Using the mean and the median
Using the mean and the median.
Introduction. Both the mean and the median are commonly used to describe what would be a "typical" value in a set of data. The mean is the usual average: add up all the observations in a data set and divide by the number of observations. The median is a value that (roughly) divides the data into halves, so that half of the values are greater than the median and half are less.
To find the median for a set of data, first put the data in order from lowest to highest. If the number of observations is odd, the single "middle-most" value is the median. If the number of observations is even, then the median is the average of the two middle most numbers.
For example, suppose you surveyed four friends and ask them how many cans of pop they have consumed in the past week. If their data are: 13, 13, 4, 10, then the mean would be 40/4 and the median would be 11.5 cans. (Arranged in order, the data are 4, 10, 13, 13. The two middle-most values are 10 and 13, which average to 11.5.) A line plot of the data would look like the following:
x
x x x .
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Activity I: Case One Scenario
Joe Basketball Player is a relatively good basketball player, but not a superstar. There are two different teams that want him to play with them. He is able to look at the average points per game stats for the "starting five" players for the last ten games in order to make his decision. He has come to you to get some advice in making his decision.
The stats for Team A are: 10, 11, 12, 13, 14.
Mean__________ Is this value a typical representation of this set of data?_________
Median__________ Is this value a typical representation of this set of data?_________
Make a line plot of the stats for Team A
The stats for Team B are: 2, 3, 3, 4, 48.
Mean___________ Is this value a typical representation of this set of data?_________
Median___________ Is this value a typical representation of this set of data?_________
Make a line plot of the stats for Team B
What is the average number of points per game for Team A? _______ Team B? ______
Which team would you advise him to join? ___________________
If the best player for each team got hurt and would not be able to play for the rest of the season which team would you advise him to join? _____________
Did your advice change with the last scenario? Why or why not?
Case Two Scenario
You have applied for a job at two small companies. Both companies have told you that the job is yours if you wish to accept it. You have been able to find out the salaries for the six employees of the two companies.
Company A: 15,000; 15,000; 15,000; 15,000; 80,000; 100,000
Mean_____________ Typical ______________
Median___________ Typical ______________
Mode____________ Typical ______________
Company B: 35,000, 36,000, 36,000, 38,000, 45,000, 50,000
Mean_____________ Typical ______________
Median___________ Typical ______________
Mode____________ Typical ______________
Which company has the highest mean salary? ___________________
Which company has the highest median salary? _________________
Which company has the highest mode? ________________________
Which of these measures of central tendency gives you as a prospective employee a better idea of what you might expect in the way of a salary from each company?
Which company would you rather take the job with? And why?
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