Unit 5 Chapter 8 Section 4 Data Variability.notebook
May 06, 2016
Unit 5 - Chapter 8 - Section 4
Data Variability
Objective: To compare data about two populations by using measures of
center and measures of variability
Box Plot: uses 5 points on a number line to
summarize a data set, the box shows the middle
50% of the data
Interquartile Range:(IQR) the difference between
the upper and lower quartiles
What is the IQR of the box plot above?
Variability: tells how much a data set is spread out
Mean Absolute Deviation: (MAD) the average
distance between the mean and each data value
You can determine the amount of overlap of two data sets by expressing the
difference between their centers as a multiple of the MAD or IQR.
• A multiple less than 1 indicates a large amount of overlap.
• A multiple of greater than 1 indicates a small or no amount of overlap.
Unit 5 Chapter 8 Section 4 Data Variability.notebook
May 06, 2016
Comparing Two Populations
1) A veterinarian collects data about the weights of
the dogs she treats. .
.
Australian Terrior
. . .
Boston Terrior
.
. .
.
.
Weight of Dog (lbs)
a) Compare the IQRs of the data sets to draw an
inference about the dogs.
b) Compare the medians of the data sets to draw
another inference about the dogs.
Unit 5 Chapter 8 Section 4 Data Variability.notebook
May 06, 2016
Determining Overlap of Data Sets
2) The data table below shows the number of points scored by each player on two basketball teams during a game. Use measures of center and variability to express the amount of overlap between the data sets.
Points Scored
Eagles
0
1
2
3
x 4
5
x x 6
x x 7
x 8
x x 9
Vikings
x x
x
x x
x
x x
a) Calculate the mean of each data set.
Eagles:
Vikings:
b) Determine the MAD of each data set.
Eagles:
Points 4 6 6 7 7 8 9 9
Mean 7 7 7 7 7 7 7 7
Distance 3 1 1 0 0 1 2 2
MAD = total of the distances =
number of data values
Vikings:
Points Mean Distance MAD = total of the distances =
number of data values
c) What multiple n of the MAD equals the difference between the means?
.
MAD n = difference of means
d) What does this number tell you about the overlap of the data set?
Unit 5 Chapter 8 Section 4 Data Variability.notebook
May 06, 2016
3) The data table below shows the number of commercials during a random sample of hour­long shows on two television stations.
a) Calculate the mean of each data set.
Commercials During
Hour­Long Shows
Station A
Station B
32 x x
33 34 x x x
x x x 35 x x
x x x 36 x x
x
37 x x
x 38
x 39
Station A:
Station A:
Station B:
b) Determine the MAD of each data set.
Points Mean Distance MAD = total of the distances =
number of data values
Station B: Points
Mean Distance MAD = total of the distances =
number of data values
c) What multiple n of the MAD equals the difference between the means?
.
MAD n = difference of means
d) What does this number tell you about the overlap of the data set?
Unit 5 Chapter 8 Section 4 Data Variability.notebook
May 06, 2016
Challenge
Two data sets have means that are very far apart, and the MADs of the data sets are very small. What can you conclude about the amount of overlap in the data sets? Explain.