The Importance of Accurate Data Representation Avo
Explore how misleading graphs and statistics can distort data interpretation. This activity reveals how axis manipulation and small sample sizes—like in average blood sugar reports—can misrepresent true trends.
Alice Edwards
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P L T W Biomedical Science
Activity 2.1.2 Student Response Sheet
Part I: Answers
Example 1:
Prosthetic, Inc. and Orthotics and Prosthetics had almost identical profit increases
between the years 1998 and 2009. The y-axis on Orthotics and Prosthetics' graph
has been altered to have a larger range than the range used for the y-axis on
Prosthetic, Inc.'s graph. If the same range was used for both graphs, they would look
as follows:
Example 2:
ABC.com presented that the average blood sugar level before meals for Americans
is 142 mg.'dL but did not specify how the average was calculated. What they did not
share was that the mean, or arithmetic average, was calculated from a sample size
of only four people. Of these four people, all of the blood sugar levels (before meals)
were in normal ranges and one person had a blood sugar level of 240 mg/dL,
causing the entire group's average to be skewed. Therefore, 75% of the blood sugar
levels of the people in the study were actually far below this average. A better
average to use would have been the median blood sugar level (i.e.. the blood sugar
level in the middle of the data range). The website should have reported how many
people were included in the study. Four people do not accurately represent the
entire population.
Example 3:
The data presented was biased as it did not present all of the pertinent information.
The number of motorcycles on the road is significantly less than the number of
passenger cars on the road, so simply using the number of vehicles involved in fatal
crashes is not enough to illustrate which vehicle is the safest. The following two
graphs, which show the rate of vehicles involved in fatal crashes per 100 million
miles travelled and the rate of vehicles involved in fatal crashes per 100,000
registered vehicles, represent the data more accurately. Using all of the data as a
whole, passenger cars are actually involved in fewer fatal crashes than the other
vehicles.
Activity 2.1.2 Student Response Sheet
Part I: Answers
Example 1:
Prosthetic, Inc. and Orthotics and Prosthetics had almost identical profit increases
between the years 1998 and 2009. The y-axis on Orthotics and Prosthetics' graph
has been altered to have a larger range than the range used for the y-axis on
Prosthetic, Inc.'s graph. If the same range was used for both graphs, they would look
as follows:
Example 2:
ABC.com presented that the average blood sugar level before meals for Americans
is 142 mg.'dL but did not specify how the average was calculated. What they did not
share was that the mean, or arithmetic average, was calculated from a sample size
of only four people. Of these four people, all of the blood sugar levels (before meals)
were in normal ranges and one person had a blood sugar level of 240 mg/dL,
causing the entire group's average to be skewed. Therefore, 75% of the blood sugar
levels of the people in the study were actually far below this average. A better
average to use would have been the median blood sugar level (i.e.. the blood sugar
level in the middle of the data range). The website should have reported how many
people were included in the study. Four people do not accurately represent the
entire population.
Example 3:
The data presented was biased as it did not present all of the pertinent information.
The number of motorcycles on the road is significantly less than the number of
passenger cars on the road, so simply using the number of vehicles involved in fatal
crashes is not enough to illustrate which vehicle is the safest. The following two
graphs, which show the rate of vehicles involved in fatal crashes per 100 million
miles travelled and the rate of vehicles involved in fatal crashes per 100,000
registered vehicles, represent the data more accurately. Using all of the data as a
whole, passenger cars are actually involved in fewer fatal crashes than the other
vehicles.
Vehicles Involved in Fatal Crashes Per 100 Million Miles
Travelled in USA, 1994 - 2008
Vehicle involvement Rate in Fatal Crashes Per 100,000
Registered Vehicles tn USA, 1994 - 2008
'*1 ft. P"J w Iintf W t I n.1
Pan II: Ways in Which Statistics Can Be Misused
Biased Study Design
Note: A sample is defined as a representative part of a population whose properties are
studied to gain information about the whole.
Travelled in USA, 1994 - 2008
Vehicle involvement Rate in Fatal Crashes Per 100,000
Registered Vehicles tn USA, 1994 - 2008
'*1 ft. P"J w Iintf W t I n.1
Pan II: Ways in Which Statistics Can Be Misused
Biased Study Design
Note: A sample is defined as a representative part of a population whose properties are
studied to gain information about the whole.
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