Mean, Median, Mode, and Range

Mean, Median, Mode, and Range Mean, median, and mode are measures of central tendency; they measure the center of data. Range is a measure of dispersion; it measures the spread of data. The mean of a data set is the sum of the values divided by the number of values. The mean is also called the average. The median of a data set is the middle value when the values are written in numerical order. If a data set has an even number of values, the median is the mean of the two middle values. The mode of a data set is the value that occurs most often. A data set can have no mode, one mode, or more than one mode. The range of a data set is the difference between the greatest value and the least value. Find the mean, median, mode(s), and range of the data. Daily High Temperatures, Week of June 21 27 Day Sunday Monday Tuesday Wednesday Thursday Friday Saturday Temperature (8F) 76 74 7 69 7 75 78 Mean Add the values. Then divide by the number of values. 76 1 74 1 7 1 69 1 7 1 75 1 78 5 512 mean 5 512 4 7 ø 73 The mean of the data is about 738F. Median Write the values in order from least to greatest. Find the middle value(s). 69, 7, 7, 74, 75, 76, 78 median 5 74 The median of the data is 748F. Mode Find the value that occurs most often. mode 5 7 The mode of the data is 78F. Range Subtract the least value from the greatest value. range 5 78 2 69 5 9 The range of the data is 98F. PRACTICE Find the mean, median, mode(s), and range of the data. 1. Apartment rents: $65, $8, $7, $525, $675, $75, $5, $65, $725 2. Ages of new drivers: 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 18, 18 3. Monthly cell-phone minutes: 581, 713, 423, 852, 948, 337, 81, 64, 897 4. Prices of a CD: $12.98, $14.99, $13.49, $12.98, $13.89, $16.98, $11.98 5. Cookies in a batch: 36, 6, 52, 44, 48, 45, 48, 41, 6, 45, 38, 55, 6, 48, 4 6. Ages of family members: 41, 45, 8, 1, 4, 44, 3, 5, 42, 42, 13, 14, 67, 7 7. Hourly rates of pay: $8.8, $6.5, $1.85, $7.9, $9.5, $9, $8.7, $12.35 8. Weekly quiz scores: 8, 9, 8, 1, 1, 7, 9, 8, 9, 9, 1, 7, 8, 6, 1, 9, 9, 8, 8, 1 9. People on a bus: 9, 14, 5, 22, 18, 3, 6, 25, 18, 12, 15, 1, 8, 22, 1, 11, 2 Skills Review Handbook 15

Graphing Statistical Data There are many ways to display data. An appropriate graph can help you analyze data. The table at the right summarizes how data are shown in some statistical graphs. Use the bar graph to answer the questions. a. On which day of the week were the greatest number of cars parked in the student lot? c The tallest bar on the graph is for Friday. So, the answer is Friday. b. How many cars were parked in the student lot on Monday? Bar Graph Circle Graph Line Graph Cars 12 8 4 Compares data in categories. Compares data as parts of a whole. Shows data change over time. Cars Parked in Student Lot c The bar for Monday shows that about 7 cars were parked in the student lot. M Tu W Th F Use the circle graph to answer the questions. a. Which type of transportation is used almost half the time? c Almost half of the total area of the circle is labeled Car 45%. So, a car is used almost half the time. b. Which type of transportation is used the least often? c The smallest part of the circle is labeled Bus 2%. So, a bus is used the least often. Transportation to School Car 45% Bus 2% Walk or bike 35% Use the line graph to answer the questions. a. In which month(s) was Jamie s balance $25? c The points on the graph to the right of $25 show that Jamie s balance was $25 in May and December. b. Between which two consecutive months did Jamie s balance increase the most? c Of the graph s line segments that have positive slope, the graph is steepest from June to July. So, Jamie s balance increased the most between June and July. Dollars Jamie s Savings Account Balance 4 3 2 1 J F M A M J J A S O N D Month 16 Student Resources

PRACTICE Use the line graph to answer Exercises 1 5. 1. At which hour did Ferraro s have 22 diners? 2. At which hour did Ferraro s have the most diners? 3. How many diners were at Ferraro s at 11 P.M.? Were they gone by midnight? 4. Between which two consecutive hours did the number of diners at Ferraro s change the most? 5. How many fewer diners were at Ferraro s at 1 P.M. than at 6 P.M.? Diners 3 2 1 Friday at Ferraro s Restaurant 5 6 7 8 9 1 11 12 Time (hours since noon) Use the bar graph to answer Exercises 6 8. 6. In which season were the fewest students born? 7. In which season(s) were 7 students born? 8. How many more students were born in spring than in summer? Students 12 8 4 Seasons of Students Birthdays Fall Winter Spring Summer Use the circle graph to answer Exercises 9 11. 9. What is the heat source of more than half the homes in the United States? 1. What percent of homes in the United States are heated with electricity? 11. If you randomly selected 5 U.S. homes, about how many would be heated with fuel oil? Heat Sources for U.S. Homes Natural gas 52% Electricity 22% Fuel oil 1% Other 16% 12. The table below shows the high temperatures in degrees Fahrenheit for one week. Display the data in a line graph. Mon. Tues. Wed. Thurs. Fri. Sat. Sun. 83 89 79 73 69 67 71 13. A high school conducted a survey to determine the numbers of students involved in various school activities. Display the survey results in a bar graph. Computer Music Yearbook Drama Student council Chess 34 75 16 57 28 12 14. The table below shows the items sold at a café in one day. Display the data in a circle graph. Juice Soda Water Muffin Cookie 95 18 1 55 4 Skills Review Handbook 17

