2.  Presentation of raw or listed data into table form showing the variable and its frequencies. (Fancy word for a table!)  3 types 1.CategoricalCategorical 2.UngroupedUngrouped 3.GroupedGrouped For quantitative variables

3. RatingFrequency Superior6 Good28 Average25 Poor12 Inferior3 Rating of a Sociology Professor

4. Farm Population of the U.S. from 1940 to 1990 YearFarm Population in millions 194030.5 195023 196015.6 19709.7 19807.9 19907.3

5. Tread DepthFrequency 0 – 34 4 – 715 8 – 1125 12 – 155 16 – 193 Tread Depth of Tires

6. Tread DepthFrequency 0 – 34 4 – 715 8 – 1125 12 – 155 16 – 193 *Boundaries show the continuous nature of the distribution.

7.  Each of the following represents one class in a grouped frequency distribution. Find the boundaries for each class. ◦ A) 20 – 29 ◦ B) 300 – 399 ◦ C) 5.5 – 6.5 ◦ D) 67.2 – 68.2

8. Tread DepthFrequency 0 – 34 4 – 715 8 – 1125 12 – 155 16 – 193 To find the width of a class, subtract any two consecutive lower class limits.

9. Tread DepthFrequency 0 – 34 4 – 715 8 – 1125 12 – 155 16 – 193 To find the midpoint of a class, average the upper and lower limits of that class.

10. 1) Generally use between 5 and 20 classes. 2) Classes must be mutually exclusive. 3) Classes must be continuous. 4) Classes must be exhaustive. 5) Classes must be the same width. (exception: open-ended distribution)

11. AgeTime 0 - 9Below 100 10 - 19101 - 110 20 - 29111 - 120 30 - 39121 - 130 40 - 49131 - 140 50 and older141 - 140

12. 8581655847305147 9285425537318235 63334493775744 74636746735253

13. 1. Find the range (Difference between the highest and lowest data value)range 2. Find an appropriate class width by using the following formula: w = R/# of classes (round up the value to the next whole #) 3. Select an appropriate starting point. (lowest value is usually sufficient) Then add the class width to get each consecutive class lower limit. 4. Subtract 1 from 2 nd lower limit to get 1 st upper class limit and then add width. 5. Tally data.

14. Tread DepthFrequency (f)Relative Frequency (rf) 0 – 34 4 – 715 8 – 1125 12 – 155 16 – 193 Tread Depth of Tires Proportion of each frequency out of the total (n). Can be expressed as a decimal or a percent n = 52 4/52=.077 or 7.7% 15/52=.288 or 28.8% 25/52=.481or 48.1% 5/52=.096 or 9.6% 3/52=.058 or 5.8% you don’t need to show all 3 values. decimal or % is fine

15. Tread DepthFrequencyCumulative Frequency 0 – 34 4 – 715 8 – 1125 12 – 155 16 – 193 Tread Depth of Tires The sum of the frequencies accumulated up to that class. 4 only show the final number in each row 4+ 15 = 19 19 + 25 = 44 44 + 5 = 49 49 + 3 = 52

16. Tread Depth Frequencyrfrcf 0 – 34 4 – 715 8 – 1125 12 – 155 16 – 193 Tread Depth of Tires The sum of the relative frequencies up to that class or the proportion of each cumulative frequency (last row should always be 100%) 7.7% 28.8% 48.1% 9.6% 5.8% 7.7% 7.7 + 28.8 = 36.5% 36.5 + 48.1 = 84.6% 84.6 + 9.6 = 94.2% 94.2 + 5.8 = 100%

17. Tread Depth Frequency 0 – 34 4 – 715 8 – 1125 12 – 155 16 – 193