Chapter 4B: Measures of Center Objective: To calculate and interpret measures of center given sets of data CHS Statistics

3 Types of Center Measurement 1)Mean 2)Median 3)Mode

3 Types of Center Measurement

1)Mean (continued) Ex) The prices (in dollars) for a sample of round trip flights from Chicago to Cancun are listed. What is the mean price of the flights?

3 Types of Center Measurement

2) Median (continued) Example: The flight priced at $432 is no longer available. What is the median price of the remaining flights?

3 Types of Center Measurement 3) Mode o The value(s) in a set of data that occurs the most. o If no value is repeated, we say that is has no mode. However, one could argue that all values are modes…. o Example: Find the mode of the flight prices

Outliers o A value that is much higher or lower than the mean. We will discuss the rule of thumb for identifying outliers at a later date. o Affect mean? o Affect median? Robert Wadlow 8 Ft 11.1 inches Bao Xishun 7 ft 9 inches He Pingping 2 ft 4 inches

Outliers Example: The President of a company makes $100,000. His 6 computer technicians make $30,000, $32,000, $35,000, $38,000, $38,000, and $42,000. The secretary makes $20,000. What are the mean, median, and mode of these data? What are the mean, median, and mode of these data, if the president’s salary is taken out?

Comparison of Center Measures Name Definition How Common?Existence Takes Every Value into Account Affected by Extreme ValuesAdvantageDisadvantage Mean Median Mode

General Notes About Center Measures When data are fairly symmetric, the mean and median tend to be about the same, but the mean is usually a better measure of center. If the data are skewed, the median is the better measure of center.

What’s Your Height in Inches? Input these data into L1 in your graphing calculator. – STAT  Edit Create a histogram of these data: – 2 nd  Statplot  ON  Select Histogram  Select L1 for data in this case  Frequency: 1 – Zoom  9: ZoomStat Are these data skewed?

What’s Your Height in Inches? Depending on the shape of the distribution, find an appropriate measure of center, mean or median: With data still in your L1: – STAT  Calc  1: One-Variable Stats

Day 1 Assignment: pp # 13ab, 14ab, 27, 28, 31, 37 Be sure to check you answers on the solutions manual online!

Day 2: Weighted Mean

Weighted Mean You are taking a class in which your grade is determined from five categories: 50% from your test mean, 15% from your midterm, 20% from your final exam, 10% from your computer lab work, and 5% from your homework. Your scores are 86 (test mean), 96 (midterm), 82 (final exam), 98 (computer lab), and 100 (homework). What is the weighted mean of your scores? Did you earn an A?

Mean of a Frequency Distribution

o Example: Class midpointsFrequency

Mean of a Frequency Distribution o Use your calculator! o STAT  Edit o Put midpoints into L1 o Put frequencies into L2 o STAT  Calc  1-Variable Stats and enter L1 (2 nd  1), L2 (2 nd  2)* Do not forget to identify L2 as the frequency list! Your calculation will be incorrect if you do not do this. * Do not forget to identify L2 as the frequency list! Your calculation will be incorrect if you do not do this.

Day 2 Assignment: pp # 29, 30 (skip standard deviation) Be sure to check you answers on the solutions manual online!