 # Describe Quantitative Data with Numbers. Mean The most common measure of center is the ordinary arithmetic average, or mean.

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Describe Quantitative Data with Numbers

Mean The most common measure of center is the ordinary arithmetic average, or mean

Mean X-bar refers to the mean of a sample- from a larger population When we need to refer to population mean we will use μ (Mu) μ is only used when we have an entire population of data available- Solve in the same way as x-bar

Student Commute to School

Mean The mean is sensitive to the influence of extreme observations If a statistic is not affected very much by extreme observations we call it a resistant measure. But what does mean really mean?

Median The median unlike the mean, is resistant

New York Travelers

Range Simplest measure of variability Subtract the smallest value from the largest value Depends on only the maximum and minimum values which may be outliers

Quartiles First Quartile (Q1)-lies one quarter of the way up the list Second Quartile (Q2)- is the median and is half way up the list Third Quartile (Q3)- lies three quarters of the way above the list These quartiles mark out the middle half of the distribution

Interquartile Range (IQR) Measures the range of the middle 50% of the data.

How to calculate Q1, Q3 and IQR Arrange in increasing order and locate median First quartile is the median of the observations to the left of the median Third quartile is the median of the observations to the right of the median IQR= Q3-Q1 Include median values if you average the two

New York Travel Times 51010151515152020 202530304040456060 6585

1.5xIQR Rule for Outliers Call an observation an outlier if it falls more than 1.5xIQR above the third quartile of below the first quarile

New York Travel Times 51010151515152020 202530304040456060 6585 IQR:27.5 minutes

Five Number Summary Minimum Q1 Median (Q2) Q3 Maximum

Box Plot/ Box-and-Whisker Plot A central box is drawn from the first quartile (Q1) to the third quartile A line in the box marks the median Lines called whiskers extend from the box out to the smallest and largest that are not outliers Outliers are marked with (*)

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Still determine… Shape- Skew, distance from minimum to median and median to max Center- median Spread- IQR and the range Outlier Values

Standard Deviation and Variance

How to find Standard Deviation

Details of Standard Deviation Measures spread about the mean and should only be used when the mean is chosen as the measure of center Standard deviation is always greater than or equal to 0 Standard deviation has the same units of measurement as the original observations Like the mean, standard deviation is not resistant

The median and IQR are usually better than the mean and standard deviation for describing skewed distribution or a distribution with strong outliers Use mean and standard deviation only for reasonably symmetric distributions that do not have outliers

Box Plots on the Calculator 1.Stat, Edit 2.Enter the travel time data for North Carolina in L1/list1 and for New York in L2/list2. 3.Set up two plots: Plot 1 to show a boxplot of NC and Plot 2 to show a boxplot of NY *Calculator offers two types Of boxplots

Travel Times North Carolina (L1) 5 10 12 15 20 25 30 40 60 New York 5 10 15 20 25 30 40 45 60 65 85

Box Plots on the Calculator Use the calculator’s zoom feature to display the parallel boxplots Then trace to view the 5-number summary Press Zoom and select ZoomStat Press Trace

Standard Deviation on Calculator Leave data from previous problem in L1 and L2 Press Stat Scroll to Calc Choose 1-Var stat 2 nd L1 Repeat Steps for L2 Values

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