1. 2.1 Frequency Distribution and Their Graphs NOTES Coach Bridges

2. What you should learn:  How to construct a frequency distribution including limits, midpoints, relative frequencies, cumulative frequencies, and boundaries  How to construct a frequency histogram

3. Frequency Distributions   Frequency Distribution- a table that shows classes or intervals of data entries with a count of the number of entries in each class.   Frequency = f is the number data entries in the class   Lower Class Limit- is the least number that can belong to the class

4. Frequency Distribution  Upper Class Limit- is the greatest number that can belong to the class  Class Width- the distance between lower or upper limits of consecutive classes  Range- is the difference between the maximum and minimum data entries

5. Steps to Construct a Frequency Distribution 1. Decide on the number of classes to include in the frequency distribution. The number of classes should be between 5-20. 2. Find the class width. Determine the Range of the data; divide the range by the number of classes. (Round up if needed)

6. Steps cont. 3. Find the class limits, lower and upper. You can use the minimum data entry as the lower limit of the first class. To find the remaining, add the class width to the lower limit of the preceding class. Classes cannot overlap. Find the upper limits. 4. Make a tally for each data entry in the row of the appropriate class. 5. Count all the tally marks to find the total frequency f for each class.

7. Definitions  Midpoint- the sum of the lower and upper limits of the class divided by two. The midpoint is sometimes called the class mark.  Relative frequency- the portion or percent of the data that falls in that class. It is found by dividing the frequency by the sample size.  Cumulative frequency- the sum of the frequency for that class and all previous classes. The cumulative frequency of the last class is equal to the sample size n

8. Frequency Histogram  a bar graph that represents the frequency distribution of a data set. A histogram has the following properties: 1. The horizontal scale is quantitative and measures the data values 2. The vertical scale measures the frequencies of the classes 3. Consecutive bars must touch

9. Definitions  Class Boundaries - are the numbers that separate classes without forming gaps between them  Sigma – the Greek letter that is used throughout statistics to indicate a summation of values