1. Statistics Unit Test Review
Chapters 11 & 12

2. 11-1/11-2
Mean(average): the sum of the data divided by the number of pieces of data
Median: the value appearing at the center of a sorted list of values, or the mean of the two central values, if the list contains an even number of values
Mode: the number or numbers that occur most often
The mean, median, and mode are called measures of center

3. 11-3 Measures of Variation
Used to describe the distribution, or spread, of data
Median
First Quartile
Third Quartile
Interquartile Range
Range

4. First Quartile Third Quartile Interquartile Range Range
Median of the first half of data values
Third Quartile
Median of the second half of data values
Interquartile Range
Distance between the first and third quartiles
If it is low, the middle data are grouped closely together
Range
Difference between the greatest and least data values

5. To find limits for outliers:
Outlier: A data value that is either much greater or much less than the other values in a data set
If the data value is more than 1.5 times the value of the IQR beyond the quartiles, it is an outlier
To find limits for outliers:
Find the IQR
Multiply IQR by 1.5
Subtract that number from the first quartile and add it to the third quartile—any number beyond limits is an outlier

6. Find the limits for the outliers and name any outliers in the data.
Find the range, median, first and third quartiles, and interquartile range for the data below.
Find the limits for the outliers and name any outliers in the data.
Test Grades 83 85 87 89 88 67 79 81

7. 11-4
Mean Absolute Deviation: the average distance between each data value and the mean
Can also be used to describe the spread of a set of data
Steps to find MAD:
Find the mean of the data set
Find the distance each value is from the mean
Find the average of these distances

8. Compare variations
A data set with a smaller mean absolute deviation has data values that are closer to the mean than a data set with a greater mean absolute deviation
Smaller mean absolute deviation = data are closer together

9. Pg. 840 #1 & 2

10. 11-5 Appropriate Measures Most appropriate when…
Mean: data have no extreme values
Median: data have extreme values and/or there are no big gaps in the middle of the data
Mode: data have many repeated numbers

11. Find the measure of center that best represents the data
Find the measure of center that best represents the data. Justify your selection and then find the measure of center.
number of parking spaces used: 46, 39, 40, 45, 44, 78, 51
golf scores over par: 3, 2, 0, 1, 3, 6, 4, 5

12. 12-1
Line Plot/Dot Plot: visual display of a distribution of data values where each data value is shown as a dot or other mark, usually an x, above a number line

13. 12-2
Histograms: type of bar graph used to display numerical data that have been organized into equal intervals
Intervals allow you to see the frequency distribution of the data, or how many pieces of data are in each interval

14. Histogram Info: There is no space between bars
Because all of the intervals are equal, all of the bars have the same width
Intervals with a frequency of 0 have a bar height of 0

15. When constructing a histogram:
Make frequency table first
Have between 4-6 intervals
Draw and label a horizontal and vertical axis
Include a title
Show the intervals from the frequency table on the horizontal axis
Label the vertical axis to show the frequencies
For each interval, draw a bar with the correct height

16. Pg. 877 #13-16

17. 12-3 Box Plot/Box-and-whisker plot
Uses a number line to show the distribution of a set of data by using the median, quartiles, and extreme values
A box is drawn around the quartile values
The whiskers extend from each quartile to the extreme data points that are not outliers
The median is marked with a vertical line
Separates the data into four parts each containing 25% of the data

18. Interpreting Box Plots
If the length of a whisker or the box is short, the values of the data in that part are concentrated
If the length of a whisker of the box is long, the values of the data in that part are spread out

19. Pg. 885 #12
After creating box plot, describe the data

20. 12-4 Shape of Data Distributions
The distribution of a set of data values shows the arrangement of data values
Symmetric: data evenly distributed between the left side and right side
Cluster: data grouped closely together
Gap: no data values
Peak: mode

21. Pg. 897 #10
Pg. 897 #12 graph only
Directions: Use clusters, gaps, peaks, outliers, and symmetry to describe the shape of the distribution.