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Calculate and interpret the mean and standard deviation of data and use these to compare data sets. Investigate the effect of individual data values including outliers, on the standard deviation(VCMSP372)
[/fusion_text][fusion_text]LO: To calculate Pearson’s Correlation (R) of a bivariate data set.
Know:
- How to calculate the mean of a set of data
- The definition of an outlier
- How to square a number
- How to find the square root of a number
Understand:
That calculating the standard deviation shows us how much the data differs from the average value of a set of data
Do:
- I can calculate the standard deviation from a set of data
- I can use the standard deviation to compare different sets of data
- I can identify outliers and eliminate them to calculate the standard deviation of a set of data.
[/fusion_text][/fullwidth][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=””][title size=”1″ content_align=”left” style_type=”none” sep_color=”” margin_top=”” margin_bottom=”” class=”” id=””]
Visual Representations
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Notes
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Pearson’s correlation coefficient is a measure of the strength of the linear relationship between two variables. Basically it tells me how strongly one variable is related to another variable.
Pearson’s correlation (r) ranges from -1 to 1. -1 indicates a perfect negative linear relationship, while +1 indicates a perfect positive linear relationship.
[/fusion_text][/one_half][fusion_text]Why do we use it?
- Tells us how strongly things are related to each other.
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Formula for Calculating Pearson’s r
[/title][imageframe lightbox=”no” lightbox_image=”” style_type=”none” hover_type=”none” bordercolor=”” bordersize=”0px” borderradius=”0″ stylecolor=”” align=”none” link=”” linktarget=”_self” animation_type=”0″ animation_direction=”down” animation_speed=”0.1″ hide_on_mobile=”no” class=”” id=””] [/imageframe][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=””][fusion_text]
Quick Steps:
-
Mulitply both x and y values for each data pairing
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Find x squared of each data pairing
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Find y squared of each data pairing
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Find the summation of all x values, y values, xy values, x squared values and y squared values.
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Plug each of the values into the Pearson’s r formula above.
[/fusion_text][/one_half][/fullwidth][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=””][title size=”1″ content_align=”left” style_type=”none” sep_color=”” margin_top=”” margin_bottom=”” class=”” id=””]
Pearson’s Correlation Videos
[/title][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=”https://www.youtube.com/watch?v=2B_UW-RweSE” 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=”https://www.youtube.com/watch?v=372iaWfH-Dg&ab_channel=FurtherMaths” 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=”https://youtu.be/2SCg8Kuh0tE” 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 10/10A
Exercise 10C pg. 495 Q. 1-13
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