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 4 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.

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 or greater than is an outlier Example:

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.