What is an average OR arithmetic mean? Activity.
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Transcript of What is an average OR arithmetic mean? Activity.
Measures of CentralTendency
What is an average OR arithmetic mean?
Activity
Where do we see averages(means)?
How are averages(means) used?
How do we calculate averages (means)?Add the numbers of the data set together and divide by the number of data points.
During the first half, Harvey ran the following number of yards for his 5 carries: 9 11 16 4 10 What is the average (mean) number of yards per carry that Harvey ran in the first half?
Data setData points
9 + 11+ 16 + 4 + 10 =
5
10
The person’s temperature is fine.
Agree Disagree
A Closer Look at Averages (Means) . . .
A Closer Look at Averages (Means) . . .
How would you determine the average(mean) wealth of the guests staying at the Ritz Hotel on a particular day?
500 Guests
Would the average(mean) be affected if Bill Gates stayed at the hotel?
Extreme values affect the mean.
62.7 Billion
Mean: $1,000,000
Mean: $126,398,000
500 guests - each having a wealth of $1,000,000
499 Guests each having a wealth of $1,000,000 and Bill Gates having a wealth of $62.7 Billion
499,000,00062,700,000,000
63,199,000,000
Comparison of Averages(Means) with an Extreme Value
What is a median?The middle number (in a sorted list of numbers).
13 15 18 21 11 12 10
Middle
10 11 12 13 15 18 21
Sort
1
2Middle
Example: Cost of Dinners at a Restaurant:
What does the median cost of dinners tell us?
Finding the median
Middle
10 11 12 13 14 15 18 21
13+14 = 13.5
2
If the number of data points is odd, the median is the mean (the average) of the middle two values:
•The median does not have to be a value in the dataset.
•The position of the median can be found by: (the number of data points + 1) ÷ 2
The restaurant adds a new dinner item to the menu:
Practice Finding the MedianWhat is the median points scored in the Falcons 2013 regular season?
40 27 27 30 24 23 30 19 27 23 24 23 20 34 31 17
17 19 20 23 23 23 24 24 27 27 27 30 30 31 34 40
Median: 25.5
•Sort•Find position of middle value(s): (Number data points + 1) 2• If necessary, average middle values
What is the mode?The mode is the number repeated most often.
40 27 27 30 24 23 30 19 27 23 24 23 20 34 31 17
Example:What is the mode of the points scored in the Falcons 2013 regular season?
Do you think every data set has a mode?
Do you think a data set could have more than one mode?
Toying with Measures Activity
1. Calculate the mean, median, and mode of purchasing the original 6 toys.
2. Make predictions about whether the purchase or return of toys will cause the measures of central tendency to increase or decrease.
3. Calculate the mean, median, and mode of the purchased/returned toys.
4. Discuss. Do the results match your predictions?