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Statistics
• Recording the results
from our studies.
• Must use a common
language so we all
know what we are
talking about.
Descriptive Statistics
• Just describes sets of
data.
• You might create a
frequency distribution.
• Frequency polygons
or histograms.
Measures of Central Tendency (know this term)
Mean = average of all scores or observations
Median = the middle number when all scores are
sorted from highest to lowest
Mode = the score that appears most frequently in the
data.
Measures of Central Tendency
Watch out for extreme scores or outliers.
Let’s look at the salaries of the
employees at Dunder Mifflen Paper
in Scranton:
$25,000-Pam
$25,000- Kevin
$25,000- Angela
$100,000- Andy
$100,000- Dwight
$200,000- Jim
$300,000- Michael
• The median salary looks good at
$100,000.
• The mean salary also looks good at
about $110,000.
• But the mode salary is only $25,000.
• Maybe not the best place to work.
• Then again living in Scranton is kind
of cheap.
Normal Distribution
• In a normal
distribution, the
mean, median and
mode are all the
same.
Distributions
Median
• Outliers skew
distributions.
• If group has one high
score, the curve has a
positive skew (contains
more low scores)
• If a group has a low
outlier, the curve has a
negative skew
(contains more high
scores)
Mean
Median
Mean
Important Idea
• The larger your sample size, the more likely it is
your data will resemble a normal curve (because
outliers will be mitigated).
Seeing Statistics – Click on Contents – Go to 7.1
Other measures of variability
• Range: distance from
highest to lowest
scores.
• Standard Deviation:
the variance of scores
around the mean.
• The higher the variance
or SD, the more spread
out the distribution is.
• Do scientists want a big
or small SD?
Dwayne Wade and Kobe
may both score 26 ppg
(same mean).
But their SDs are very
different.
68% are within one standard deviation
95% are within 2 standard deviations
99.7 are within 3 standard deviations
Correlation
Remember the scatter plots!
Positive Correlation
right)
(bottom left to upper
Negative Correlation
(upper left to bottom right)
Practice Question #1
1.Which of the following events is the most probable?
A) flipping 6 or more heads in 10 coin flips
B) flipping 60 or more heads in 100 coin flips
C)flipping 600 or more heads in 1000 coin flips
D)All these results are equally probable.
Practice Question #2
1. For which of the following distributions of scores would
the median most clearly be a more appropriate measure
of central tendency than the mean?
A) 10, 22, 8, 9, 6
B) 12, 6, 8, 5, 4
C)12, 15, 12, 9, 12
D)23, 7, 3, 27, 16
What would be another way of asking this question?
Practice Question #3
3. Professor Connolly uses a scatterplot to display the
relationship between students' intelligence test scores
and the number of failing grades they have received.
The points on the plot are most likely clustered in a
pattern that:
A) resembles a Ushaped curve.
B) extends from the upper left to the lower right of the plot.
C)resembles a bellshaped curve.
D)extends from the lower left to the upper right of the plot.
Practice Question #4
4. In a single day, 45 babies were born in hospital X, 65
babies in hospital Y, and 25 babies in hospital Z. At
which hospital is there the greatest probability that more
than 60 percent of the babies are of the same sex?
A) hospital X
B) hospital Y
C)hospital Z
D)The probability is the same at all three hospitals.
Practice Question #5
5. Approximately what percentage of the cases
represented by the normal curve fall between –3 and +3
standard deviations from the mean?
A) 34
B) 68
C)95
D)100
Practice Question #6
6. When Mr. Adams calculated his students' algebra test
scores, he noticed that two students had extremely low
scores. Which measure of central tendency is affected
most by the scores of these two students?
A) mean
B) standard deviation
C)mode
D)median
Practice Question #7
7. If IQ scores are normally distributed, having a mean of
100 and a standard deviation of 15, approximately what
percentage of people have IQ scores somewhere
between 70 and 130?
A) 34
B) 50
C)68
D)95
Practice Question #8
8. What is the standard deviation if the variance is equal to
36?
A) 4
B) 5
C)6
D)9
E) 36
Answers
1.
2.
3.
4.
5.
6.
7.
8.
A
A
B
C
D
A
D
C