Means & Medians Unit 2

Parameter - ► Fixed value about a population ► Typically unknown

Statistic - ► Value calculated from a sample

Measures of Central Tendency ► Median - the middle of the data; 50 th percentile  Observations must be in numerical order  Is the middle single value if n is odd  The average of the middle two values if n is even NOTE: n denotes the sample size

Measures of Central Tendency ► Mean - the arithmetic average  Use  to represent a population mean  Use x to represent a sample mean  Formula:  is the capital Greek letter sigma – it means to sum the values that follow parameter statistic

Measures of Central Tendency ► Mode – the observation that occurs the most often  Can be more than one mode  If all values occur only once – there is no mode  Not used as often as mean & median

Suppose we are interested in the number of lollipops that are bought at a certain store. A sample of 5 customers buys the following number of lollipops. Find the median The numbers are in order & n is odd – so find the middle observation. The median is 4 lollipops!

Suppose we have sample of 6 customers that buy the following number of lollipops. The median is … The numbers are in order & n is even – so find the middle two observations. The median is 5 lollipops! Now, average these two values. 5

Suppose we have sample of 6 customers that buy the following number of lollipops. Find the mean To find the mean number of lollipops add the observations and divide by n.

Using the calculator... 1.Press Stat and chose option 1: Edit 2.Clear anything in the list and enter your values into L1 3.Hit 2 nd Quit to get back to the home screen 4.Hit 2 nd Stat (List) 5.Move to Math and chose the option you would like to compute 6.Inside the parenthesis you must tell it what list to use. (in this case we are using L1). Then press enter.

What would happen to the median & mean if the 12 lollipops were 20? The median is... 5 The mean is What happened?

What would happen to the median & mean if the 20 lollipops were 50? The median is... 5 The mean is What happened?

Resistant - ► Statistics that are not affected by outliers ► Is the median resistant? ► Is the mean resistant? YES NO

Look at the following data set. Find the mean

Look at the following data set. Find the mean & median. Mean = Median = Create a histogram with the data. (use x-scale of 2) Then find the mean and median. 27 Look at the placement of the mean and median in this symmetrical distribution.

Look at the following data set. Find the mean & median. Mean = Median = Create a histogram with the data. (use x-scale of 8) Then find the mean and median Look at the placement of the mean and median in this right skewed distribution.

Look at the following data set. Find the mean & median. Mean = Median = Create a histogram with the data. Then find the mean and median Look at the placement of the mean and median in this skewed left distribution.

Recap: ► In a symmetrical distribution, the mean and median are equal. ► In a skewed distribution, the mean is pulled in the direction of the skewness. ► In a symmetrical distribution, you should report the mean! ► In a skewed distribution, the median should be reported as the measure of center!