Determine quartiles and interquartile range and investigate the effect of individual data values, including outliers on the interquartile range (VCMSP349)

Construct and interpret box plots and use them to compare data sets (VCMSP350)

Compare shapes of box plots to corresponding histograms and dot plots and discuss the distribution of data (VCMSP351)

LO: To determine quartiles and interquartile range of a data set and use them to construct and compare box-and-whisker plots.

Know:

  • How to create a box and whisker plot from a given data set.

  • How to identify the five-number summary (minimum/maximum values, median and lower/upper quartiles) from a data set.

  • How to place values on a number line.

Understand:

  • that box plots are an efficient and common way of representing and summarising data and can facilitate comparisons between data sets.

Do:

  • I can construct and interpret box plots and use them to compare different data sets.

  • I can compare shapes of box plots to corresponding histograms and dot plots.

Elaborations

  • finding the five-number summary (minimum and maximum values, median and upper and lower quartiles) and using its graphical representation, the box plot, as tools for both numerically and visually comparing the centre and spread of data sets

  • exploring the effect of varying data values, including outliers, on the interquartile range for different sets of data

  • using parallel box plots to compare data about the age distribution of Aboriginal and Torres Strait Islander people with that of the Australian population as a whole

  • investigating data in different ways to make comparisons and draw conclusions

  • using a dot plot, box-plot or histogram to construct a cumulative frequency distribution for a set of data

Visual Representations

Box and Whisker plots are an easy way of organizing data. It shows our mininmum/maximum values as well as median of our data.

They also split the data set into four equal parts which are called quartiles.

The lower quartile splits the first and second quartiles of the data set, while the upper quartile splits the data set from the third and fourth quartile.

Teaching Notes

Creating Box and Whisker Plots Step by Step Process

  1. Organize your data in ascending order (smallest to biggest)

  2. Find the min/max values

  3. Find the median (middle number) of the data

  4. Find the median value of Quarter 1

  5. Find the median value of Quarter 3

  6. Draw your lines with min/max values

  7. Add in Q1 and Q3 values and draw box around the two values

  8. Add in your median value and draw a line to split the box.

Box Plots Videos

Practise Questions

My Maths 10/10A

Exercise 10D pg. 489 Q. 2-15

Exercise 10D pg. 501 Q. 1-5, 12

Exercise 10D pg. 501 Q. 6-11

Next Lesson – Scatterplots