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
- $($ $($ (8) $,$ $,$ (5) $)$ $)$
  
  $($ $($ (20) $,$ $,$ (9) $)$ $)$
  
  $($ $($ (36) $,$ $,$ (13) $)$ $)$
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A data set with two variables $x$ $x$ and $y$ $y$ can have a median point $(X, Y)$ $(X,Y)$ where $X$ $X$ and $Y$ $Y$ are the medians of a section of $x$ $x$ and $y$ $y$ respectively.

First, break the data into three sections

Next, find the median point for each section.

$1$ $1$ st section:

Arrange each row in ascending order

Umbrella: $X [4, 8, 12]$ $X[4,8,12]$

Rainfall: $Y [2, 5, 6]$ $Y[2,5,6]$

Take each middle value and use them as coordinates of the $1$ $1$ st median point

$1$ $1$ st median point: $(8, 5)$ $(8,5)$

$2$ $2$ nd section:

Arrange each row in ascending order

Umbrella: $X [16, 20, 25]$ $X[16,20,25]$

Rainfall: $Y [8, 9, 12]$ $Y[8,9,12]$

Take each middle value and use them as coordinates of the $2$ $2$ nd median point

$2$ $2$ nd median point: $(20, 9)$ $(20,9)$

$3$ $3$ rd section:

Arrange each row in ascending order

Umbrella: $X [32, 36, 40]$ $X[32,36,40]$

Rainfall: $Y [11, 13, 15]$ $Y[11,13,15]$

Take each middle value and use them as coordinates of the $3$ $3$ rd median point

$3$ $3$ rd median point: $(36, 13)$ $(36,13)$

$(8, 5)$ $(8,5)$

$(20, 9)$ $(20,9)$

$(36, 13)$ $(36,13)$
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
- 1.
- 2.
- 3.
- 4.
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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 $\frac{1}{3}$ $1/3$ 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 $10$ $10$ mm.
- (24) umbrellas
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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 $10$ $10$ 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 $x$ $x$ axis.

Notice that the vertical line touches $24$ $24$

Therefore, if the rainfall level is $10$ $10$ mm, $24$ $24$ umbrellas will be sold

$24$ $24$ umbrellas

Median Regression Line

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