# means & medians unit 2. parameter - ► fixed value about a population ► typically unknown

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• Means & MediansUnit 2

• Parameter -Fixed value about a populationTypically unknown

• Statistic -Value calculated from a sample

• Measures of Central TendencyMedian - the middle of the data; 50th percentileObservations must be in numerical orderIs the middle single value if n is oddThe average of the middle two values if n is evenNOTE: n denotes the sample size

• Measures of Central TendencyMean - the arithmetic averageUse m to represent a population meanUse x to represent a sample meanFormula:

S is the capital Greek letter sigma it means to sum the values that followparameterstatistic

• Measures of Central TendencyMode the observation that occurs the most oftenCan be more than one modeIf all values occur only once there is no modeNot 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.2 3 4 8 12The 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 2 3 4 6 8 12The 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.2 3 4 6 8 12To find the mean number of lollipops add the observations and divide by n.

• Using the calculator . . .Press Stat and chose option 1: EditClear anything in the list and enter your values into L1Hit 2nd Quit to get back to the home screenHit 2nd Stat (List) Move to Math and chose the option you would like to computeInside 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?2 3 4 6 8 20The median is . . .5The mean is . . .7.17What happened?

• What would happen to the median & mean if the 20 lollipops were 50?2 3 4 6 8 50The median is . . .5The mean is . . .12.17What happened?

• Resistant -Statistics that are not affected by outliers

Is the median resistant?Is the mean resistant?

YESNO

• Look at the following data set. Find the mean.2223242525262930

• Look at the following data set. Find the mean & median.

Mean =Median =212323242525262626272727272830303031323227Create a histogram with the data. (use x-scale of 2) Then find the mean and median.27Look at the placement of the mean and median in this symmetrical distribution.

• Look at the following data set. Find the mean & median.

Mean =Median =222928222425282125232423263638622325Create a histogram with the data. (use x-scale of 8) Then find the mean and median.28.176Look 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 =214654475360555560565858585862636458Create a histogram with the data. Then find the mean and median.54.588Look 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!

*Use scale of 2 on graph*Use scale of 2 on graph*Use scale of 2 on graph