Intro to Stats

1. Intro to Stats Measures of Central Tendency

2. Order of Operations • Parentheses • Exponents • Multiplication or division • Addition or subtraction • *remember that signs form the skeleton of the formula • X + Y / 2 (divide y by 2 and add to x) • X + Y (add X and Y, then divide by 2) 2

3. Measures of Central Tendency (an “average”) • Number that best represents a group of scores • Represents the “typical” individual • Describes a large amount of data with a single number • No single measure is best • Mean • Median • Mode • Each gives different information about a group of scores

4. Mean • A measure of where most values tend to fall in a dataset • What we often refer to as an “average”

5. Mean • Sum the values in a group & divide by number of values • *Every score is represented • X = ΣX/n • X= mean value of a group of scores • Σ = summation sign • X = each score in the set • n = sample size in set • .

6. Practice • Data: 41, 38, 56, 19, 31, 14, 52, 35, 34, 10, 38, 39, 20

7. Mean Properties • 1. Most reliable and most often used • 2. Isn’t necessarily an actual score • 3. Strongly influenced by outliers • 4. Sum of the deviations equals zero

8. Weighted Mean • Multiply the value by the frequency of occurrence for each value, sum all the values, then divide by total frequency

9. Median • Midpoint in a set of scores • 50% below and 50% above the median value • No formula to compute • List values in order, from lowest to highest & find the middle score • If there are 2 middle scores, find the mean of these 2 scores

10. Practice • Data: 41, 38, 56, 19, 31, 14, 52, 35, 34, 10, 38, 39, 20

11. Mean vs. Median • The median is not sensitive to extreme scores and can be the most accurate centermost value (i.e., average) • Means can skew due to extreme scores

12. Mode • Value that occurs most frequently • No formula to compute • List all values once, tally the number of times each occurs, find the value that occurs most frequently • Can have bimodal or multimodal sets

13. When it’s useful • Only way to capture an average for nominal data

14. Practice • Data: 41, 38, 56, 19, 31, 14, 52, 35, 34, 10, 38, 39, 20

15. How do you choose? • Nominal data can only be described with the mode • The mean is usually the most precise with interval/ratio data • Median is best in the presence of extreme values or if some values are imprecise • *You might report more than one

16. When to use the median • 1. When you have extreme scores or skew • 2. When you have undetermined values • 3. When you have an ordinal scale

17. When to use the mode • 1. When you have a nominal scale (and sometimes ordinal) • 2. When you have discrete variables • 3. When you are interested in describing the shape of a distribution

18. Interpreting statistics • When asked to write as you would for a journal • Write the statistic of central tendency to 2 decimal places • Clearly state what you are reporting • Include the units of measurement • The mean time to run a mile was 2.7 minutes • The median home price in Texas is $80,000. • When asked to interpret a finding “for someone unfamiliar with statistics” • Describe the meaning of the statistic rather than using jargon • Include the units of measurement • The average runner completed a mile in about 2.7 minutes • The middlemost home price in Texas is $80,000