2 MCC6.SP.1Examples:Statistical questions that anticipate variabilityStatistical questions that do not anticipate variabilityRecognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.Unit cubes/centimeter cubesVocabulary WordsStatistical QuestionVariability
3 Statistical Variability Identify if the statement below is a statistical question?What is a statistical question?A question that generates a variety of answers is called a statistical question.Depending on the question, the type of data gathered can be either categorical or numerical.An example of a categorical question is “What is your favorite type of pizza?” The answers generated by this question will be categories of pizza types such as pepperoni, cheese, or sausage.An example of a numerical question is “How many pencils does each member of our class have in his or her desk?” A variety of numerical answers about the number of pencils would be given by a typical 6th grade class.What is the height of each person in my class?What are the math test scores of the students in my class?How old am I?How many letters are in the names of each person in my class?What is my height?How many pets are owned by each student in my grade level?How many letters are in my name?What is my math test score?Examples of Statistical Questions:Non-Examples of Statistical Questions:
4 MCC6.SP.2Examples:Describe a set of data by its centerDescribe a set of data by its spreadDescribe a set of data by its overall shapeUnderstand 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.Vocabulary WordsCenter: mean, median, modeSpread: range, mean absolute deviationShape: cluster, gap, outlierMini-monster activity or Shaq activity
8 Center of Data Mean, Median, Mode Fifteen students were asked to rate how much they like Middle school on a scale from one to ten.Here is the data collected: 1, 10, 9, 6, 5, 10, 9, 8, 3, 3, 8, 9, 7, 4, 5The first step is to put your data in ascending order.1, 3, 3, 4, 5, 5, 6, 7, 8, 8, 9, 9, 9, 10, 10Let’s find the Mean = average value for the data159715== 6.5
9 Center of Data Mean, Median, Mode Fifteen students were asked to rate how much they like Middle school on a scale from one to ten.1, 3, 3, 4, 5, 5, 6, 7, 8, 8, 9, 9, 9, 10, 10Let’s find the Median = the value for which half the numbers are longerand half the numbers are smaller.Let’s find the Mode = the number that occurs most oftenMean: 6.5Median: 7Mode: 9
10 Variability of Data Mean Absolute Deviation Range Fifteen students were asked to rate how much they like Middle school on a scale from one to ten.1, 3, 3, 4, 5, 5, 6, 7, 8, 8, 9, 9, 9, 10, 10RangeFifteen students were asked to rate how much they like Middle school on a scale from one to ten.1, 3, 3, 4, 5, 5, 6, 7, 8, 8, 9, 9, 9, 10, 10MEAN| 6.5 – 1 | + | 6.5 – 3 | + | 6.5 – 3 | + | 6.5 – 4 | + | 6.5 – 5 | +| 6.5 – 5 | + | 6.5 – 6 | + | 6.5 – 7 | + | 6.5 – 8 | + | 6.5 – 8 | +| 6.5 – 9 | + | 6.5 – 9 | + | 6.5 – 9 | + | 6.5 – 10 | + |6.5 – 10| = 36.5Let’s find the Range = Difference between maximum and minimum data.10 – 1 = 9Range = 936.515= 2.43
11 MCC6.SP.3Examples:How a number that describes the measure of center is different from a number that describes the measure of variationRecognize 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.Vocabulary WordsCenterVariation
12 Center Vs Variability Center: Summarizes all the values with a single numberMedian: the middle numberMean: the average numberVariability:Describes how all the values vary with a single numberRange: shows the greatest amount of variation between two data valuesMAD: shows the average variation between the data values
13 MCC6.SP.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots.Examples:Draw a dot plotDraw a histogramDraw a box plotVocabulary WordsDot plotHistogramBox Plot
17 Box Plot How to Create a Box-and-Whisker Plot 1) Write the data in order from least to greatest.2) Draw a horizontal number line that can show the data in equal intervals.3) Find the median of the data set and mark it on the number line.4) Find the median of the upper half of the data. This is called the upper quartile (Q3). Mark it on the number line.5) Find the median of the lower half of the data. This is called the lower quartile (Q1). Mark it on the number line.6) Mark the lower extreme (minimum) on the number line.7) Mark the upper extreme (maximum) on the number line.8) Draw a box between the lower quartiles and the upper quartile. Draw a vertical line through the median to split the box.9) Draw a “whisker” from the lower quartile to the lower extreme.10) Draw a “whisker” from the upper quartile to the upper extreme.
19 Dot Plots How to Create a Dot Plot 1) Draw a horizontal number line. 2) Determine and mark a scale of numbers below the line. Make sure to include the minimum and maximum values in the data set and all consecutive number values in between.Example: In the data set, there is a minimum value of 1 and a maximum value of 5. The number line must include tick marks for every number value from 1 through 5. A fewnumbers before the minimum and a few numbers after the maximum can be included.3) A dot is tallied for each value above the corresponding number. Keep the imaginary y-axis as a frequency mark to ensure that dots are plotted correctly.4) Put a title on the graph.
21 How to Create a Frequecty Chart & Histogram 1) Make a frequency table of the data by selecting a range that will contain all of the data and then divide it into equal intervals. In the example above, the range of ages is from 0 to 69 soequal intervals of 10 years were selected.2) Using graph paper, draw an x-axis where each box will represent an interval of numbers to represent the ranges.3) Draw a y-axis with a scale of numbers appropriate for the data. Common scales are multiples of 1, 2, 5, 10 or 20.4) Draw each bar on the histogram to correlate the intervals with the frequency of occurrence.5) Title the graph and the x and y-axis.
22 Reporting the number of observations. MCC6.SP.5Summarize numerical data sets in relation to their context, such as by:Examples:Draw a frequency chart to report the number of observationsDescribe a graph or information on how it was measured and its unit of measurementMCC6.SP.5aReporting the number of observations.MCC6.SP.5bDescribing the nature of the attribute under investigation, including how it was measured and its units of measurement.Vocabulary WordsFrequency Chart
23 Reporting # of Observations How many families have 3 children? 12 families How many families have less than 3 children? 11 families
24 Describing the UnitsWhat information was collected to create this graph?28 families with 1 – 5 children were surveyedFamilies reported how many children they hadWhat are the units of measurement used within this graph?Number of children in familiesNumber of families with specified amount of children
25 MCC6.SP.5Summarize numerical data sets in relation to their context, such as by:Examples:Describe a box plot in terms of median and interquartile rangeDescribe a histogram in terms of median, mean, and mean absolute deviationDescribe a dot plot in terms of mean, median, and mean absolute deviationMCC6.SP.5cGiving 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 was gathered.Vocabulary WordsOutlier
28 MCC6.SP.5Summarize numerical data sets in relation to their context, such as by:Examples:How does the measure of center relate to the shape of the data set?How does the measure of variability relate to the shape of the data set?MCC6.SP.5dRelating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.
29 Representative Measures of Center Use the Dot Plot to identify the Mean, Median & ModeMode = Number used most in the set1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,4,4,4,5Mode = 1Median = Number in middle of set1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,4,4,4,5Median = 2Mean = Average= 4444/20 = 2.2Mean = 2.2
30 Representative Measures of Variability Use the Dot Plot to identify the Range, IQR, and MADRange = 5 – 1 = 4IQR:1,1,1,1,1,1,1,1,2,2,2,2,2,3,3,3,4,4,4,51st Quartile: 13rd Quartile: 3IQR: 3 – 1 = 2