General Divisions

1. General Divisions Descriptive Statistics • Goal is to summarize or describe the data Inferential Statistics • Using data from a sample to make inferences (generalizations) about the population

2. Major Descriptors • Center: Where the “middle” of the data is • Variation: How spread out the data is • Distribution: The shape of the distribution of the data (if the data follows a pattern) • Outliers: Data that is unusually separated from rest of data • Time: How data changes over time

3. Frequency Distribution • A frequency distribution lists data values (or groups of data values) along with how many data had that value (the frequency, or count)

4. Some data: Quiz scores

5. Quiz scores: Frequency Distribution

6. Quiz scores: Frequency DistributionUsing Classes

7. Definitions • Lower class limits • Smallest numbers that can belong to a class • Upper class limits • Largest numbers that can belong to a class • Class boundaries • Numbers used to separate classes so that there are no gaps • For our purposes, we will just use lower class limits • Class midpoint • Add upper and lower limits and divide by 2 • Class width • The difference between consecutive lower class limits

8. Example Lower class limits 12, 15, 17 Upper class limits 14, 17, 20 Class midpoints 13, 16, 19 Class width 3

9. Constructing a Frequency Distribution • Choose number of classes you want • Usually 5 to 20, based on data and convenience • Calculate class width • (highest value – lowest)/number classes • Usually round (up) • Sometimes handy to work backwards • Choose starting point • Usually lowest value, or a little smaller

10. Constructing a Frequency Distribution • Use starting point and class width to list other lower class limits • Add class width to previous lower limit • Add upper class limits • Tally data into frequency table

11. Example: Hours slept by caffeine drinkers Data: 1.2, 2.9, 3.1, 3.5, 4.1, 4.6, 4.8, 5.0, 5.3, 5.3, 5.4, 5.7, 6.3, 6.7, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.5, 7.8, 8.1, 8.2, 8.2, 8.5, 8.6, 9.3, 10.1 Choose number of classes: 5 (?) Class width: (10.1 – 1.2)/5 = 1.78 Lets round up to 2 and use that

12. Example: Hours slept by caffeine drinkers Data: 1.2, 2.9, 3.1, 3.5, 4.1, 4.6, 4.8, 5.0, 5.3, 5.3, 5.4, 5.7, 6.3, 6.7, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.5, 7.8, 8.1, 8.2, 8.2, 8.5, 8.6, 9.3, 10.1 Starting point: Probably 1.0 (could start at 0.0)

13. Example: Hours slept by caffeine drinkers Data: 1.2, 2.9, 3.1, 3.5, 4.1, 4.6, 4.8, 5.0, 5.3, 5.3, 5.4, 5.7, 6.3, 6.7, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.5, 7.8, 8.1, 8.2, 8.2, 8.5, 8.6, 9.3, 10.1 List lower class limits

14. Example: Hours slept by caffeine drinkers Data: 1.2, 2.9, 3.1, 3.5, 4.1, 4.6, 4.8, 5.0, 5.3, 5.3, 5.4, 5.7, 6.3, 6.7, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.5, 7.8, 8.1, 8.2, 8.2, 8.5, 8.6, 9.3, 10.1 Add upper class limits

15. Example: Hours slept by caffeine drinkers Data: 1.2, 2.9, 3.1, 3.5, 4.1, 4.6, 4.8, 5.0, 5.3, 5.3, 5.4, 5.7, 6.3, 6.7, 6.7, 6.8, 6.9, 7.0, 7.1, 7.2, 7.2, 7.4, 7.5, 7.5, 7.8, 8.1, 8.2, 8.2, 8.5, 8.6, 9.3, 10.1 Tally data

16. Relative Frequency Relative frequency = class frequency / sum of all frequencies Relative frequencies are expressed as percents

17. Example: Hours slept by caffeine drinkers Sum of Frequencies: 32 = sample size

18. Cumulative Frequency Distribution • Class limits are replaced with “less than” statements • Frequency is frequency of data less than the class

19. Example: Hours slept by caffeine drinkers

20. Homework 2-2: 1, 5, 9, 15 The answer the books gives for class boundaries will be different than what we’ve discussed in class.