Statistics Vocabulary

1. STATISTICS Definition The study of collecting, organizing, and interpreting data Example Statistics are used to determine car insurance rates, home mortgages, etc.

2. INDIVIDUAL Definition person or object in the study Example If a study is about teachers, each teacher interviewed or observed is called an individual.

3. VARIABLE Definition The characteristic of the individual to be observed or measured Example Test scores

4. QUANTITATIVE VARIABLE Definition Variable that quantifies Assigns a numerical value Example A person’s weight

5. QUALITATIVE VARIABLE Definition Variable that categorizes or describes Example Gender

6. POPULATION Definition Every individual of interest Example All living presidents – not just a few of them

7. SAMPLE Definition A subset of the population (some of the individuals of interest) Example Some living presidents

8. NOMIAL DATA Definition Data consisting of only names or qualities No numerical values Example Colors

9. ORDINAL DATA Definition Data that has an order but differences between data values are meaningless Example Student high school rankings (1 st, 9 th, 28 th, etc)

10. INTERVAL DATA Definition Data that has an order, meaningful differences, but may or may not have a starting point which makes ratios meaningless Example Temperature readings

11. RATIO DATA Definition Data with the same characteristics as interval data but with a starting point which makes ratios meaningful Example Measures of hei

12. DESCRIPTIVE STATISTICS Definition The practice of collecting, organizing, and summarizing information from samples or populations Example Graphs, measures of center and spread

13. INFERENTIAL STATISTICS Definition The practice of interpreting sample values gained from descriptive techniques and drawing conclusions about the population Example Polling 100 voters and using the results to predict a winner

14. STANDARD DEVIATION Definition A measure of how spread out numbers are. Its symbol is σ (the greek letter sigma) The formula is easy: it is the square root of the Variance. Formulas The "Population Standard Deviation“ The "Sample Standard Deviation

15. VARIANCE Definition The average of the squared differences from the Mean. To calculate the variance follow these steps: – Work out the Mean – Then for each number: subtract the Mean and square the result (the squared difference). – Then work out the average of those squared differences.

16. DISCRETE DATA Definition Is counted Can only have certain values Example Number of students in a class (Can’t have half a student); numbers on a die

17. CONTINUOUS DATA Definition Is measured Can take any value within a range Example A person's height: could be any value (within the range of human heights), not just certain fixed heights, Time in a race: you could even measure it to fractions of a second, A dog's weight, The length of a leaf,

18. Range (Statistics) Definition The difference between the lowest and highest values. Example In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9. – So the range is 9-3 = 6.

19. Quartiles Definitions The values that divide a list of numbers into quarters. Examples First put the list of numbers in order Then cut the list into four equal parts. The Quartiles are at the "cuts" Example: 5, 8, 4, 4, 6, 3, 8 – Put them in order: 3, 4, 4, 5, 6, 8, 8 – Cut the list into quarters: – And the result is: Quartile 1 (Q1) = 4 Quartile 2 (Q2), which is also the Median, = 5 Quartile 3 (Q3) = 8

20. INTERQUARTILE RANGE Definition The "Interquartile Range" is from Q1 to Q3. To calculate it just subtract Quartile 1 from Quartile 3. Example The Interquartile Range is: Q3 - Q1 = = 4

Data Displays Advantages & Disadvantages

Line Plot Advantages Individual data is not lost Easy to create Shows range, minimum, maximum, gaps, clusters, & outliers Disadvantages Can be cumbersome if there are a large number of data values Needs a small range of data

Bar Graph Advantages Easy to create Easy to read Makes comparisons easy Disadvantages Only used for discrete data Individual data is lost

Circle Graph Advantages Easy to read Shows percentages Disadvantages Only used for discrete data Individual data is lost Good for only about 3- 7 categories Total is often missing

Stem-Leaf Plot Advantages Easy to create Stores a lot of data in a smaller space Shows range, minimum, maximum, gaps, clusters, & outliers Disadvantages Can be cumbersome if there are a large number of data values Can be difficult to read Not visually appealing

Box Plot Advantages Identifies outliers Makes comparisons easy Shows 5-point summary (minimum, maximum, 1 st Quartile, Median, & 3 rd Quartile) Disadvantages Individual data is lost Can be confusing to read Not visually appealing