Statistics2.1: Frequency Distributions and Their Graphs

Statistics2.1: Frequency Distributions and Their Graphs

Objective 1: I can construct an extended frequency distribution.

A ______is a table that shows ______or ______of data entries with the ______in each class. The ______, f, of a class is the ______in the class.

Lower Class Limit:

Upper Class Limit:

Class Width:

Range:

Guidelines to Constructing a Frequency Distribution:

1. Decide on the

2. Find class width--

3. Find class limits—

4. Make a tally mark

5. Count the tally marks to find the

* Read Example 1, pg 41

TIY 1: Construct a freq. dist. for the # of touchdowns data set on pg 39. Use 8 classes.

a) # of classes = b) class width = c) fill in the class limits below

d) tally the data entriese) Write the frequency for each class

Class / Tally / Frequency

After learning how to construct a frequency distribution such as the one above, we can include other features that help provide a better understanding of the data. These features can be included as columns in your table. We will use these columns later in the chapter to create some graphical displays of the data.

Midpoint:

Relative Frequency:

Cumulative Frequency:

*Read Example 2, pg 43

TIY 2: Use our frequency distribution from TIY 1 to find the midpoint, relative frequency, and cumulative frequency for each class.

Class / Freq, f / Midpoint / Relative Freq. / Cumulative Freq.

Objective 2: I can create graphs using the columns of a frequency distribution.

Now that we can create a table for our data, let’s look at the type of graphs we can make using this data.

1) Frequency Histogram

A frequency histogram is a ______that represents the ______of a data set. A histogram has the following properties:

i)

ii)

iii)

Because the bars of a histogram touch (unlike a regular bar graph), bars must begin and end at ______instead of class limits. Class boundariesare the numbers that

______. To find class boundaries we ______0.5 to each ______limit and ______0.5 to each ______limit.

*When creating a frequency histogram, you can label the horizontal (x-axis) with either

______or ______.

**Read Example 3, pg 44

TIY 3: Use the frequency distribution from TIY 1 to construct a frequency histogram for the touchdown data.

Class* / Class Boundaries / Freq / Midpoint / Rel. Freq. / Cumulative Freq.
15-24 / 16 / 19.5 / 13.00% / 16
25-34 / 34 / 29.5 / 29.00% / 50
35-44 / 30 / 39.5 / 25.00% / 80
45-54 / 23 / 49.5 / 19.00% / 103
55-64 / 13 / 59.5 / 11.00% / 116
65-74 / 2 / 69.5 / 2.00% / 118
75-84 / 0 / 79.5 / 0.00% / 118
85-94 / 1 / 89.5 / 1.00% / 119

a) Fill in the class boundaries above.

b) Choose appropriate scales for the vertical and horizontal axes.

c) What 2 values could we use for the horizontal axis?

Frequency Polygon

A frequency polygon is a ______that emphasizes the continuous change in the individual frequencies. When we graph a frequency polygon, we must use the ______on the horizontal axis. To create the “polygon”, this graph must start and end on the ______, so we have to go back and forward a ______. We do this by subtracting the ______

______from the first midpoint and ______the class width to the last midpoint. Then connect the dots!

Read Example 4, page 45

TIY 4: Create a frequency polygon (above right graph) using the football data.

Relative Frequency Histogram

A relative frequency histogram has the same shape and scale as the corresponding frequency histogram. The difference is that the ______scale measures the ______frequency, not just the frequency. On the horizontal axis, we can use either ______or ______, just like in a frequency histogram.

Read Example 5, page 46

TIY 5: Create a relative frequency histogram of the football data.

Ogive (Cumulative Frequency Line Graph)

An ogive, or a cumulative frequency graph, is a ______that displays the ______

______of each class at its ______. The upper boundaries are marked on the ______axis and the cumulative frequencies are marked on the

______axis. Much like the frequency polygon, we need to start on the ______, so we must go back an ______for the starting value. An ogive shows the total frequency at the end of each class.

Read Example 6, pg 47

TIY 6: Create an ogive(above right graph) of the football data.

RECAP:

We use ______or ______on the horizontal axis to graph frequency or relative frequency histograms.

We use ______on the horizontal axis to graph a frequency polygon.

We use ______on the horizontal axis to graph an ogive.