Describing & Comparing DataUnit 7 - Statistics

Describing Data

ShapeSymmetric or Skewed or Bimodal

CenterMean (average) or Median

SpreadRange 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?

Co

un

t

2

4

6

8

10

12

14

Ages22 24 26 28 30 32 34

Collection 1 Histogram

Test_Grades

40 50 60 70 80 90 100

Collection 1 Box Plot

SKEWED LEFTSKEWED RIGHT

APPROXIMATELY SYMMETRIC

APPROXIMATELY SYMMETRIC

SKEWED LEFT

1

2

3

4

5

6

7

example

1 2 3 4 5 6 7 8 9

Collection 1 Histogram

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 6th 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?

Test_Grades

40 50 60 70 80 90 100

Collection 1 Box Plot

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.

Day Josh’s Tips Richard’s Tips

Mon $40 $40

Tue $20 $45

Wed $36 $53

Thur $28 $41

Fri $31 $28

Example #5

These are quiz scores for a 1st and 2nd period Algebra class.

a) Compare their distributions.

b) T or F

Almost 75% of 1st period did better than 50% of 2nd

c) T or F

All but one person in 1st did better than 25% of 2nd

First_Period

20 30 40 50 60 70 80 90 100

Collection 1 Box Plot

Second_Period

20 30 40 50 60 70 80 90 100

Collection 1 Box Plot

Example #5

d) T or F

The median for 1st is greater than Q3 for 2nd.

e) T or F

Q1 for 2nd is lower than the minimum for 1st.

f) T or F

The maximum in both periods appears to be the same.

First_Period

20 30 40 50 60 70 80 90 100

Collection 1 Box Plot

Second_Period

20 30 40 50 60 70 80 90 100

Collection 1 Box Plot