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Construct back-to-back stem-and-leaf plots and histograms and describe data, using terms including ‘skewed’, ‘symmetric’ and ‘bi modal’ (VCMSP325)

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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.

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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’

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Visual Representations

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Teaching Notes

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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.

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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.

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Stem-and-Leaf and Histogram Descriptions

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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.

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Stem-and-Leaf plots can be classified as “skewed”, when the data leans more towards one side than the other.

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Stem-and-Leaf plots can be classified as “symmetric”, when the data is spread out in an “even” manner.

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Stem-and-Leaf plots can be classified as “bimodal”, when the data has two major areas (humps).

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Back-to-Back Stem and Leaf Plots Videos

[/title][fullwidth background_color=”” background_image=”” background_parallax=”none” enable_mobile=”no” parallax_speed=”0.3″ background_repeat=”no-repeat” background_position=”left top” video_url=”” video_aspect_ratio=”16:9″ video_webm=”” video_mp4=”” video_ogv=”” video_preview_image=”” overlay_color=”” overlay_opacity=”0.5″ video_mute=”yes” video_loop=”yes” fade=”no” border_size=”0px” border_color=”” border_style=”” padding_top=”20″ padding_bottom=”20″ padding_left=”0″ padding_right=”0″ hundred_percent=”no” equal_height_columns=”no” hide_on_mobile=”no” menu_anchor=”” class=”” id=””][one_half last=”no” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”G-kXDofrj3I” width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][one_half last=”yes” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”_84JyTh7tZo” width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][one_half last=”no” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”achLJ8PRyBw” width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][one_half last=”yes” spacing=”yes” center_content=”no” hide_on_mobile=”no” background_color=”” background_image=”” background_repeat=”no-repeat” background_position=”left top” border_position=”all” border_size=”0px” border_color=”” border_style=”” padding=”” margin_top=”” margin_bottom=”” animation_type=”” animation_direction=”” animation_speed=”0.1″ class=”” id=””][youtube id=”-PwugYB9Zjs” width=”600″ height=”350″ autoplay=”no” api_params=”” class=””][/youtube][/one_half][title size=”1″ content_align=”left” style_type=”none” sep_color=”” margin_top=”” margin_bottom=”” class=”” id=””]

Practise Questions

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My Maths 9

Exercise 8F pg. 391 Q. 1-12

Exercise 8C pg. 373 Q. 1-6

Exercise 8D pg. 379 Q. 1-14

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