Describing & Comparing Data Unit 7 - Statistics

Describing Data  Shape Symmetric or Skewed or Bimodal  Center Mean (average) or Median  Spread Range or Interquartile Range

Shape Symmetric  “Normal” distributions  Data is spread evenly on both sides of the center  Median=Mean Skewed  Data is pulled in one direction  Likely to have an outlier  The side that has the outlier (or the tail of the graph) is the side it is skewed Bimodal  Has two distinct peaks (two modes)

Symmetric, Skewed or Bimodal? SKEWED LEFT SKEWED RIGHT APPROXIMATELY SYMMETRIC SKEWED LEFT BIMODAL

Center  Median is less variable, better measure of center (doesn’t move as much when new data is added)  If data is skewed, use median  If data is symmetric, mean or median (mean = median in normal distributions)

Example #1 If your test scores on the first 5 tests in Algebra were 80, 83, 91, 87 and 79 what are your mean and median? What happens to the mean if you score a 60 on the 6 th test? What happens to the median?

Example #2  Marie and Tony are both in the same World History class. Their homework grades are given, compare the mean and median of each. Marie – 8, 9, 9, 9, 10 Tony – 3, 9, 9, 9, 10

Spread  Range shows the overall spread of the data (max – min). Is it affected by outliers?  Interquartile Range is the spread of the middle 50% of the data. Is it affected by outliers?  Which is less variable?

Describing the distribution  Give the center, shape and spread of the data. Example #3 Following are the SAT math scores for an AP Statistics class of 10 students: 664, 658, 610, 670, 640, 643, 675, 650, 676 and 575. Describe the distribution.

Comparing Data Example #4 Josh and Richard each earn tips at their part-time job. This table shows their earnings from tips for five days. Compare their distributions. DayJosh’s TipsRichard’s Tips Mon$40 Tue$20$45 Wed$36$53 Thur$28$41 Fri$31$28

Example #5 These are quiz scores for a 1 st and 2 nd period Algebra class. a)Compare their distributions. b)T or F Almost 75% of 1 st period did better than 50% of 2 nd c)T or F All but one person in 1 st did better than 25% of 2 nd

Example #5 d)T or F The median for 1 st is greater than Q3 for 2 nd. e)T or F Q1 for 2 nd is lower than the minimum for 1 st. f)T or F The maximum in both periods appears to be the same.