4 9-2 CONTINUED Eample 2 List the data values in the stem-and-leaf plot Key: 1 2 means 12 The data values are Eample 3 Use the given data to make a back-to-back stem-and-leaf plot. U.S. Representatives for Selected States, 1950 and 2000 IL MA MI NY PA Eample 4 Make a Venn diagram to show how many 8th grade students play soccer. Survey Results Grade Sport Grade Sport 6 baseball 8 tennis 6 tennis 7 soccer 8 soccer 7 baseball 8 baseball 6 soccer 7 soccer 8 soccer Draw two circles. Label one circle 8th Grader and the other circle Soccer Player. The region that overlaps represents the characteristics that are shared by both sets of data. 184 Holt Mathematics

5 9-3 Measures of Central Tendency Find appropriate measures of central tendency Vocabulary mean (p. 472) median (p. 472) mode (p. 472) outlier (p. 472) range (p. 472) Additional Eamples Eample 1 Find the mean, median, mode, and range of the data set. 21, 21, 28, 29, 30, 28, 32 mean: the values Divide by, the number of values. median: values 3 values the values. mode: The values occur two times. range: 185 Holt Mathematics

6 9-3 CONTINUED Eample 2 Determine and find the most appropriate measure of central tendency or range for each situation. Justify your answer. A. Competitors received the following scores for their performance in a gymnastic competition: 9.0, 8.3, 8.5, 9.1, 8.2, 8.9, 8.2, 9.0, 8.8, 8.3, 9.2, 9.0, 8.6. What score occurred most often? Find the mode.,,,, 8.5, 8.6, List the scores in. 8.8, 8.9,,,, 9.1, 9.2 Underline the scores that appear more than. Nine appears most frequently. The is. Eample 3 Employees at a store earned $275, $330, $290, $300, $350, $365, and $310 during one week. What measure of central tendency or range would make the salaries look the highest? Find each measure of central tendency and range of the data set. mean: $275 $330 $290 $300 $350 $365 $310 7 $2, 220 $ 7 median: $275, $290, $300, $, $330, $350, $365 Underline the value. mode: There is mode. range: $310 $275 $ The would make the salaries look the highest. 186 Holt Mathematics

7 9-4 Variability Find measures of variability Vocabulary variability (p. 476) quartile (p. 476) bo-and-whisker plot (p. 477) Additional Eamples Eample 1 Find the first and third quartiles of each data set. A. 15, 83, 75, 12, 19, 74, 21 21, the values. first quartile: third quartile: 187 Holt Mathematics

8 9-4 Variability Find measures of variability Vocabulary variability (p. 476) The spread of values in a set of data. quartile (p. 476) Three values, one of which is the median, that divide a data set into four equal parts. bo-and-whisker plot (p. 477) A graph that displays the highest and lowest quarters of data as whiskers, the middle two quarters of the data as a bo, and the median. Additional Eamples Eample 1 Find the first and third quartiles of each data set. A. 15, 83, 75, 12, 19, 74, 21 12, 15, 19, first quartile: 21, 74, 75, 83 Order the values. 15 third quartile: Holt Mathematics

9 9-5 Displaying Data Display data in bar graphs, histograms, and line graphs Vocabulary double-bar graph (p. 485) frequency table (p. 485) histogram (p. 485) double-line graph (p. 486) Additional Eamples Eample 1 Make a double-bar graph. The following are the number of books read in one month by some boys and girls in Grade 8: Books read Boys Girls The frequencies are the the bars in the bar graph. Use a different each gender. to represent of Books Read Boys Girls Frequency Number of Books Read by 8th-grade Students 189 Holt Mathematics

10 9-5 CONTINUED Eample 2 Jimmy asked 12 children how much money they received from the tooth fairy. Use the data to make a histogram First, make a intervals of $1.00. Then make a. table with Frequency Data Data Set 1 Set Data Eample 3 Make a double-line graph of the given data. Use the graph to estimate the number of CDs and DVDs sold in Create two sets of ordered pairs and plot them on a grid. Connect each set of points with different color lines Then find the points on the graph that correspond to The graph shows about sold. CDs sold and DVDs The Music Shop CD and DVD Sales Year CDs sold DVDs sold Frequency Data Data Set 1 Set Data 190 Holt Mathematics

11 9-6 Misleading Graphs and Statistics Recognize misleading graphs and statistics Additional Eamples Eample 1 Eplain why the graph is misleading Stock Value The graph suggests that the stock will continue to increase through, but there s no way to foresee the. Eample 2 Eplain why each statistic is misleading. A. Four out of five dentists surveyed preferred UltraClean toothpaste. This statement does not give the size or state what UltraClean toothpaste was with. B. Shopping at Save-a-Lot can save you up to $100 a month! The words save up to $100 mean that the is $100, but there is no you can save that you will save that amount. 191 Holt Mathematics

12 9-7 Scatter Plots Create and interpret scatter plots Vocabulary scatter plot (p. 494) correlation (p. 494) line of best fit (p. 494) Additional Eamples Eample 1 Use the given data to make a scatter plot of the weight and height of each member of a basketball team. Height (in.) Weight (lb) Weight (lb) Height (in.) The points on the scatter plot are ( ), ( ), ( ), ( ), and ( ). 192 Holt Mathematics

13 9-7 CONTINUED Eample 2 Do the data sets have a positive, a negative, or no correlation? A. the size of a jar of baby food and the number of jars of baby food a baby will eat correlation: The food in each jar, the number of jars of baby food a baby will eat. B. the speed of a runner and the number of races she wins correlation: The the runner, the races she will win. C. the size of a person and the number of fingers he has correlation: The size of a person number of fingers he has. affect the Eample 3 Use the data to predict how much a worker will earn in tips in 10 hours. Tips ($) Hours According to the graph a worker who works 10 hours should earn about $. 193 Holt Mathematics

14 9-8 Choosing the Best Representation of Data Select the best representation for a set of data Additional Eamples Eample 1 A. Which graph is a better display of the data on temperature? Temperature Measurements Temperature (F) Time of Day 8 Since the question asks about change in data over, the is the better representation. B. Which graph is a better display of the data on temperature? Gasoline Prices Price ($) Gallons Since the question asks about the relationship of two data sets, the is the better representation. 194 Holt Mathematics

15 9-8 CONTINUED Eample 2 The Singer family keeps the budget shown below for their monthly epenses. Choose an appropriate data display and draw the graph. Which two categories account for one-fifth of their budget? Groceries $400 Utilities $330 Mortgage $850 Clothing $200 Entertainment $100 Auto $500 Savings $500 Misc. $ Understand the Problem You are looking for the best data display and the two categories that account for one-fifth of the budget. 2. Make a Plan You need to compare each category to the whole. Find the percentage of each category and make a graph. 3. Solve Make a circle graph. To find which two categories account for one-fifth of the budget, convert one-fifth to a percent. One-fifth equals %. The two categories that add to 20% are or and. 4. Look Back Look at the table. Saving or auto plus entertainment equals $, which is about 20% or one-fifth of the budget. 195 Holt Mathematics