chapter 2 part 2

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Chapter 2: Descriptive Statistics PART 2

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Page 1: Chapter 2 part 2

Chapter 2: Descriptive StatisticsPART 2

Page 2: Chapter 2 part 2

Get out your TI-83 or TI-84

We’re going to work though the example on the top of page 79 to learn how to graph a histogram on your calculator

Page 3: Chapter 2 part 2
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Next, we’re going to create a histogramOn the next slide is a poll asking you how many hours you play video games each week

You need to answer a whole number; if you don’t play any, answer 0

I would like you to create a histogram at your desk with this data

When you are finished, check with a neighbor, and then check with me

Let’s use the ‘Square Root’ method to decide on the number of classes

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Measures of the Location of Data

Quartiles and Percentiles

Quartiles are special percentilesThe first quartile, Q1 , is the same as the 25th percentileQ3 is the same as the 75th percentileThe median, M, is both the 2nd quartile and the 50th percentileIf you score in the 90th percentile means that 90% or more of the test scores are the same or less than

your score This also means that 10% are the same or greater than your test score

The median is a number that measures the center of your data Consider the following data, ordered from smallest to largest:

1, 4, 7, 7, 9, 12, 25 1, 4, 7, 7, 8, 9, 12, 25

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Measures of the Location of Data

Quartiles and Percentiles

Quartiles are numbers that separate the data into two quartersAn easy way to think of quartiles is that they are the medians of the two halves of the data.

Separate the data into two halves (leave out the median if odd number of data) Find the median of the first half of the data – this is Q1

Follow the same procedure with the 2nd half of the data to find Q3

The interquartile range is a number that indicates the spread of the middle half or the middle 50% of the data. It is the difference between the third quartile and the first quartile

The IQR can help determine potential outliers A value is suspected to be a potential outlier if it is less than 1.5*IQR below the first quartile, or more than 1.5*IQR above the

third quartile Potential outliers always require further investigation

1, 4, 7, 7, 9, 12, 25 1, 4, 7, 7, 8, 9, 12, 25

IQR = Q3 – Q1

• QUESTIONS:• What is the IQR for the two data sets below?• Are their outliers in the two data sets below?

Page 8: Chapter 2 part 2

To find the kth Percentile

k = kth percentile

i = the index (ranking or position of data value)

n = the total number of dataOrder the data from smallest to largestCalculate If i is an integer, than the kth percentile is the data value in the ith position in the ordered set of dataIf i is not an integer, then round i up and round i down to the nearest integers

Average the two data values in these two positions in the ordered data set

Try It 2.17, Page 91

Page 9: Chapter 2 part 2

Interpreting Percentiles, Quartiles, and Median

Percentile: Indicates the relative standing of data when data are sorted into numerical order from smallest to largest

Percentages of data values are less than or equal to the pth percentile Exmaple: 15% of data values are less than or equal to the 15th percentile Remember, low percentiles always correspond to lower data values, and high to high.

Whether a low or high percentile is good or bad depends on the context Being in the high percentile of grades is more desirable Being in the low percentile of cancer risk is desirable

Page 10: Chapter 2 part 2

Box Plots (or Box-and-Whisker Plots)

…give a good graphical image of the concentration of data (and allows us to have more cats!)

More importantly, they also show how far the extreme values are from most of the data

To construct a box plot, we need the following five pieces of information from the data:

1. Minimum Value2. Q1 (first quartile)3. Median4. Q3 (third quartile)5. Maximum Value

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Box Plots (or Box-and-Whisker Plots)

Let’s take a look at an example; consider take the following values:1. Minimum Value2. Q1 (first quartile)3. Median4. Q3 (third quartile)5. Maximum Value

Min = 1Q1 = 2Med = 7Q3 = 9Max = 11.5

It is important to start the box plot with a scaled number line; otherwise the box plot may not be useful

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Create a Box-and-Whisker PlotThe reported shoe sizes for the class are as follows:

12; 8; 7; 7.5; 7.5; 10; 10; 10.5; 12; 10; 7.5; 10.5; 7; 8; 8.5; 6; 8.5; 8.5; 13; 9; 9; 8; 8; 8; 11.5; 10.5

Enter the values in your calculator in list 1

Go into the STAT menu, and choose 2:SortA(

Hit 2nd STAT (this is the list function), and choose L1; close the parenthesis and hit ENTER

Next, hit STAT, arrow to CALC, and hit 1:1-Var Stats (Choose L1 if it is not there)

Go to Calculate and hit ENTER

Scroll down to find what you are looking for

NOW, create the Box-and-Whisker plot by hand

Page 13: Chapter 2 part 2

Create a Box-and-Whisker Plot Hit 2nd, STAT PLOT (above y=)

Scroll to Plot1, hit enter, arrow to On

Arrow down to TYPE and choose the bottom middle graph

In Xlist, choose L1

For Freq, enter 1 (if it’s not already there)

Hit 2nd, Quit (above Mode, next to 2nd)

Hit ZOOM

Choose 9: ZoomStat

Hit TRACE and use the arrow keys to examine the box plot