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?