Median Regression Line
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Question 1 of 3
1. Question
An umbrella store recorded the daily rainfall in millimetres and the number of umbrellas sold. It was listed on a table and then translated into a scatter plot as shown below. Find the three median points of the data
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`(` (8)`,` (5)`)``(` (20)`,` (9)`)``(` (36)`,` (13)`)`
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A data set with two variables `x` and `y` can have a median point `(X,Y)` where `X` and `Y` are the medians of a section of `x` and `y` respectively.First, break the data into three sections
Next, find the median point for each section.`1`st section:
Arrange each row in ascending orderUmbrella: `X[4,8,12]`Rainfall: `Y[2,5,6]`Take each middle value and use them as coordinates of the `1`st median point`1`st median point: `(8,5)``2`nd section:
Arrange each row in ascending orderUmbrella: `X[16,20,25]`Rainfall: `Y[8,9,12]`Take each middle value and use them as coordinates of the `2`nd median point`2`nd median point: `(20,9)``3`rd section:
Arrange each row in ascending orderUmbrella: `X[32,36,40]`Rainfall: `Y[11,13,15]`Take each middle value and use them as coordinates of the `3`rd median point`3`rd median point: `(36,13)``(8,5)``(20,9)``(36,13)` -
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Question 2 of 3
2. Question
An umbrella store recorded the daily rainfall in millimetres and the number of umbrellas sold. It was listed on a table and then translated into a scatter plot as shown below. Draw the median regression line of the following data
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A median regression line for a scatter plot is drawn by plotting and connecting median points. This can be used to make predictions about the data.First, drawn a line to connect the first median point and the third median point
Finally, move the line towards the second median point for `1/3` of the way.You can measure the distance of the line from its current point up to the second median point for better accuracy. -
Question 3 of 3
3. Question
Using the median regression line below, predict how many umbrellas will be sold when the rainfall is `10`mm.- (24) umbrellas
Hint
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A median regression line for a scatter plot is drawn by plotting and connecting median points. This can be used to make predictions about the data.First, mark the amount of rainfall by drawing a horizontal line across `10` until it touches the median regression line
Next, starting from the point where it touched the regression line, draw a vertical line until it touches the `x` axis.
Notice that the vertical line touches `24`Therefore, if the rainfall level is `10`mm, `24` umbrellas will be sold`24` umbrellas