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Graphing
“There are three types of lies.
Lies, damn lies, and Statistics”
-Benjamin Disraeli
• Problem: Which halloween candy is the
most popular?
• Hypothesis: If several halloween candies
are collected then ___________ will be
the most popular.
Data
• Tables are a neat and organized way to collect data
• Graphs allow you to easily show the data in a way
that people can draw conclusions easily.
• There are several types of graphs:
– Pie charts: These show data in terms of a percentage
– Line graphs: These show data over time
– Bar graphs: These compare one group of data to another
• Statistics are mathematical tests that can tell us useful
things about data
– Example: the mean, median, mode
– Standard Deviation: the mean of the mean
Candy Collected on Halloween
Trial
Kitkat
Snickers
Milkyway
3 Musketeers
Hershey’s
Other
How to calculate
• Mean: add up all the numbers from a
column and divide by how many
numbers there are
• Median: Line up all the numbers in
order and then pick the one in the
center
• Mode: The most repeated number
• Standard deviation: the mean of the
mean
Calculating Bees and Flowers
Calculating Standard Deviation
x
(x-mean)
(x-mean)2
∑ (x-mean)2
∑ (x-mean)2
Divided by (number of
items minus 1)
What does Standard Deviation
mean?
• Standard Deviation is a measurement of
how closely clumped or how far apart data
is.
– Example: Student test grades
Period 3
Period 6
3
4
2
0
1
4
2
0
Mean= 2
Mean=2
• In period 3, most of the students had
test scores around the mean. The
mean is a good indicator of the
performance of a student in period 3.
In period 6, however, students either
did very poorly or very well on the
test…but the mean was the same as
period 3! The mean is not a good
measurement of the performance of
the students in Period 6 because most
students didn’t get a C.
• We use standard deviation to figure
out if the mean is representing an
accurate view of what is going on.
Standard Deviation
• The standard deviations is how far from the
average numbers in a data set are.
• In the example with class test scores, Period
3 had a standard deviation of 0.8 (less than
one standard deviation!) meaning that the
numbers were all close to the mean and that
the mean was a good measurement of how
well students scored. Period 6 had a
standard deviation of 1.6 showing that the
data was very spread out and the mean was
not as valid a measurement of how students
did.
How to make a bar graph
• Bar graphs compare groups of different
items.
• Add up the total number of candy collected
from each type.
How to make a bar graph
How to make a pie chart
• Pie charts are graphs showing
PARTS of a WHOLE.
• Add up the total amount of
candy collected for each type
and the total amount collected
of all types.
• Then, write each candy type
as a fraction of the whole.
– Ex. 36 Hershey’s were collected.
120 total candies were collected.
Hershey’s are 36/120
How to make a pie graph
• You and your friends visit various houses
to collect candy. The amount of candy you
collected at each time is shown in the
table below. Make a line graph showing
the candy you collected that evening.
Which time is it best to go out collecting
candy?
Time
Candy
7
56
8
107
9
32
10
6
How to make a line graph
Quiz
• Students in two periods took a test on
graphing. Create a table showing the
student scores for 2 periods. Find the
mean for each period. Find the standard
deviation for each period. Graph the
results in a bar graph.
– Period 1: 1,2,3,4,0,5
– Period 2: 3,3,2,4,0,3