1. 15.1 Histograms & Frequency Distributions

2. Ranking: a simple way to organize a set of data
list numbers from lowest to highest or highest to lowest
Frequency: if values repeat it is convenient to list the number of times it occurs
Ex 1) A supermarket manager studies the amount of time customers stand in line before being checked out by tracking one customer each half hour. The times in minutes the first 20 customers wait are 3, 2, 5, 2, 0, 1, 2, 4, 6, 4, 4, 8, 3, 0, 2, 1, 6, 3, 3, 1. Organize this into a set of ranked data indicating frequency.
Minutes Waiting Frequency
0 2
1 3
2 4
3 4
4 3
5 1
6 2
7 0
8 1
*Note: 7 is included even though no one waited 7 minutes
*Note: frequency adds to 20

3. Large sets of data can be grouped into classes
Grouping sacrifices some specifics but makes large data sets more manageable
Table is called a frequency distribution
Ex 2) A careers publication surveyed 23 companies and asked the average starting salaries of jobs offered in The info is summarized in the frequency distribution.
Starting Salaries Frequency
$19,000 – 22,
23,000 – 26,
27,000 – 30,
31,000 – 34,
35,000 – 38,
39,000 – 42,
How many of the starting salaries were:
less than $23,000?
less than $31,000?
equal to $31,000? 3
= 9
Cannot tell

4. Some notes about classes:
Classes should cover equal ranges of values
All data must fall into one of the classes
Classes may not overlap
Try to use between 6 and 15 classes
Cannot tell specifics such as lowest, highest, etc.

5. Let’s do 7 classes covering 15 possible readings
Ex 3) A health professional studying the effects of smoking on blood pressure collected the following reading of systolic blood pressure from a control group of 26 people: 150, 121, 134, 129, 165, 148, 125, 130, 182, 164, 142, 110, 177, 139, 188, 151, 190, 205, 128, 160, 125, 178, 162, 149, 156, Construct a frequency distribution.
Data ranges from 110 to 205
Let’s do 7 classes covering 15 possible readings
Systolic Blood Pressure Frequency
105 –
120 –
135 –
150 –
165 –
180 –
195 –

6. Ex 4) Other ways to represent the same data:
Histogram
Bar graph, no spaces
Classes on horizontal axis
Frequency on vertical axis 8 7 6 5 4 3 2 1
105– – – – – – 195–

7. Ex 4) Other ways to represent the same data (continued):
Frequency Polygon
Line graph, no spaces
Midpoint of each class on horizontal axis
Frequency on vertical axis
Makes a polygon by “tying” it down on each side (by plotting midpts of classes immediately below and above the distribution) 8 7 6 5 4 3 2 1

8. Record the stem once and then its associated leaves
If we want to organize data without losing detail, we can use a stem-and-leaf plot
Record the stem once and then its associated leaves
Ex 5) An independent marketing firm gathered data on the ages of people who watched the pilot of a new TV show. The following data represents the ages of 30 viewers:
Use a stem-and-leaf plot to display the data. 22 26 37 64 18 10 12 55 32 45 49 50 27 68 59 71 43 17 15 70 29 61 73 67 65 20 62 48
Stem Leaf
Key: | 6 represents 26
Note: If leaves are missing, you still include the stem!
For example, if this data didn’t have 32 or 37, you would still write 3 for the stem but leave the leaf side blank
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