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The Statistical Enquiry Cycle Step 4: Analysis Displaying Data: Box Plots / Dot Plots

The Statistical Enquiry Cycle Step 4: Analysis Displaying Data: Box Plots / Dot Plots. Lesson Objective. To learn how to create Dot Plot and Box Plot graphs from a dataset. Lesson Success Criteria. Can accurately create a Dot Plot and Box Plot from a dataset. What it involves….

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The Statistical Enquiry Cycle Step 4: Analysis Displaying Data: Box Plots / Dot Plots

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  1. The Statistical Enquiry Cycle • Step 4: Analysis • Displaying Data: Box Plots / Dot Plots

  2. Lesson Objective To learn how to create Dot Plot and Box Plot graphs from a dataset Lesson Success Criteria • Can accurately create a Dot Plot and Box Plot from a dataset

  3. What it involves… • This is where you look at the data to see what it tells you about your problem. • i.e. summarising and making sense of the data, so you can answer your question • This will involve • Calculate statistical measures which summarise your data • Central Tendency (averages: mean, median, mode) • Spread (range, interquartile range) • Display the data into relevant tables and graphs • Using “I notice…” statements in relation to your observations of any • patterns, or special features of the data set • Unusual values (outliers) • Symmetry of distribution • Are your predictions still the same, or would you change them? • NOTE: it is important that any statements are supported with evidence

  4. Types of plots There are many ways to display data. Dot Plot Box Plot Stem and Leaf Graph Histogram Pie Chart Scatter Graph Line Graph Bar Plot Pictograph … The main two we will concentrate on

  5. 1. The Dot Plot

  6. Dot Plot • Simple to plot • Normally with counted data • Dots stacked to represent repeated data values • Frequency of each value shown by the number of dots in each column • Good for data sets up to about 30 values • Can be applied to continuous data, by subgrouping into approx. 12-15 groups • Provides a good visual representation of the shape of a distribution • i.e. symmetrical, bi-modal, uniform or skewed • Clusters and gaps in the data set can be seen easily • Unusual values also identified easily

  7. Dot Plot • Can draw a box-plot directly from a dot plot – can be an easier way to draw the box-plot as you don’t have to order the data • Ensure the same scale is used by both plots

  8. Practice Chapter 7: page 236,237 Exercise D: Dot Plots

  9. 2. The Box Plot

  10. Box Plot (also known as Box and Whisker Plot) • Requires data to be ordered, before finding the 5-number summary • Ideal for comparing two or more sets of data • Useful for assessing symmetry, and skewness of all data, and middle 50% 25% of data values 25% 25% 25% Lowest value Lower quartile Median Upper quartile Highest value

  11. Boxplot showing outliers, and extreme values Outliers are values that lie outside 1.5 x IQR, but within 3 x IQR Extreme values lie outside 3 x IQR Whiskers extend to the highest value within 1.5 IQR The same applies to the lower end values

  12. Practice Chapter 7: page 239 Exercise F : Box Plots Exercise E : Stem and Leaf Plots (if interested)

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