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CCGPS Advanced Algebra
Day 1
UNIT QUESTION: How do we use
data to draw conclusions about
populations?
Standard: MCC9-12.S.ID.1-3, 5-9, SP.5
Today’s Question:
How do I represent and compare
univariate data?
Standard: MCC9-12.S.ID.1
Unit 1
Day 1 Vocabulary and Graphs
Review
Standards
MCC9-12.S.1D.2 and MCC9-12.S.ID.3
Vocabulary
• Quantitative Data – Data that can be
measured and is reported in a numerical form.
• Categorical/Qualitative Data – Data that can
be observed but not measured and is sorted by
categories.
Vocabulary
• Center – the middle of your set of data;
represented by mean, median, and/or mode.
• Spread – the variability of your set of data;
represented by range, IQR, MAD, and standard
deviation.
• Outlier – a piece of data that does not fit with
the rest of the data. It is more than 1.5IQRs
from the lower or upper quartile, or it is more
than 3 standard deviations from the mean.
Mean
The average value of a data set, found by
summing all values and dividing by the
number of data points
Example:
5 + 4 + 2 + 6 + 3 = 20
20
4
5
The Mean is 4
Median
The middle-most value of a data set; 50%
of the data is less than this value, and
50% is greater than it
Example:
First Quartile
The value that identifies the lower 25% of the
data; the median of the lower half of the
data set; written as
Q1
Example:
Third Quartile
Value that identifies the upper 25% of the
data; the median of the upper half of
the data set; 75% of all data is less than
this value; written as Q
3
Example:
Interquartile Range
The difference between the third and first
quartiles; 50% of the data is contained within
this range
Example:
Subtract
Third Quartile ( Q3 ) – First Quartile ( Q1) = IQR
Outlier
A data value that is much greater than or much less
than the rest of the data in a data set;
mathematically, any data less than Q1 1.5( IQR )
or greater than Q3  1.5( IQR ) is an outlier
Example:
The numbers below represent the number of homeruns hit by
players of the Wheeler baseball team.
2, 3, 5, 7, 8, 10, 14, 18, 19, 21, 25, 28
Q1 = 6
Q3 = 20
Interquartile Range: 20 – 6 = 14
Do the same for Walton: 4, 5, 6, 8, 9, 11, 12, 15, 15, 16, 18, 19, 20
5-Number Summary
• A 5-Number Summary is composed of the
minimum, the lower quartile (Q1), the median
(Q2), the upper quartile (Q3), and the
maximum.
• These numbers discuss the spread of the data
and divide the data into 4 equal parts.
Box Plot
• From a five-number summary, I can create a
box plot on a graph with a scale.
• Minimum – left whisker
Lower Quartile – left side of box
Median – middle of box
Upper Quartile – right of box
Maximum – right whisker
• Each portion of the box plot represents 25% of
the data.
Box Plot - Example
2, 4, 4, 5, 6, 8, 8, 8, 9, 10, 11, 11, 12, 15, 17
Min: 2 Q1: 5 Med: 8 Q3: 11 Max:17
Range:17 – 2 = 15 IQR: 11 – 5 = 6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
The numbers below represent the number of homeruns hit by
players of the Wheeler baseball team.
2, 3, 5, 7, 8, 10, 14, 18, 19, 21, 25, 28
Q1 = 6
Q3 = 20
Interquartile Range: 20 – 6 = 14
6
12
20
Box Plot
A plot for quantitative data showing the minimum,
maximum, first quartile, median, and third
quartile of a data set; the middle 50% of the
data is indicated by a box.
Example:
Box Plot: Pros and Cons
Advantages:
• Shows 5-point summary and outliers
• Easily compares two or more data sets
• Handles extremely large data sets easily
Disadvantages:
• Not as visually appealing as other graphs
• Exact values not retained
Dot Plot
A frequency plot for quantitative data that
shows the number of times a response
occurred in a data set, where each data
value is represented by a dot.
Example:
Dot Plot: Pros and Cons
Advantages:
• Simple to make
• Shows each individual data point
Disadvantages:
• Can be time consuming with lots of data
points to make
• Have to count to get exact total. Fractions
of units are hard to display.
Histogram
A frequency plot for quantitative data that
shows the number of times a response or
range of responses occurred in a data set.
Ranges should not have overlapping values.
Example:
Histogram: Pros and Cons
Advantages:
• Visually strong
• Good for determining the shape of the data
Disadvantages:
• Cannot read exact values because data is
grouped into categories
• More difficult to compare two data sets
Pie Chart
A chart for categorical data that shows the
percentage of responses that fell into
each category as a fraction of a pie.
Example:
Pie Chart: Pros and Cons
Advantages:
• Visually strong
• Good for comparing the popularity of each
category
Disadvantages:
• Cannot read exact values because data is
represented as proportion instead of number of
responses.
• Could be skewed comparison if charts have
substantially different numbers of responses.
Bar Graph
A graph that represents categorical data by the
number of responses received in each category.
Example:
Bar Graph: Pros and Cons
Advantages:
• Shows number of each answer
• Good for comparing the popularity of each
category
Disadvantages:
• Graph categories can be reorganized to
emphasize certain effects since it resembles a
histogram.