Unit 6: Statistics Mean, Median, Mode, Range Measures of Variation Box Plots Line Plots Histograms

CCGPS Standards MCC6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. MCC6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. MCC6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. MCC6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots. MCC6.SP.5. Summarize numerical data sets in relation to their context, such as by: MCC6.SP.5.a. Reporting the number of observations. MCC6.SP.5.b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement MCC6.SP.5.c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Mathematical Practices Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning

Lesson 3: Measures of Variation Vocabulary: Measures of Variation: are used to describe the distribution, or spread, of the data. They describe how the values of a data set vary within a single number. Quartiles: are values that divide a set of data into four equal parts First Quartile: The first quartile is the median of the data less than the median. Third Quartile: The third quartile is the median of the data greater than the median. Interquartile Range: The distance between the first and third quartiles of the data set. Range: The difference between the greatest and least data values Outlier: is a data value that is either much greater or much less than the median.

Lesson 3: Measures of Variation

Lesson 3: Measures of Variation Example 1: Find the measures of variation for the data. Range: Median: Quartiles: Interquartile Range:

Lesson 3: Measures of Variation Example 1: Find the measures of variation for the data. Range: 70-1 = 69 mph Median: 30 + 25 = 27.5 2 Quartiles: Order the numbers 1 8 25 30 50 70 Interquartile Range: Q1 – Q3 50 – 8 = 42 Q1 Q3 Median: 27.5

Lesson 3: Measures of Variation Got it? Do this problem to find out. Determine the measures of variation for the data: 64, 61, 67, 59, 60, 58, 57, 71, 56, 62 Range: Median: Quartiles: Interquartile Range:

Lesson 3: Measures of Variation Got it? Do this problem to find out. Determine the measures of variation for the data: 64, 61, 67, 59, 60, 58, 57, 71, 56, 62 Range: 15 Median: 60.5 Quartiles: Q1: 58 Q3: 64 Interquartile Range: 6

Lesson 3: Measures of Variation Example 2: The ages of candidates in an election are 43, 48, 49, 55, 57, 63, and 72. Range: Median: Quartiles: Interquartile Range:

Lesson 3: Measures of Variation Example 3: The table shows a set of scores on a science test in two different classrooms. Compare and contrast their measures of variation. Room A Range: Median: Q1: Q3: IQR:

Lesson 3: Measures of Variation Example 3: The table shows a set of scores on a science test in two different classrooms. Compare and contrast their measures of variation. Room B Range: Median: Q1: Q3: IQR: