Back to Back Stem and Leaf Plots/Describing Histograms (9)
Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ (VCMSP325)
LO: To construct back-to-back stem-and-leaf plots and histograms while using vocabulary such as ‘skewed’, ‘symmetric’ and ‘bimodal’ to describe a data set.
Know:
What is a stem-and-leaf plot.
How to interpret a stem-and-leaf plot.
How to interpret a histogram.
The definition of key vocabulary such as skewed, symmetrical and bimodal.
Understand:
Data can be visually represented using stem-and-leaf plots and can easily be compared using back-to-back stem-and-leaf plots as well as histograms.
Do:
To construct and compare data from a stem-and-leaf plot.
To construct and compare data from histograms.
To interpret a data set using key vocabulary such as skewed, symmetric and bimodal.
Elaborations
using stem-and-leaf plots to compare two like sets of data such as the heights of girls and the heights of boys in a class
describing the shape of the distribution of data using terms such as ‘positive skew’, ‘negative skew’ and ‘symmetric’ and ‘bi-modal’
Visual Representations
Teaching Notes
Stem-and-leaf plots are an easy way of organising data.
You basically break the numbers apart (partitioning).
Eg.) 47 can be broken into 4-10s and 7-1s.
The 4 then becomes your stem, and 7 becomes your leaf.
In a back-to-back stem-and-leaf plots, it’s basically 2 stem-and-leaf plots put back-to-back with each other. They share the same stem, but the leafs go opposite ways. This can be used to quickly compare 2 data sets to draw conclusions.
The close the leafs are to the stem the smaller the number, the further away from the stem the leafs are the larger the number.
Stem-and-Leaf and Histogram Descriptions
Histograms and Stem and Leaf plots can be classified as “skewed”, “bi-modal”, “uniform” or “normal” depending on how the data falls.
Skewed displays show a tendency for the data to lean towards 1 side (either positive or negative). They have a general trend of sloping upwards or downwards.
Bi-modal (bi means 2, modal means mode – common) displays show a tendency for the data to have 2 “humps” in the data.
Uniform displays show a tendency for the data to be even across the board (same amount of results for each item).
Symmetrical/Normal displays show a tendency for the data to be like a “bell curve“, lower on the opposite ends and much more congregated in the middle values.
Stem-and-Leaf plots can be classified as “skewed”, when the data leans more towards one side than the other.
Stem-and-Leaf plots can be classified as “symmetric”, when the data is spread out in an “even” manner.
Stem-and-Leaf plots can be classified as “bimodal”, when the data has two major areas (humps).