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More Graphs and Displays
Stem-and-Leaf PlotsEach number is separated into a
STEM and LEAF component. The STEM is the leftmost digit(s).The LEAF is the rightmost digit.It’s important to include a key to
identify values. For example… Key: 15 | 5 = 155
Use the stem-and-leaf plot to list the actual data entries.
Make a stem-and-leaf plot:Ages of the top 30 highest paid CEOs
(Forbes Magazine).
64 74 55 55 62 63
50 67 51 59 50 52
50 59 62 64 57 61
49 63 62 60 55 56
48 58 64 60 60 57
Pie Chart (for Qualitative Data)A circle divided into sectors that
represent categories. The area of each sector is proportional to
the frequency of the category.
Find RELATIVE Frequency and multiply by 360o to get the central angle for each category.
Use a Pie Chart to display data2010 NASA budget request (in millions
of dollars)
Science, aeronautics, exploration
8947
Space Operations 6176
Education 126
Cross-agency support 3401
Inspector general 36
Pareto Chart (for Qualitative Data)Vertical bar graph in which the height of
each bar represents the frequency or relative frequency.
Bars are positioned in order of decreasing height, left to right.
EX: Make a Pareto chartUltraviolet indices for 5 cities at noon:
Atlanta
Boise
Concord
Denver
Miami
9 7 8 7 10
Scatter Plot (for Paired Data Sets)Paired data Ordered pairs. Plot on a coordinate plane.Independent variable on the x-axis.
EX: make a scatter plot:# of students per teacher
Avg teacher’s salary (in thousands$)
17.1 28.7
17.5 47.5
18.9 31.8
17.1 28.1
20.0 40.3
18.3 33.8
14.4 49.8
16.5 37.5
13.3 42.5
18.4 31.9
Measures of Central Tendency
Measure of Central Tendency:A value that represents a typical, or
central, entry of a data set. 3 most common are MEAN, MEDIAN,
and MODE
MEAN: sum of the data entries divided by n
MEDIANThe data entry in the MIDDLE.
List data from least to greatest.Find the middle value.(For even n, find the average of the 2
middle values)
MODEData entry that occurs MOST often
(highest frequency)
A data set may have no mode or have more than mode.
BIMODAL = 2 modes.
EX: Find mean, median, and mode for the data set.
Weighted MEAN: data values have different
weights.
EX: find the weighted mean
Mean of a Frequency Distribution
EX: Find the mean
Shapes of DistributionsDistributions may look ..
SymmetricUniformSkewed LeftSkewed Right
Symmetric
Uniform
Skewed Left
Skewed Right