Describing Data

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Describing Data
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Gather some data

• Write your answers on a note card
• Heart rate
• Number of minutes you slept last night
• Number of days until your next birthday
• Number of contacts in your cell phone
• Gender

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Ways to look at the data
Box plot
Dot plot
Histogram
Number of hurricanes that occurred each year from
1944 through 2000 as reported by Science magazine
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3 Characteristics of data
Shape Center Spread
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Shape of the data Symmetric
The IQ scores of 60 randomly selected 5th graders
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Shape of the data Symmetric
The age of all US Presidents at the time they
took office Notice that this distribution has
only one mode
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Shape of the data Bimodal
The winning times in the Kentucky Derby from 1875
to the present. Why two modes?
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Shape of the data Bimodal
The winning times in the Kentucky Derby from 1875
to the present. Why two modes?
The length of the track was reduced from 1.5
miles to 1.25 miles in 1896. The race officials
thought that 1.5 miles was too far.
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Shape of the data skewed
Data for two different variables for all female
heart attack patients in New York state in one
year. One is skewed left the other is skewed
right. Which is which?
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Shape of the data skewed
LEFT
RIGHT
Data for two different variables for all female
heart attack patients in New York state in one
year. One is skewed left the other is skewed
right. Which is which?
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Center and Spread of Data
Maximum Q3 Median Q1 Minimum
100th percentile 75th percentile 50th
percentile 25th percentile 0th percentile
These numbers are called the 5 number
summary. The median measures the center of the
data. Q3 Q1 Interquartile range (IQR)
measures the spread.
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Five number summary
A simple example
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Center and spread of data
The mean or average is a measure of the center of
a distribution
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Center and spread of data
The mean of the absolute deviation of each
number Mean absolute deviation (mad) measures
the spread of the data (you learned this last
year).
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Center and spread of data
The mean of the squares of the deviation of each
number The formula given above is for the
population variance
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Center and spread of data
The square root of the variance. This quantity
has the same units as the data. This is one of
the most common measures of the spread of a
distribution. The formula given above is for the
population standard deviation.
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Center and spread of data
Mean Absolute Deviation
Standard Deviation
Variance
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Center and spread of data
Calculate the mean absolute deviation,
variance, and standard deviation for the
following data.
1, 2, 3, 4, 5
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Homework
Find a graph of some data from a magazine or
newspaper on the internet find something
interesting bring it in for Monday
Math 2 Book p. 261 15, 17 In addition, find the
five number summary and the IQR for these two
problems