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: = 20 The Mean is 4

Median 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 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 Example:

Interquartile Range The difference between the third and first quartiles; 50% of the data is contained within this range Example: Subtract Third Quartile ( ) – First Quartile ( ) = 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 or greater than 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 Q 1 = 6Q 3 = 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: Q1: Med: Q3: Max: Range: IQR: – 2 = – 5 =

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 Q 1 = 6Q 3 = 20 Interquartile Range: 20 – 6 =

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.