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Part 2 Descriptive Statistics: Measures of Central Tendency and Variability. Statistics for Everyone Workshop Fall 2010. Workshop presented by Linda Henkel and Laura McSweeney of Fairfield University

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statistics for everyone workshop fall 2010
Part 2

Descriptive Statistics:

Measures of Central Tendency and Variability

Statistics for Everyone Workshop Fall 2010

Workshop presented by Linda Henkel and Laura McSweeney of Fairfield University

Funded by the Core Integration Initiative and the Center for Academic Excellence at Fairfield University

descriptive statistics
Once you know what type of measurement scale the data were measured on, you can choose the most appropriate statistics to summarize them:

Measures of central tendency: Most representative score

Measures of dispersion: How far spread out scores are

Descriptive Statistics
measures of central tendency
Central tendency = Typical or representative value of a group of scores

Mean: Average score

Median: middlemost score; score at 50th percentile; half the scores are above, half are below

Mode: Most frequently occurring score(s)

Measures of Central Tendency
measures of variability
Knowing what the center of a set of scores is is useful but….

How far spread out are all the scores?

Were all scores the same or did they have some variability?

Range, Standard deviation, Interquartile range

Measures of Variability
variability extent to which scores in a distribution differ from each other are spread out
Variability = extent to which scores in a distribution differ from each other; are spread out
the range as a measure of variability
Difference between lowest score in the set and highest score

Ages ranged from 27 to 56 years of age

There was a 29-year age range

The number of calories ranged from 256 to 781

The Range as a Measure of Variability
sample standard deviation
Sample Standard Deviation
  • Standard deviation = How far on “average” do the scores deviate around the mean?
  • s = SD =
  • In a normal distribution, 68% of the scores fall within 1 standard deviation of the mean (M  SD)
  • The bigger the SD is, the more spread out the scores are around the mean
interquartile range
Quartile 1: 25th percentile

Quartile 2: 50th percentile (median)

Quartile 3: 75th percentile

Quartile 4: 100th percentile

Interquartile range = IQR =

Score at 75th percentile – Score at 25th percentile

So this is the midmost 50% of the scores

Interquartile Range
interquartile range on positively right skewed distribution
Interquartile Range on Positively (Right) Skewed Distribution

IQR is often used for interval or ratio data that are skewed

(do not want to consider ALL the scores)

presenting measures of central tendency and variability in text
The number of fruit flies observed each day ranged from 0 to 57 (M = 25.32, SD = 5.08).

Plants exposed to moderate amounts of sunlight were taller (M = 6.75 cm, SD = 1.32) than plants exposed to minimal sunlight (M = 3.45 cm, SD = 0.95).

The response time to a patient’s call ranged from 0 to 8 minutes (M = 2.1, SD = .8)

Sentences should always be grammatical and sensible. Do not just list a bunch of numbers. Use the statistical information to supplement what you are saying

Presenting Measures of Central Tendency and Variability in Text
presenting measures of central tendency and variability in tables symmetric data
Presenting Measures of Central Tendency and Variability in Tables(Symmetric Data)

Be sure to include the units of measurement! You can include an additional column to put the sample size (N)

presenting measures of central tendency and variability in tables skewed data
Presenting Measures of Central Tendency and Variability in Tables(Skewed Data)

Be sure to include the units of measurement! You can include an additional column to put the sample size (N)

what s the difference between sd and se
Sometimes instead of standard deviation, people report the standard error of the mean (SE or SEM) in text, tables, and figures

Standard deviation (SD) = “Average” deviation of individual scores around mean of scores

Used to describe the spread of your (one) sample

Standard error (SE = SD/N) = How much on average sample means would vary if you sampled more than once from the same population (we do not expect the particular mean we got to be an exact reflection of the population mean)

Used to describe the spread of all possible sample means and used to make inferences about the population mean

 Standard error usually looks better in figures because it is not as large

What’s the Difference Between SD and SE?
slide18
Dangers of low N: Be sure to emphasize to students that with a small sample size, data may not be representative of the population at large and they should take care in drawing conclusions

Dangers of Outliers: Be sure your students look for outliers (extreme values) in their data and discuss appropriate strategies for dealing with them (e.g., eliminating data because the researcher assumes it is a mistake instead of part of the natural variability in the population = subjective science)

Teaching Tips

slide19
Finding descriptive statistics

Teaching tips:

Hands-on practice is important for your students

Sometimes working with a partner helps

Time to Practice