1. Bell Work: Olivya is 6 feet 2 inches tall. How many inches tall is Olivya?

2. Answer: 74 inches

3. Lesson 7: Rates and Average, Measures of Central Tendency

4. Rate*: a division relationship between two measures. Unit Rate*: a division relationship between two measures where the second measure is 1.

5. Unit Rate Examples: 65 miles per hour (65mph) 24 miles per gallon (24mpg) 32 feet per second (32ft/sec) 15 cents per ounce ($0.15/oz)

6. Rate problems involve the two units that form the rate. Number of hours x 65 miles per hour = number of miles Number of gallons x 24 miles per gallon = number of miles

7. Example: Driving at an average speed of 55 mph, about how far will the driver travel in 6 hours?

8. Answer: We are given the rate and the number of hours. We will find the number of miles. 6 hours x 55 miles per hour = n miles The driver will travel about 55 miles each hour, so in 6 hours the driver will drive 6 x 55 or 33o miles.

9. Example: Madalyn finished the 100 km bike race in four hours. What was her average speed in kilometers?

10. Answer: 100km/4hr = 25km/1hr Madalyn’s average speed was 25km/hr

11. Example: Traveling at an average rate of 58 miles per hour, about how long would it take a car to travel 20 miles?

12. Answer: At 60 mph a car travels on mile each minute. Since 58 mph is nearly 60 mph, the trip would take a little more than 20 minutes.

13. In these examples, we used the term average speed. The speed of the truck in the first example probably fluctuated above and below its average speed. However, the total distance traveled was the same as if the truck had traveled at a steady speed – the average speed.

14. Average*: a central number that is found by dividing the sum of the elements of a set by the number of elements. (the average is more specifically called the mean)

15. Calculating an average usually involves two steps. First we find the total by combining, then we make equal groups.

16. Example: In the four 8 th grade classrooms at Keeler School there are 28, 29, 31 and 32 students. What is the average number of students in an 8 th grade classroom?

17. Answer: Average = (28 + 29 + 31 + 32) / (4) =120 / 4 =30 students on average

18. The average or mean is one measure of central tendency. We will now discuss 2 other measures.

19. Median*: the central number in a set of data. Mode*: the most frequently occurring number.

20. To find the median we arrange the number in order from least to greatest and select the middle number or the average of the two middle numbers. To find the mode we select the number that appears most often.

21. Example: Find the mean, median and mode of the following numbers. 170, 208, 185, 209, 181, 183, 191, 175, 175, 187, 195, 219

22. Answer: Mean = about 190

23. Answer: Median = 185 and 187 = 185 + 187 / 2 = 186

24. Answer: Mode = 175

25. Range*: the difference between the greatest and least numbers in the set. What was the range of the last set of numbers?

26. Answer: 219 – 170 = 49

27. HW: Lesson 7 #1-30 Due tomorrow