11.2 Notes - Comparing Data Sets
Vocabulary to know:
Different Centers of the Data:
Mean – average that involves adding the data and dividing by the number of scores
Median – average that involves putting the data in order and finding the middle score
Mode – average that involves finding the score that appears in the data most often
Other vocabulary:
Outlier – data value that is very different from the others
Interquartile range – the difference of the third and first quartiles
- represents the spread of the middle 50% of the data values
Mean Absolute Deviation – (MAD) – measure of variability that describes how much the data is
spread out from the mean
**We use the center and spread to compare data sets.**
Example: Comparing dot plots
The dots plots above show the data for miles run per week for two different classes.
1.)Compare the centers of the two data sets.
Class A mode: The mode is 4 miles, but the data shows two clusters – one around 4 miles and another
around 13 miles.
Class B mode: The mode is 7 miles.
Class A median: The middle number is 6 miles.
Class B median: The middle number is 6 miles.
Class A mean: 8.2 miles
Class B mean: 5.9 miles
2.)Compare the spread of the two data sets.
Class A range: 14 – 4 = 10 miles
Class B range: 9 – 3 = 6 miles
Class A data is spread out more than Class B data.
Class A mean absolute deviation: Each score minus the mean, then made positive, added and divided
buy the number of scores.
Mean = 8.2
4 – 8.2 = - 4.2 -> 4.2
4 – 8.2 = - 4.2 -> 4.2
4 – 8.2 = - 4.2 -> 4.2
4 – 8.2 = - 4.2 -> 4.2
4 – 8.2 = - 4.2 -> 4.2
5 – 8.2 = - 3.2 -> 3.2
5 – 8.2 = - 3.2 -> 3.2
5 – 8.2 = - 3.2 -> 3.2
6 – 8.2 = - 2.2 -> 2.2
6 – 8.2 = - 2.2 -> 2.2
12 – 8.2 =
3.8
13 – 8.2 =
4.8
13 – 8.2 =
4.8
13 – 8.2 =
4.8
13 – 8.2 =
4.8
14 – 8.2 =
5.8
14 – 8.2 =
5.8
69.6 ÷ 17 scores = 4.1 miles
3 – 5.9 = - 2.9 -> 2.9
4 – 5.9 = - 1.9 -> 1.9
Mean = 5.9
4 – 5.9 = - 1.9 -> 1.9
4 – 5.9 = - 1.9 -> 1.9
5 – 5.9 = - 0.9 -> 0.9
5 – 5.9 = - 0.9 -> 0.9
5 – 5.9 = - 0.9 -> 0.9
5 – 5.9 = - 0.9 -> 0.9
6 – 5.9 =
0.1
6 – 5.9 =
0.1
7 – 5.9 =
1.1
7 – 5.9 =
1.1
7 – 5.9 =
1.1
7 – 5.9 =
1.1
7 – 5.9 =
1.1
8 – 5.9 =
2.1
8 – 5.9 =
2.1
9 – 5.9 =
3.1
25.2 ÷ 17 scores = 1.5 miles
Class A's data points are farther from the mean than those of Class B. Class A's data shows greater variability.
Class B MAD:
Class A data has a greater mean, two modes, and greater spread and variability than Class B data.
Example: Compare box plots
Store A
Store B
Maximum value
76
74
Minimum value
25
41
First quartile
30
48
Median
43
51
Third quartile
55
65
Interquartile range (IQR)
25
17
Store A's median is close to Staore B's minimum, so Store A's average day is comparable to Store B's worst
day.
Store B's values are almost all greater than Store A's comparable values meaning Store B has greater overall
sales. Store A has a greater spread, both interquartile range and overall range.
Example: Compare histograms
Machine 1 has an average torque around 16 to 20. Machine 2's average torque is around 24.
Machine 1 has a torque as low as 10 and as high as 24. Machine 2's torques range from 14 to 38 and are much
more spread out than Machine 1's torques.