Aim #89: How do we create box plots from dot plots? How do we use the calculator to find the 5-number summary?Homework: HandoutDo Now: A television game show, “Fact or Fiction”, was canceled after nine shows. Many people watched the nine shows and were rather upset when it was taken off the air. A random sample of eighty viewers of the show was selected. Viewers in the sample responded to several questions. The dot plot below shows the distribution of ages of these eighty viewers:

1) What does the left most dot in this dot plot tell us?

2) Is this distribution symmetrical?

3) How does the direction of the tail affect the location of the mean age compared to the median age?

4) Using the above dot plot, construct a box plot. What is the 5-number summary?

Minimum: _______Lower quartile (Q1): _______Median (Q2): _______Upper quartile (Q3): _______Maximum: _______

What percent of the data does the box part of the box plot capture? _______ What percent of the data falls between the minimum value and Q1? _______What percent of the data falls between Q3 and the maximum value? _______

What percent of the viewers have ages between Q1 and Q3? _______. What is the interquartile range (IQR) for this data distribution?

The IQR provides a summary of the variability for a skewed data distribution. The IQR is a number that specifies the length of the interval that contains the middle half of the ages of viewers.

Do you think producers of the show would prefer a show that has a small or large interquartile range? Explain your answer.

The 5-number summary can be found on the calculator!

STEP 1:STAT enter

Type Data in L1

NOTE: data DOES NOT have

to be in order!!

STEP 2:

Press Stat --> CALC

Option 1: 1-Vars Stats

Hit ENTER 3 times

scroll down

1) For each data set, determine to the nearest tenth, the 5-number summary, range, and interquartile range.

2) Using your calculator, determine the 5-number summary and create a box plot for the data below.

20, 27, 28, 29, 30, 31, 33, 33, 37, 39, 55

3) The box plot below represents the math test scores of 20 students.

a) What percentage of the test scores are less than 72?

b) How many of the 20 students scored below or equal to an 88?

c) Which interval contains the most test scores from this data: 60s, 70s, 80s, or 90?

d) Which of the following cannot be determine from the box plot: {Range, Mean, Median, Mode}

4) The data below are the calories in an ice cream bar.

a) Find Q1, median and Q3.

b) Create a box plot.

c) What is the interquartile range (IQR) for this distribution? What percent of the ice cream bars fall within this interval?

d) Do you think the data distribution represented by the box plot is a skewed distribution? Why or Why not?

5) The table below provides the average retail price (cents per kilowatt-hour) to residential customers of the New England states in October of 2009.

a) Compute the mean and the median.

b) If you wanted to describe a typical price for electricity, would you use the mean or the median? Explain your choice.

6) MULTIPLE CHOICE: The data set 5, 6, 7, 8, 9, 9, 9, 10, 12, 14, 17, 17, 18, 19, 19 represents the number of hours spent on the Internet in a week by students in a mathematics class. Which box plot represents the data?

7) Given the box plot below:

a) What is the value of the lower quartile.

b) What is the interquartile range?

c) What percent of the data is contained in the interval [6, 12]?

Sum it up!