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
Mean
• 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)
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).
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
(bottom left to upper right)
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