CCGPS Advanced AlgebraCCGPS Advanced AlgebraDay 1Day 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 4Unit 4Vocabulary and Graphs Vocabulary and Graphs

ReviewReviewStandards

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.

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

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

Pie ChartPie ChartA 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 Pie Chart: Pros and ConsCons

Advantages:•Visually strong•Good for comparing the popularity of each categoryDisadvantages:•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 GraphBar GraphA graph that represents categorical data by the number of responses received in each category.

Example:

Bar Graph: Pros and Bar Graph: Pros and ConsCons

Advantages:•Shows number of each answer•Good for comparing the popularity of each categoryDisadvantages:•Graph categories can be reorganized to emphasize certain effects since it resembles a histogram.