Data Analysis Goal: I can use shape, center, and the spread to describe characteristics of the data set. I can understand the effects of outliers on a data set. (S-ID.3) Outliers

Outliers Effect on Measures of Center  Within a data set, one or more values may be much higher or lower than most of the data. These extreme values are called outliers.

VOCABULARY:  Mean –  Median –  Mode – I can find measures of center. the sum of the values in the set divided by the number of data in the set the middle value when the set is ordered from greatest to least or least to greatest the value or values that occur most often

Test Scores- Outliers Effect on Measures of Center Calculate the measures of center for Peter's test scores.  Mean –  Median –  Mode –

Test Scores Calculate the measures of center for the new data set: {0, 82, 85, 88, 89, 92, 94, 94}  Mean –  Median –  Mode – Peter was out sick for the next test and hade to make it up. So the teacher entered a 0 for his grade. How does the 0 affect the measures of center for his test score data? With the 0 (outlier) the mean decreased significantly from to 78 because the outlier skewed the data to the left. With the 0 (outlier) the median decreased slightly from 89 to 89 because the outlier skewed the data to the left. With the 0 (outlier) the mode stayed the same and was not effect.

When should one measure of center be used over another?  Mean  Median  Mode

Which measure of center would be appropriate for this data? Since the data set includes outliers, the measure of center that best represents the data is the median than the mean. Quantitative data is better represented by the mean or median.

Which measure of center would be appropriate for this data? Since the data set does not includes outliers, the measure of center that best represents the data is the mean than the median. Quantitative data is better represented by the mean or median.

Which measure of center would be appropriate for this data? Categorical data is better represented by the mode.

Example 2:Your Turn Below is the wait time to get a driver’s license at the AZ DMV. {25, 26, 35, 47, 60, 18, 15, 33, 42, 54} Tell whether the mean, median or mode best represent the data. Explain your reasoning. Mean:Median:Mode: 355/10 = 35.5 {15, 18, 25, 26, 33, 35, 42, 47, 54, 60} = 34 {No Mode} Since the data set does not includes outliers, the measure of center that best represents the data is the mean than the median.

Example 3:Your Turn Dexter bowled five games one night with scores of 161, 178, 163, 183, and 161. Find the mean, median, mode and range Find the mean, median, mode and range. Tell which would best represent the data. Explain.Mean:Median:Mode: 846/5 = {161, 161, 163, 178, 183} = Since the data set does not includes outliers, the measure of center that best represents the data is the mean than the median.