Understanding Graphs
Bar Graph Easy to make
Information is easily understood
Each bar represents counts for a category
The length of the bar represents the percent of the total that falls into that category
Bar Graphs
Favorite Pizza Toppings
05
10152025303540
ExtraCheese
Pepperoni Sausage Mushrooms
Toppings
Fre
qu
ency
x-axis
y-axistitle
labels
origin
Box-and-Whisker Plots Good for large data sets — at least 15
Give five important pieces of data: median, maximum, minimum, lower and upper quartiles
Can be used to compare sets with different number of data points
Box-and-Whisker Plots
Math Test Scores
median
maximumminimum
lower quartile upper quartile
title
number line
Easy to read
Each piece represents a percent of the whole
Can also calculate the degree of the circle
Shows the whole as 100 percent
Circle Graphs
Favorite Sport
Baseball36%
Basketball18%
Soccer18%
Football21%
Wrestling7%
Baseball
Basketball
Soccer
Football
Wrestling
Circle Graphs title
legendpercent of total
Histogram Kind of a bar graph
Easy to make
Bars represent an interval of data—not just one number (e.g., 0 to 5)
The length of the bar represents the number that falls into that category
Histogram
Hours Playing Video Games /Week
0
2
4
6
8
10
12
0-5 5.1-10 10.1- 15 15.1-20
Number of Hours
Nu
mb
er o
f S
tud
ents
title
label for x-axis
label for y-axis
interval of data for each category
Line Plots Easy to read
Easy to make
Best when you have 25 data points or less
Shows clusters (groups of points), gaps (large spaces between points), outliers (points much larger or smaller in value) and variability (how the data is spread)
Line Plots
Represents 1 cookie
title
Number line
Organizes bivariate data (two variables)
Shows the association between two variables
Involves causation and association
Shows clusters and outliers
Have the independent variable on the x-axis
Can only connect points in a time-series
Scatter Plots
Scatter Plots
McDonald's Sandwiches
0
200
400
600
800
1000
0 10 20 30 40 50
Grams of Fat
Cal
ori
es
title
Dependent variabley-axis
label for y-axis
label for x-axis
Independent variablex-axis
Stem-and-Leaf Plots
Easy to make
Best with more than 25 values
Allows the identification of largest and smallest values, clusters, gaps and outliers
Other varieties include back-to-back plots
Stem-and-Leaf Plot
Stems Leaves
01 2, 4,5,6,82 33 6
2|3 means 23
Legend
Measure of Center
Mean — A number that represents the middle point, or average.
It is the quotient obtained by dividing the sum total of a set of figures by the number of figures.
MeanMean Health Care Salaries
Surgeon $184,150
Home health aides
$20,960
Nurses aides $22,960
Dental assistants $30,850
Physical therapists
$41,410
Athletic trainers $38,860
• The sum of the salaries is $339,190
• There are six values.
• $339,160/6 = $56,531
• The mean is $56,531
Median — The value in an ordered set of values that represents the point of which there are as many instances higher as there are lower.
Measures of Center
MedianMean Health Care Salaries
Surgeon $184,150
Home health aides
$20,960
Nurses aides $22,960
Dental assistants $30,850
Physical therapists
$41,410
Athletic trainers $38,860
• Put the numbers in order by value:184,150 41,410 38,860 30,850 22,960 20,960
• Find the middle. In this case, the middle is between 38,860 and 30,850. So find the mean of those 38,860 + 30,850
2• $69,720/2 = 34,855
• The median is $34,855
Mode — The most frequent value of a set of data.
Measures of Center…continued
Mean Health Care Salaries
Surgeon $184,150
Home health aides
$20,960
Nurses aides $22,960
Dental assistants $30,850
Physical therapists
$41,410
Athletic trainers $38,860
• There is no number that appears most often, therefore:
• There is no mode.
The mean is $56,531. The median is $34,855. There is no mode.Why are the mean and the median so
different if they are both measures of center?
The mean is greatly affected by very large or very small numbers. The surgeon’s salary is much greater than the others and that gives us a larger mean.
Look at the measures of center
For more information about data, go to
Quiz Bus: Dealing With Data http://westernreservepublicmedia.org/quizbus/index.htm
Dealing With Data Hotlist http://westernreservepublicmedia.org/quizbus/index.htm
Understanding Graphs
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