Unit 5: One Variable Statistics


5.1 Presenting Data


Introductory Terminology


Raw data – unprocessed information

continuous variable – same definition as before

discrete variable – same definition as before

frequency table – a table that presents the number of occurrences for a specific outcome (aka tally chart)

relative frequency – the frequency of this entry with respect to the whole.

cumulative frequency – the sum of the entries up to and including this one.


Histogram/Bar Graph


A bar graph is used to show the frequencies of different entries with the area of a rectangle. A histogram is used for continuous data and a bar graph for discrete data. The difference between a histogram and a bar graph is the fact that the bars touch in a histogram to indicate that there is no space in between the entries-just like continuous data has no gaps.


Frequency Polygons


Instead of a bar graph, you can use a frequency polygon. Draw a dot where the midpoint of the top of the bar would be and connect the dots with straight lines.


Cumulative Frequency Polygon


If you are drawing a cumulative frequency polygon, then align the dot with the right-hand part of where the bar would go. This indicate that the value includes this one and all before it.


Ex 1 Go to p. 92 and enter in all the numbers from Ex 1, put them all in the same column (A)


  1. Calculate the mean, median, and the mode using formulas

  2. Calculate the frequencies of each entry using formulas

  3. Calculate the relative frequencies, find the sum of the relative frequencies

  4. Calculate the cumulative frequencies

  5. Create charts for each of b, c, d

  6. Sort the numbers in ascending order


Grouped Data


When the number of entries gets large, it is usually best to switch to grouped data. You genderally want to have between 5 and 20 groups, depending on the range of your data. Generally, the larger the range the larger the number of intervals should be, but there are few hard and fast rules on this.


Ex 2 p. 94 Ex 2


Another type of data (other than discrete and continuous) is categorical. Categorical data is discrete but doesn't take a numerical value.


Categorical data can be represented with bar graphs and pictographs or pie charts. Pie charts are especially useful for representing relative frequencies.


p. 101#1,3ab,8,9,12,14abc,15