Foundations of Elementary Math 3

Fun with Statistics. pattern blocks

Notes on Statistics
Spring 2020

Chapter 7 Statistics

§ 7.1 Collecting and Graphing Data
Descriptive Statistics part 1
  • Types of Graphs
    • Line Plots aka Dot Plots
    • Stem and Leaf Plots
    • Pictographs
    • Bar or Column Charts
    • Pie Charts
    • Histograms and Frequency Table
    • Line Graphs, time series
    • Scatter Plots
      • Trend line
      • Curves of Best Fit
      • Regression Equations
      • Correlation
      • Linear
      • Exponential
      • Power
  • Spreadsheets
Math Activity: Build Basic Charts

Purpose: Explore building charts appropriate to the data.

Materials: Imagination, paper, color.

Directions: Find data for each of the chart types below. For each chart you will need a table to summarize the data, then build the chart. When you are done, take a picture of each page to upload.

Keep in mind that some charts are not appropriate for some data. Proceed with care.

Look through section 7.1 for ideas. Look online for ideas. Look around your house, inside and out. Think about your family and friends. What can you categorize into two or more groups and count? If you do find a good idea online, then personalize it or just reproduce it.

  1. Pie Chart
    gary's typical day as a pie chart, Food 2.5 hours, Work 8 hours, Play 2 hours, Chores 2.5 hours, Exercise 1 hour
  2. Bar Chart
    Parker family water usage. Month	Water Usage: 
                April	14,
                May	9,
                June	13,
                July	15,
                August	12,
                September	17,
                October	7,
                November	6,
                December	5,
                January	5,
                February	4,
                March	4
  3. Pictograph
    cats possessed by Gary 3, Linda 6, Margaret 3, Chuck 2, and Kathy 1
  4. Line Plot aka Dot Plot
    The number of times I have to ask my daughter each day to clean her room, last 30 days
  5. Line Graph
    women vs men with college degrees in labor force
    I wouldn't turn this graph in for my assignment. I would need to reproduce it and cite my source.
Math Activity: Build a Histogram

Purpose: Explore building a histogram based on a large data set.

Materials: Imagination, paper, color.

Directions: Find or make a data set with at least 30 entries. StatKey has some good data set to think about.

  1. Raw data
  2. Grouping decision 1
  3. Frequency table 1
  4. Histogram 1
  5. Grouping decision 2
  6. Frequency table 2
  7. Histogram 2
Math Activity: Build a Scatter Plot and Trend Line

Purpose: Explore bivariate data and correlation.

Materials: Imagination, paper, color.

Directions: Find or make a bivariate data set with at least 10 entries.
Spurious Correlations has some interesting? examples, as does StatKey.

  1. Definitions of each variable
  2. Table of data
  3. Scatter plot, well labeled
  4. Line drawn through points that "fits" trend
  5. Equation of line
  6. Is the line a good fit? Why?
  7. Use the equation to make a prediction? Explain the prediction.

Chapter 7 Statistics

§ 7.2 Describing and Analyzing Data
Descriptive Statistics part 2
  • Descriptive Statistics the science of describing data with charts and summary calculations.
  • Measures of Center
    • Mean
      average = `"sum"/"count"`
    • Median
      middle value when ranked, position = `(n+1)/2`
      the value where 50% of the data is less than or equal.
    • Mode
      most frequently occuring
  • Measures of Spread
    • Range = max - min
    • Quartiles
      The first quartile, `Q_1` is the value where 25% of the data is less than or equal.
      The third quartile, `Q_3` is the value where 75% of the data is less than or equal.
    • InterQuartile Range = `Q_3-Q_1`
    • Standard Deviation
      a measure of average spread from the mean.
  • Box and Whisker Plots
    a graph of the 5-number summary, min, `Q_1`, median, `Q_3`, max
  • Data Distribution
    a graph of description of the center and spread of the data
  • Spreadsheets
    Using spreadsheets to do descriptive statistics.

Chapter 7 Statistics

§ 7.3 Sampling, Predictions, and Simulations
Inferential Statistics
  • Sample vs Population
  • Statistic vs Parameter
  • Random Sampling
    each group of size `n` in a population has the same chance of being selected as any other group of size `n`.
  • Stratified Sampling
  • Data Distributions
    • Skewed Distributions

      The skew is to the tail.

      • Symmetrical
        mean `~~` median
      • Skewed left
        mean < median
      • Skewed right
        mean > median
    • BiModal
      a bimodal distribution of values shown in a histogram
    • Bell Shaped
      a bell shaped distribution, 50 percent free throw, 12 shots
    • Normal
      a normal distribution with 95% shown
  • Measures of Relative Standing
    • Percentiles
    • z-scores
    • Rare events
  • Simulations