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## Box Plots

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**Mean ( x ):**Statistical Measures Statistics practice of analyzing a set of data Measures of Central Tendency: numbers that represent the middle of the data (mean, median, mode) Arithmetic average Median: Middle of the data listed in ascending order Mode: Most common number (if modes – can be more than One) Skewed Right (positively): Less data to the right Skewed Left (negatively): Less data to the left**5 Number Summary:**Min: Minimum Value (0 Percentile) Q1: Quartile 1 (25th Percentile) Med (Q2): Median (50th Percentile) Q3: Quartile 3 (75th Percentile) Max: Maximum or Q4 (100th Percentile) Min Med Max Q1 Q2 Q3 Q4**Test Scores**Between what scores do the middle 50% lie? Between what scores does the lowest 25% lie? Which range of scores has more density? (more numbers in a smaller number) 4. What type of distribution does this have?**1) Which date has the most variability?**2) Make a statement about airline delays 3) Which would you expect to have larger variability (interquartile range) A) Heights of freshmen B) Ages of freshmen C) Weights of freshmen D) Heights of 5 year-olds?**Calculator Commands**• Enter data into STATEDIT • STAT → CALC → 1: 1-Var STATS • → represents mean • n = no. of entries • med = median • Etc…**Mode: Most often number.**Mean: Average. Median: The middle number when arranged from smallest to largest. Best to show when there are outliers!!! 1) Find the mode, mean, and median: 5,7,9,9,30 2) Which is the largest? 3) Now include a 90 in the data. Which of the three changed the most? 4) Now include a 90 in the data. Which of the three changed the most? 5) When they list salaries, why do they state the median price and not the mean price?**Ex. Find the mean, median, and mode of 85, 76, 88, 91, 85,**58, 88, 91, 97, 91, 88, 97, 97 • Mean ( ) = median = , mode = Draw a box plot of the data.**Deeper Understanding**• Suppose there are 20 tests and the scores are all an 80%. What would change if 2 more tests were added that were both a 90%, mean or median? • What if there were 20 tests, 4 were 70%, 12 were 80%, and 4 were 90%. Three more tests were added to group scoring 70%, 90%, and 100%. How would the mean or median change?**Trick or Treat**• Ten neighborhood kids went out to get candy. Here is a list of the number of treats they received: 45, 34, 56, 32, 10, 32, 62, 11, 55, 34 • Find the mean, median, and IQR of the treats. • The kid who got 62 treats, went back out and got 262 treats. Find the new mean, median and IQR. • Which does a better job of describing the typical number of treats for the new data? Why? • Draw a box plot.**Which way is the data skewed?**Suppose you wanted to open restaurants. Where would you put a few of them? Where would you want a lot of them?