lesson 1.1 day #2
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Lesson 1.1 Day #2. Histograms, Ogives , and Timeplots !. Chapter 1 Quiz #1. a ) the monetary damages b) all Honda Accords c) the 3 Honda Accords d) the type of collision e) none of the above. - PowerPoint PPT PresentationTRANSCRIPT
Lesson 1.1 Day #2Histograms, Ogives, and Timeplots!
Chapter 1 Quiz #1Cars magazine decides to test the safety of the Honda Accord. Three randomly chosen cars of this particular model are subjected to sideswipe (shallow-angle) collisions and the monetary damages are notes.
(1)Identify the sample(2) Identify the population(3) Identify the variable
a) the monetary damagesb) all Honda Accordsc) the 3 Honda Accordsd) the type of collisione) none of the above
Chapter 1 Quiz #1Cars magazine decides to test the safety of the Honda Accord. Three randomly chosen cars of this particular model are subjected to sideswipe (shallow-angle) collisions and the monetary damages are notes.
(1)Identify the sample(2) Identify the population(3) Identify the variable
a) the monetary damagesb) all Honda Accordsc) the 3 Honda Accordsd) the type of collisione) none of the above
4. A professor records the values of several variables for each student in her class. These include the variables listed below. Which of these variables are categorical?
a) Score on the final exam (out of 100 points)b) Final grade for the course (A, B, C, D, F0c) The total number of points earned in the class.d) The number of classes the student missede) None of the above
Making and interpreting stemplots can be tedious for large data sets. For larger amounts of data, ___________ are the most common way to display the distribution of a ___________variable. The disadvantage of a histogram is that you ___________________.
Displaying Quantitative Variables: Histograms
Histograms
Quantitativelose individual values
Divide data into classes of equal width such that each data point falls into only one class.
There is no single correct choice for the number of classes. FIVE is usually a good minimum.
Prepare a frequency table by counting the number of observations in each class.
Tips:
Number and Label your axes and Title your graph.
Draw a bar to represent the count in each class. Remember, NO SPACES between bars (unless the count for that class is ___).
Tips:
0
Shape – Unimodal? Bimodal? Symmetric? Skewed?
Center – estimate the medianSpread – What is the range?Outliers – Do any values seem too far outside the expected range?
ALWAYS Discuss what you see:
When you describe the shape of a distribution, concentrate on the main features. Distributions with a single peak (___________) can be described as
Symmetric –
Skewed right –
Skewed left –
Shape!
UNIMODAL
Of course, not all distributions will be unimodal. A distribution could have two peaks (__________), or show no real peaks (___________).
Shape!
BIMODALUNIFORM
Histograms can be made using the STAT PLOT feature on your calculator (see p. 59).
Be sure to set your own WINDOW - Do not ONLY use the ZOOM STAT feature of your calculator!
On your Calculator
Make a frequency table and a histogram of the salary data BY HAND.
Make a histogram in your calculator. BE SURE TO SET THE WINDOW APPROPRIATELY!
Practice
A histogram does not always tell us everything we want to know about a distribution. Sometimes we want to describe the relative position of an individual within a distribution. For this we use a relative cumulative frequency plot (Ogive).
The pth percentile of a distribution is the value such that p percent of the observations fall at or below it.
Relative Cumulative Frequency Plots (Ogives)
Suppose we want to know the percentile of Statistics majors. In other words, we want to know what percent of majors make less money than Stats majors.
Start with the frequency table and add two columns, Cumulative Frequency and Relative Cumulative Freq:
Interval Frequency
Cum Freq.
Rel. Cum. Freq.
30 < $ < 35
1 1 .06
35 < $ < 40
6 7 .41
40 < $ < 45
5 12 .71
45 < $ < 50
1 13 .76
50 < $ < 55
1 14 .82
55 < $ < 60
1 15 .88
60 < $ < 65
1 16 .94
65 < $ < 70
1 17 1.00
Now, construct a plot with the x-coordinates being the upper end of each class and the y-coordinates being the cumulative frequency.
Interval RCF30 < $ <
35.06
35 < $ < 40
.41
40 < $ < 45
.71
45 < $ < 50
.76
50 < $ < 55
.82
55 < $ < 60
.88
60 < $ < 65
.94
65 < $ < 70
1.00
Ogives
a) In what percentile is a Statistician’s salary? b) Find the center of the distribution. What degree earns a salary closest to the center?
Time Plots show how a variable changes with time. The time scale goes on the horizontal axis. The variable of interest goes on the vertical axis.
Look for trends (long-term upward or downward movement) and seasonal variations.
Time Plots
Look for trends (long-term upward or downward movement) and seasonal variations.
Time Plots
Look for trends (long-term upward or downward movement) and seasonal variations.
Time Plots