CCGPS Advanced AlgebraCCGPS Advanced Algebra

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 4Unit 4Day 1 Vocabulary and Day 1 Vocabulary and

Graphs ReviewGraphs ReviewStandards

MCC9-12.S.1D.2 and MCC9-12.S.ID.3

VocabularyVocabulary• 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.

VocabularyVocabulary• 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.

MeanMeanThe 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

45

20

The Mean is 4

MedianMedianThe middle-most value of a data

set; 50% of the data is less than this value, and 50% is greater than it

Example:

2Q

First and Third First and Third QuartilesQuartiles

The value that identifies the lower and upper 25% of the data; the median of each half.

Example:

1Q 3Q

Interquartile RangeInterquartile Range

The difference between the third and first quartiles; 50% of the data is contained within this range

Example:

3Q 1QSubtract Third Quartile ( ) – First Quartile ( ) = IQR

OutlierOutlier 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

or greater than is an outlier

Example:

)(5.11 IQRQ

)(5.13 IQRQ

5-Number Summary5-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 PlotBox Plot

• From a five-number summary, I can create a box plot on a graph with a scale.

• Minimum – left whiskerLower Quartile – left side of boxMedian – middle of boxUpper Quartile – right of boxMaximum – right whisker

• Each portion of the box plot represents 25% of the data.

Box Plot - ExampleBox Plot - Example

2, 4, 4, 5, 6, 8, 8, 8, 9, 10, 11, 11, 12, 15, 17Min: Q1: Med: Q3: Max: Range: IQR:

2 5 8 11 17 17 – 2 = 15 11 – 5 = 6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Box PlotBox PlotA 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 Box Plot: Pros and Consand 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 PlotDot PlotA 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 Dot Plot: Pros and Consand Cons

Advantages:•Simple to make•Shows each individual data pointDisadvantages:•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.

HistogramHistogramA 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 Histogram: Pros and ConsCons

Advantages:•Visually strong•Good for determining the shape of the dataDisadvantages:•Cannot read exact values because data is grouped into categories •More difficult to compare two data sets