Organizing Statistical Data Because it is difficult to analyze unorganized data, it is helpful to organize data using a line plot, stem-and-leaf plot, histogram, or box-and-whisker plot. Sydney s math test scores are 9, 85, 88, 95, 1, 77, 85, 1, 8, 77, and 9. a. Draw a line plot to display the data. Make a number line from 75 to 1. Each time a value is listed in the data set, draw an X above the value on the number line. 3 3 3 3 3 3 3 75 77 8 85 88 9 95 1 b. Draw a stem-and-leaf plot to display the data. First write the leaves next to their stems. Then order the leaves from least to greatest. 7 7 7 7 7 7 8 5 8 5 8 5 5 8 9 5 9 5 1 Key: 7 7 5 77 1 Key: 7 7 5 77 c. Draw a histogram to display the data. First make a frequency table. Use equal intervals. Score Tally Frequency 71 8 3 3 81 9 5 5 91 1 3 3 Then make a histogram. Sydney s Math Test Scores 6 Frequency 4 2 71 8 81 9 91 1 Score d. Draw a box-and-whisker plot to display the data. Write the data in order from least to greatest. Ordered data are divided into a lower half and an upper half by the median. The median of the lower half is the lower quartile, and the median of the upper half is the upper quartile. 77 77 8 85 85 88 9 9 95 1 1 Low Lower Median Upper High value quartile quartile value Plot the median, quartiles, and low and high values below a number line. Draw a box between quartiles with a vertical line through the median as shown. Draw whiskers to the low and high values. 75 Sydney s Math Test Scores 8 85 9 95 1 77 8 88 95 1 18 Student Resources

PRACTICE Use the following list of ticket prices to answer Exercises 1 4: $5, $42, $65, $54, $7, $65, $59, $3, $67, $49, $54, $3, $73, $47, and $54. 1. Draw a line plot to display the data. 2. How many ticket prices are $5 or less? 3. Draw a stem-and-leaf plot to display the data. 4. What is the range of ticket prices costs? Use the following list of hourly wages of employees to answer Exercises 5 8: $8.5, $6, $1, $14.25, $5.75, $7, $6.5, $14, $1, $9, $6.5, $8.25, $8.5, $11.25, $7, $16, $12, $6, $6.75. 5. Draw a histogram to display the data. Begin with the interval $5. to $6.99. 6. Copy and complete: The greatest number of employees earn from? to? per hour. 7. Draw a box-and-whisker plot to display the data. 8. Copy and complete: About half of the employees have an hourly wage of? or less. Use the line plot, which shows the results of a survey asking people the average number of e-mails they receive daily, to answer Exercises 9 and 1. 9. Copy and complete: Most people surveyed receive an average of? e-mails per day. 1. How many people receive an average of more than 1 e-mails per day? 3 3 3 3 3 3 3 4 5 7 1 12 15 17 Use the stem-and-leaf plot, which shows the weights (in pounds) of dogs at an animal shelter, to answer Exercises 11 13. 11. How many dogs were at the shelter? 12. Find the median of the data. 13. Find the range of the data. 2 2 5 5 9 3 1 3 5 8 4 1 2 2 5 6 7 5 3 5 8 9 6 4 5 Key: 2 2 5 22 Use the histogram to answer Exercises 14 16. 14. Which age group had the greatest attendance at the baseball game? Which had the least? 15. How many children up to the age of 9 years attended the baseball game? 16. Which age group had the same attendance as the oldest group? People 4 2 Baseball Game Attendance 9 1 19 2 29 3 39 Age (years) 4 49 5 59 6 69 Use the box-and-whisker plot to answer Exercises 17 19. 17. What is the median number of songs on Sam s CDs? 18. What is the upper quartile of songs on Sam s CDs? 19. What is the least number of songs on one of Sam s CDs? What is the greatest number? Number of Songs on Sam s CDs 1 12 14 16 18 1 11 12 14 18 Skills Review Handbook 19