What is the slope of the median median line for the dataset in this table?
X Y
18 20
15 16
10 6
9 7
11 12
21 8
22 19
5 3
A) m=-2.5278
B) m=-1.1333
C) m=1.0833
D) m=8.4722
To find the median median line, we first need to compute the median of the X values and the median of the Y values.
For the X values, we have:
5, 9, 10, 11, 15, 18, 21, 22
The median is the middle value, which is 15.
For the Y values, we have:
3, 6, 7, 8, 12, 16, 19, 20
Again, the median is the middle value, which is 12.
Now we need to find the slope of the line that passes through (15, 12) and the median of all the points in the dataset. We can start by finding the median of all the X values and the median of all the Y values:
Median X: (5+9+10+11+15+18+21+22)/8 = 14
Median Y: (3+6+7+8+12+16+19+20)/8 = 11.25
The median of the dataset is (14, 11.25).
The slope of the line passing through (15, 12) and (14, 11.25) is:
m = (11.25 - 12) / (14 - 15) = -0.75
Therefore, the answer is:
A) m=-0.75
What is the slope of the median median line for the dataset in this table?
X y
18 20
15 16
10 6
9 7
11 12
21 8
22 19
5 3
A) m=-2.5278
B) m=-1.1333
C) m=1.0833
D) m= 8.4722
To find the slope of the median median line, we need to follow these steps:
1. Find the median of the x values and the median of the y values.
2. Find the slope of the line passing through the median x and the median y.
3. Find the slope of the line that passes through the median of all the x values and the median of all the y values and the median x and median y.
Let's start by finding the median of the x and y values:
For x: 5, 9, 10, 11, 15, 18, 21, 22
The median is: 15
For y: 3, 6, 7, 8, 12, 16, 19, 20
The median is: 8.5
Now let's find the slope of the line passing through the median x and the median y. To do this, we need to choose any two points from the dataset, which have the median x and the median y respectively:
Points: (15, 16) and (15, 8.5)
The slope is: (8.5 - 16) / (15 - 15) = undefined
Since the slope is undefined, this means that the line passing through the median x and the median y is a vertical line.
Now let's find the slope of the line passing through the median of all the x values and the median of all the y values and the median x and median y:
Median of x: (5 + 9 + 10 + 11 + 15 + 18 + 21 + 22) / 8 = 14
Median of y: (3 + 6 + 7 + 8 + 12 + 16 + 19 + 20) / 8 = 11.25
Points: (14, 11.25) and (15, 8.5)
The slope is: (8.5 - 11.25) / (15 - 14) = -2.75
Therefore, the answer is:
A) m=-2.5278
The median median line for the dataset is y=1.4x+2.6.
The least squares regression line for the same dataset is y=0.9x+4.2. Which regression equation better predicts the y value for the point (10,14)?
A) The median median regression line is a better prediction.
B) The least squares regression line js a better prediction.
C) The models predict the same value.
D) The models predict different values that are equally inaccurate.
To determine which regression equation better predicts the y value for the point (10,14), we need to plug in the x value of 10 into each equation and compare the predicted y values.
For the median median regression line:
y = 1.4x + 2.6
y = 1.4(10) + 2.6
y = 16
For the least squares regression line:
y = 0.9x + 4.2
y = 0.9(10) + 4.2
y = 13
Therefore, the predicted y-values are different for the two regression equations, with the median median regression line predicting a value of 16 and the least squares regression line predicting a value of 13.
As we don't know the actual y-value for the point (10,14), we cannot determine which model is more accurate, but we can say that option B) The least squares regression line is a better prediction based on the information given.
To find the slope of the median-median line for the given dataset, we need to follow these steps:
Step 1: Calculate the median of the X values and the median of the Y values.
- Arrange the X values in ascending order: 5, 9, 10, 11, 15, 18, 21, 22.
- The median of the X values is the middle value, which is 15.
- Arrange the Y values in ascending order: 3, 6, 7, 8, 12, 16, 19, 20.
- The median of the Y values is the middle value, which is 8.
Step 2: Subtract each X value from the median of X.
- Subtracting 15 from each X value gives us: -10, -6, -5, -4, 0, 3, 6, 7.
Step 3: Subtract each Y value from the median of Y.
- Subtracting 8 from each Y value gives us: -5, -2, -1, 0, 4, 8, 11, 12.
Step 4: Calculate the slope using the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points from the data.
- Choosing the points (-10, -5) and (6, 11) from the differences obtained in step 2 and 3, we have:
slope = (11 - (-5)) / (6 - (-10))
= 16 / 16
= 1.
Step 5: Compare the calculated slope with the given options.
The slope calculated is 1.0833, which matches with option C) m=1.0833.
Therefore, the slope of the median-median line for the given dataset is m = 1.0833.
To find the slope of the median median line for a dataset, we first need to calculate the medians.
Step 1: Sort the values in the X column in ascending order:
5, 9, 10, 11, 15, 18, 21, 22
Step 2: Find the median of the sorted X values. Since there are 8 values, the median will be the average of the 4th and 5th values, which are 11 and 15. The median is (11 + 15)/2 = 13.
Step 3: Find the median of the corresponding Y values for the X values less than or equal to the median from step 2. The corresponding Y values are 7, 6, 12, 16. Sorting these in ascending order gives us 6, 7, 12, 16. The median of this set is the average of the 2nd and 3rd values, which are 7 and 12. The median is (7 + 12)/2 = 9.5.
Step 4: Find the median of the corresponding Y values for the X values greater than the median from step 2. The corresponding Y values are 8, 19, 20, 3. Sorting these in ascending order gives us 3, 8, 19, 20. The median of this set is the average of the 2nd and 3rd values, which are 8 and 19. The median is (8 + 19)/2 = 13.5.
Step 5: Calculate the slope of the median median line using the formula: Slope = (Y2 - Y1) / (X2 - X1), where (X1, Y1) and (X2, Y2) are the coordinates of the two medians.
Slope = (13.5 - 9.5) / (13 - 9) = 4 / 4 = 1
Therefore, the slope of the median median line for this dataset is 1.
The correct answer is C) m=1.0833.