2.1 HW - Frequency Distributions and Their Graphs

Midpoint

(lower class limit + upper class limit) / 2

Min=16, Range=124, 8 classes

Class width=16 (124/8) Lower class limits=16,32,48,64,80,96,112,128 (16, 16+16=32,...,112+16=128) Upper class limits=31,47,63,79,95,111,127,143 (2nd lower limit less one = 31, 31+16=47...)

Min=8, Max=68, 7 classes

Class width=9 (68-8=60/7= 8.5, rounded to 9) Lower class limits=8,17,26,35,44,53,62. (8, 8+9, 17+9,..., 53+62) Upper class limits=16,25,34,43,52,61,70.(start by 1 less than 2nd lower class limit =17-1=16, then add by 9)

Where should the number of classes in a frequency distribution be between 5 and 20?

If the number of classes in a frequency, distribution is not between 5 and 20 it may be difficult to detect any patterns

Cumulative frequency graph = ogive

Line graph that displays cumulative frequency of each class at its upper class boundary

What are some benefits of representing data sets using frequency distributions? What are some benefits of using graphs of frequency distributions?

Organizing the data into a frequency distribution can make patterns within the date more evident. It can be easier to identify patterns of a data set by looking at a graph of the frequency distribution.

Sample size

Sum of all frequencies

Approximate number for ogive graph

Top graphed y-axis number

cumulative frequency

the sum of the frequencies for that class and all previous classes

relative frequency

Class frequency / sample size = f / n

What is the difference between class limits in class boundaries?

Class limits are the least and greatest numbers that can belong to the class. Class boundaries are the numbers that separate classes without forming gaps between them. For integer data, the corresponding class limits in class boundaries differ by .5.