# Exploring Some Concepts Via Applets

Math 116 – Activity 4

Objective:

Exploring some Concepts via Applets

(1) Exploring Mean and Median

Access my web page: http://montgomerycollege.edu/~maronne/

Click on Math 116

Click on Applets

Click on Mean and Median 1

Click on Mean and Median

Read Instructions and play with it

Make sure you drag a point along the line

a) Observe what happens. Explain.

b) Which of the two measures of the center is said to be resistant? Explain.

(2) Exploring Mean and Median

Objective: To stress the concept: The median is a resistant measure of the center while the mean is affected by extreme values.

Access the Applets window in my web page

Click on Mean and Median 2

Click on Mean versus Median

Read instructions and play with it

a) If you were reporting results about a skewed distribution, what measure of the center would you use? Explain.

b) Dates of coins

Suppose you and your friends emptied your pockets of coins and recorded the year marked on each coin. What do you think the shape of the distribution looks like? Explain. What measure of the center is more appropriate to use, the mean or the median? Explain why.

c) A class of 5th graders takes a test designed for 7th graders. What direction is the skewness of the test scores? Two averages have been reported: 37% and 33%. Identify the mean and the median. Explain your reasoning.

Math 116 – Activity 4

Objective:

Exploring some Concepts via Applets

Exploring Histograms – How the class width (“bin width”) affect a histogram.

Objective: Observing how the selection of the class width “changes” the “story” portrayed by the graph. Deciding what class width provides the best picture of the data.

Access the Applets window in my web page

Click on Histogram 2

(3) Assume the data represents grades of students in a test.

i) What is a convenient number to use as the class width?

ii) What class width is convenient to use if we want to know if there are any students who scored above 95%?

(4) Assume the data represent the number of cars that go through a busy intersection from 4 am until 10 am. To save time in entering new data that fits this situation, and to be able to use the given histogram, we’ll have to make the assumption that 40 = 4 a.m., 50 = 5 a.m., etc.

A class width of 10 will mean 1-hour intervals.

A class width of 5 will mean .....-minute intervals

A class width of 2.5 will mean ...... -minute intervals

Change the class width from 10 to 5 and then to 2.5. You can use the slider, but it’s more exact if you just type the number and press enter.

a) Give the time interval in which the most cars go through the intersection if you use

i) A class width of 10:

ii) A class width of 5:

iii) A class width of 2.5:

b) You leave for work before 6 a.m. What is the most convenient time interval to go through the intersection?

c) What if you leave home between 6 and 7 a.m.?

d) Indicate which choice will be better if we want to pinpoint rush hour and avoid the time when the most cars go through the intersection.