Unit 7 Statistics Describing Comparing Data Describing Data

Unit 7 - Statistics Describing & Comparing Data

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 BIMODAL SKEWED LEFT

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, 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. Day Josh’s Tips Richard’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 Q 3 for 2 nd. e) T or F Q 1 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.