Describing

1
Describing Comparing Data

• Unit 7 - Statistics

2
Describing Data

• Shape
• Symmetric or Skewed or Bimodal
• Center
• Mean (average) or Median
• Spread
• Range or Interquartile Range

3
Shape

• Symmetric

• Skewed

• Normal distributions
• Data is spread evenly on both sides of the center
• MedianMean

• 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)

4
Symmetric, Skewed or Bimodal?
SKEWED LEFT
APPROXIMATELY SYMMETRIC
SKEWED RIGHT
APPROXIMATELY SYMMETRIC
BIMODAL
SKEWED LEFT
5
Center

• Median is less variable, better measure of center
• (doesnt 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)

6
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
  6th test?
• What happens to the median?

7
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

8
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?

9
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.

10
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 Joshs Tips Richards Tips
Mon 40 40
Tue 20 45
Wed 36 53
Thur 28 41
Fri 31 28
11
Example 5

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

12
Example 5

• T or F
• The median for 1st is greater than Q3 for 2nd.
• T or F
• Q1 for 2nd is lower than the minimum for 1st.
• T or F
• The maximum in both periods appears to be the
  same.