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| 5 | 9
5 2 1 1| 6 |3 9
5 1 0| 7 |0 2 3 6 7 8
2 1| 8 |3
0| 9 |
Key: 9|6 means. Key: 5|8 means
69. 58
Calculate the (MAD) of each data set
To calculate the MAD of each data set, we will first need to compute the residual (deviation from the median) of each data point, then take the absolute value of each residual, and finally find the median of all the absolute residuals.
Here are the steps we can follow:
For the first data set:
- Median: 6
- Residuals:
- |-1-6| = 7
- |3-6| = 3
- |9-6| = 3
- Absolute residuals: 7, 3, 3
- MAD: median(7, 3, 3) = 3
Therefore, the MAD of the first data set is 3.
For the second data set:
- Median: 5
- Residuals:
- |3-5| = 2
- |6-5| = 1
- |7-5| = 2
- |0-5| = 5
- |2-5| = 3
- |3-5| = 2
- |6-5| = 1
- |7-5| = 2
- |8-5| = 3
- Absolute residuals: 2, 1, 2, 5, 3, 2, 1, 2, 3
- MAD: median(2, 1, 2, 5, 3, 2, 1, 2, 3) = 2
Therefore, the MAD of the second data set is 2.
Which set is more variable
To determine which set is more variable, we can compare the MADs of the two sets. The data set with the larger MAD is more variable, since the MAD is a measure of variability that takes into account the absolute distance of each data point from the median.
Using the MADs we calculated earlier, we have:
- MAD of first data set: 3
- MAD of second data set: 2
Since the MAD of the first data set is larger than the MAD of the second data set, we conclude that the first data set is more variable.
Calculate the mean of each data set
To calculate the mean of each data set, we need to sum up all the data points in the set and divide by the number of data points. Here are the calculations:
For the first data set:
- Sum of data points: 1 + 1 + 2 + 3 + 5 + 5 + 9 = 26
- Number of data points: 7
- Mean: 26 / 7 = 3.71 (rounded to two decimal places)
Therefore, the mean of the first data set is 3.71.
For the second data set:
- Sum of data points: 0 + 1 + 2 + 3 + 5 + 6 + 7 + 8 + 9 = 41
- Number of data points: 9
- Mean: 41 / 9 = 4.56 (rounded to two decimal places)
Therefore, the mean of the second data set is 4.56.
A radio signal travels at 3.00 ⋅10^8
meters per second. How many seconds will it take for a radio signal to travel from a satellite to the surface of Earth if the satellite is orbiting at a height of
3.54 ⋅10^7 meters? Show your work.
The distance between the satellite and the surface of the Earth can be calculated by adding the radius of the Earth to the height of the satellite. The radius of the Earth is approximately 6.37 x 10^6 meters.
Distance from satellite to Earth's surface = 3.54 x 10^7 meters + 6.37 x 10^6 meters = 4.18 x 10^7 meters
The time it will take for the radio signal to travel this distance can be calculated using the formula:
time = distance / speed
where distance is the distance between the satellite and the Earth's surface, and speed is the speed of the radio signal, which is 3.00 x 10^8 meters per second.
Plugging in the values, we get:
time = 4.18 x 10^7 meters / (3.00 x 10^8 meters per second) = 0.139 seconds
Therefore, it will take approximately 0.139 seconds for the radio signal to travel from the satellite to the surface of the Earth.
Micah is making a cinnamon and sugar mixture to sprinkle on toast. His recipe uses 1/8
cup of cinnamon and 1/2
cup of sugar. Find 1/8+1/2
and interpret this sum in the context of the problem.