One Variable Statistics



Unit 1 – Interpreting Graphs and Statistics

Class Notes - Central Tendency and Histograms

I. Definitions

1) Frequency Table vs Regular Table

2) Mean (average):

3) Median:

4) Mode:

5) Distribution - Skewed Right Skewed Left Normal Distribution

6) Min Value:

7) Max Value:

8) Range:

9) Outlier:

10) Frequency Distribution:

11) Histogram:

II. Group Exercise

1. Look around the room and silently count the number of people you know.

2. Make a list of these numbers on the board.

3. Create a frequency distribution and a histogram for the data.

III. Interpreting Histograms

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IV. Creating a Histogram – Hurricane Problem

Create a histogram that shows the number of hurricanes there are as the hurricane season progresses.

In the United States, hurricane season starts June 1 and lasts about 26 weeks. Meteorologists record the number of weeks into the season each hurricane occurs. The number of weeks into the hurricane season in which Atlantic hurricanes occurred from 1997 to 2000 are listed below.

6, 7, 14, 12, 13, 14, 16, 16, 17, 17, 19, 21, 26, 12, 12, 13, 15, 15, 20, 20, 24, 10, 12, 15, 16, 17, 17, 18, 20

1. Order the numbers first.

2. What does the number 6 represent?

3. How many hurricanes occurred during week 20?

4. What is the range of values?

5. When we make the histogram the intervals have to have the same width. How many units wide should each interval be?

6. It might be a little easier to consider all the data if we make a frequency table first.(You’ll probably want to do this anytime you come across a problem and you have to make a histogram.)

7. Now construct the histogram. Label the horizontal axis (what the bins represent) and the vertical axis (“times appearing” or “frequency”)

V. Analyzing Histograms

1. Examine this histogram, which shows a set of 40 answers on a Customer Satisfaction survey ranging from a 1 being the lowest (not satisfied) and 10 being the most satisfied.

a) What is the position of the median when there are 40 values? Find the median of this set of values.

b) What is the minimum value? What is the maximum value?

c) How is the distribution skewed?

VI. Homework

1. Consider the set {3, 11, 12, 19, 22, 23, 24, 25, 27, 29, 35, 36, 37, 45, 49}.

a. What is the range of the data?

b. How wide should each interval?

c. Construct a frequency distribution and histogram for this data set.

2. Your bowling scores in your last 15 games are as follows:

125, 158,143, 177, 135, 117, 101, 158, 160, 144, 199, 129, 122, 131, 116.

a. Make a frequency distribution and histogram for your bowling scores.

b. What scores do you usually bowl?

c. Are your scores distributed evenly over all intervals?

d. How unusual is it for you to bowl a game over 150?

3. Make a list of steps that you can follow to create a histogram.

4. How you can tell which interval on a histogram has the greatest frequency?

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