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Transcript
Statistics
Recording the results from our
studies.
Descriptive Statistics
• Just describes sets of
data.
• You might create a
frequency distribution.
• Frequency polygons or
histograms.
Measures of Central Tendency
• Mode – score that occurs most often
EX: 3,5,5,7,5,4,9,6,8,7,10 5 is the mode
• Median – score in the halfway point
EX: 3,4,5,5,5,6,7,7,8,9,10  6 is the
median
• Mean – average score
EX: 3+5+5+7+5+4+9+6+8+7+10=69
69/11  6.27 is the mean
Mean, Median, Mode
• The weekly salaries of six employees at
McDonalds are $140, $220, $90, $180, $140,
$200.
– For these six salaries, find:
• (a) the mean
• (b) the median
• (c) the mode
Mean, Median, Mode
• Answers
Mean:
90+ 140+ 140+ 180 + 200 + 220 =$ 161.67
6
Median:
90,140,140,180,200,220
The two numbers that fall in the middle need to be averaged.
140 + 180 = 160
2
Mode:
90,140,140,180,200,220
The number that appears the most is 140
Central Tendency
• Watch out for extreme scores or outliers.
Let’s look at the salaries of the employees at Dunder Mifflin 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.
Statistical Reasoning
A Skewed Distribution
15 20 25 30 35 40 45 50
90
475
70
Mode Median
One Family
Mean
Income per family in thousands of dollars
710
Distributions
• 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)
Normal Distribution
• In a normal
distribution, the
mean, median and
mode are all the
same.
Other measures of variability
• Range: distance from
highest to lowest
scores.
• Standard Deviation:
the variance of scores
around the mean.
Shaq and Kobe may both
score 30 ppg (same mean).
• The higher the
variance or SD, the But their SDs are very
different.
more spread out the
distribution is.
• Do scientists want a
big or small SD?
Calculating the Standard Deviation
Data: 2,2,4,8
1. Figure out the Mean: 16 4 = 4
2. Take mean & figure out difference from
each point: 2-4=-2, 2-4=-2, 4-4=0, 8-4=4
3. Square each difference:4,4,0,16
4. Add together: 4+4+0+16=24
5. Divide by #: 24 4 = 6  This is the
variance
6. Take square root: 2.45
Normal Distribution
A normal distribution
is a bell shaped curve.
A standard deviation of 15 accounts for about 68% of responses.
Scores
• A unit that
measures the
distance of one
score from the
mean.
• A positive z score
means a number
above the mean.
• A negative z score
means a number
below the mean.
Statistical Significance
• How likely it is that an obtained result
occurred by chance
• Odds must be less than 5% (.05) in order for
results to be statistically significant
• This means that your results are 95% (.95) a
result of your IV