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Warm Up 1. Tell me the mean and the median for the following data sets Math Test Scores Class 1: 99, 76, 84, 70, 45, 73, 88 Class 2: 75, 100, 65, 70, 88, 95, 94 2. Which class did better? Elaborate and clarify with details to support your answer. Comparing Data Sets by Measures of Center (Central Tendency) and Spread Measures of Center (Central Tendency) • Tells us something about the middle of the distribution. • Mean – tells us the average value • Median – tell us the middle value • Mode – tell us the most frequent value -Median and Mean can be effected by extreme values (very high or very low scores) outliers Measures of Center: Normal Distribution -in a normal distribution, the mean, median and mode is the max. value (highest point) of the graph: Shapes of Distribution Non Symmetric Skewed Left (negatively skewed) Left Skew tail Skewed Right (positively skewed) Right Skew tail 5 Right Skew Skew on shape of distribution in relation to mean and median If you have right skew, the mean will be to the right of (greater than) the median, as the mean follows the tail of the distribution. median mean Right Skew tail 6 Left Skew Skew on a dot plot in relation to mean and median If you have left skew, the mean will be to the left of (less than) the median, as the mean follows the tail of the distribution. median mean tail Left Skew 7 Measure of Center: Box Plots • The median value on a box plot is the line drawn inside the box. • Tell me the median for each of the different countries: Center: Comparing Data Sets • Compute and compare the mean for the three data sets graphed below: • A: Class 1; B: Class 2; C: Class 3 Math Test Scores Explain your reasoning. Measures of Spread • Interquartile Range = Upper quartile (Q3) – lower quartile (Q1) Example: What is the interquartile range (IQR) for the following first and second shifts ? Compare the two. Measures of Spread • Standard Deviation – shows the distance/spread of the data points from the mean. • High value – means the spread of values from the mean is far. • Low Value – means the spread of values from the mean is close Standard Deviation Turn and Talk: Standard Deviation • Compare, and elaborate on, the spread of the two data distributions shown in the graph below: Title: Number of Video Games Owned Key Blue = high school students Red = College students Classwork For each of the two scenarios below, compare and interpret the center and spread of the data sets. Graph 1 Title: Life expectancy for different animals Key Red = Turtle Blue = Wolf Green = Ant Graph 2