Q25. - Algebra 2

Question

For exercise 25-30, use the following information.

A median-fit line is a particular type of line of fit. Follow the steps below to find the equation of the median-fit line for the data.

25. Divide the data into three approximately equal groups. There should always be the same number of points in the first and third groups. Find $x_1,x_2, and x_3$, the medians of the x values in Groups 1, 2 and 3, respectively. Find $y_1,y_2, and y_3$ , the medians of the y values in Groups 1, 2, and 3 respectively. 

Step-by-Step Solution

Answer

The medians of x-values $x_1=1988,x_2=1993,x_3=1998$ and medians of y-values is $y_1=247,y_2=360.5,y_3=461$

Step-1 – Divide the data.

Group 1: $(1986,217),(1988,247),(1990,297)$

Group 2: $(1992,332),(1994,389)$

Group 3: $(1996,427),(1998,461),(1999,476)$

Step-2 – Medians of x -values.

Median is the value separating the higher half from the lower half.

The median of group 1 is $x_1=1988$.

The median of group 2 is $x_2=\frac{1992+1994}{2} or 1993$

 

The median of group 3 is $x_3=1998$

Step-3 – Medians of y -values.

The median of group 1 is $y_1=247$.

The median of group 2 is $y_2=\frac{332+389}{2} or 360.5$

 

The median of group 3 is $y_3=461$