Summarizing Data Review!

Summarizing Data

Lesson Goals

• Relate the measure of center or variablility to the shape of the data distribution.

• Summarize a numerical data set, how it was measured and units of measure.

• Summarize numerical data sets by reporting the number of observations.

• Analyze data represented on a histogram.

  Interpret data on a line plot.

  Determine the interquartile range of a numerical data set.

Standards

• 6.DS.4 Summarize numerical data sets in relation to their context in multiple ways

• 6.DS.2 Select, create, and interpret graphical representations of numerical data, including line plots, histograms, and box plots.

Unit 6 Test Review!

• There are 2 parts to the Test!

• Make sure to do them both!

Multiple Choice

Is the mean to the left of the median in this chart?

• Yes

• No

Multiple Choice

What is the MEDIAN of this data

• 95

• 90

• 100

• 40

Choosing a Measure of Center

• The mean and median are both measures of center.

• When a distribution is normal or uniform the mean and median are equal (+/-) and represent the data accurately.

• If the data is skewed left or skewed right the mean is skewed away from the center, so the median is a better measure of center.

Mean or median?

• Which measure of center best represents the middle of the set of data?

• This histogram is very close to symmetrical (normal, regular)

• The mean and median are close enough that either will work as a representation of the middle of the data set.

Mean or Median?

• What is the type of distribution? The data is stretched to the right (right tailed) so it is skewed right.

• Compare the mean and median. When a distribution is skewed right the mean is greater than the median.

• Because the mean is pulled to the right the median is a better measure of center.

Mean or Median?

• What type of distribution?

• Though the heights are different neither end seems much taller or shorter. This is a uniform distribution

• It is fair to assume that the mean and median are approximately equal.

Multiple Choice

What is the shape of the data?

• symmetrical

• skewed left

• skewed right

• bell curve

Multiple Choice

How would you describe this distribution?

• Left skewed

• Uniform

• Right Skewed

• Symmetrical

Multiple Choice

What is the best measure of center for this set of data?

• mean

• median

• either

Multiple Choice

What is the best representation of the center of the data

• mean

• median

• Either

Multiple Choice

What is the best representation of the center of the data

• mean

• median

• Either

Data Values

• Each x is a single data value

• The number the x is above is the value of that x.

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5 Number Summary

• The 5 number summary includes the minimum, Q1, the median (Q2), Q3, and the maximum.

• Determine the minimum and maximum, then find the median (Q2), the median of the first haf of the data,(Q1) then the median of the second half of the data(Q3)

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Multiple Choice

What is the 5 number summary of this data set?

• 0, 2, 4, 5.5, 14

• 0, 1, 2.5, 9, 14

• 0, 1, 3.5, 6, 14

• 0, 1, 3, 6, 10

Mean

• The mean is also know as the average.

• To find the mean add together all of the data points and divide the sum by how many data points there are in the set.

•  $\frac{1+2+3+4+5}{5}=\frac{15}{5}=3,\ 3\ is\ the\ mean\ or\ average$  

Multiple Choice

What is the mean of this data set?

• 4.25

• 3.5

• 5

• 85

Range

• Range is found by subtracting the minimum from the maximum.

• So in a data set that looks like this: {23, 34, 45, 56, 78} you would subtract 23 from 78 (78 - 23)

• The range of the data is 55 (78-23 = 55)

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Interquartile Range (IQR)

• Interquartile range (IQR) is the middle 50% of a data set.

• IQR is found by subtracting Q1 from Q3

• Q1 and Q3 of this set are in red (the median is in blue) {3,4,5,6,7,8,9}

• The IQR is found by 8-4

• The interquartile range is 4

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Outliers

• An outlier is a data point that is WAY outside of most of the data.

• To find any technical outliers we need to first find the upper and lower fence.

• Lower fence is $Q_1-1.5\left(IQR\right)$  

• Upper Fence is  $Q_{3\ }+\ 1.5\left(IQR\right)$  

• Any data outside of the fences is an outlier. 

Multiple Choice

Are there any outliers this data set?

• Yes

• No

Open Ended

What are the lower and upper fences?

Open Ended

What was the outlier?

Multiple Choice

Which choice is the best description of the distribution data set?

• Uniform

• Symmetrical

• Skewed left

• Skewed right

Multiple Choice

What is the best measure of center for this data set?

• mean

• mode

• median

MAD Mean Absolute Deviation

• MAD shows the average difference the data set has from the mean or how far on average the data deviates from the mean.

• To find it, first find the mean.

• Then, find the absolute distance each data point has from the mean.

• Finally, find the mean of those absolute values.

MAD Mean Absolute Deviation

• {3,4,5,6,7,8,9}

• To find it, first find the mean.  $\frac{3+4+5+6+7+8+9}{6}=\frac{42}{7}=6$  

• Then, find the absolute distance each data point has from the mean. The absolute value of (3-6, 4-6, 5-6, 6-6, 7-6, 8-6, 9-6) or (3, 2, 1, 0, 2, 3)

• Finally, find the mean of those absolute values. $\frac{3+2+1+0+1+2+3}{6}=\frac{12}{2}=2$  

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Make Sure:

• You've completed all of you quizzes! (Especially 6.11!)

• To do the test once now! (Part 1 and Part 2)

Questions?