Statistics

1
Statistics

• Recording the results from our studies.
• Must use a common language so we all know what we
  are talking about.

2
Descriptive Statistics

• Just describes sets of data.
• You might create a frequency distribution.
• Frequency polygons or histograms.

3
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.

4
Measures of Central Tendency

• Watch out for extreme scores or outliers.

Lets 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.

5
Normal Distribution

• In a normal distribution, the mean, median and
  mode are all the same.

6
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
7
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
8
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.
9
68 are within one standard deviation95 are
within 2 standard deviations99.7 are within 3
standard deviations
10
Correlation

• Remember the scatter plots!

Positive Correlation (bottom left to upper right)
Negative Correlation (upper left to bottom right)
11
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.

12
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
• 12, 6, 8, 5, 4
• 12, 15, 12, 9, 12
• 23, 7, 3, 27, 16
• What would be another way of asking this question?

13
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.

14
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.

15
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

16
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

17
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

18
Practice Question 8

• 8. What is the standard deviation if the variance
  is equal to 36?
•  
• A) 4
• B) 5
• C) 6
• 9
• 36

19
Answers

1. A
2. A
3. B
4. C
5. D
6. A
7. D
8. C