49, 55, 52, 46, 47, 42, 38
What is the Mean Absolute Deviation(MAD) of this data set?:My answer was 4.28571428571
What is the Mean of this data set?:My answer was 47
What is the distance of each number from the mean?:? <Im having trouble with this one<
49+55+52+46+47+42+38=329
329/7=47
the mean is 47
49-47 = 2
55-47 = 8
...
funny how you got the MAD, but could not figure the distance (deviation) of the data points.
I figures out the mean but i couldnt figure out the distancie and the M.A.D
To calculate the Mean Absolute Deviation (MAD) of a data set, you need to find the absolute deviation of each data point from the mean and then take the average of these deviations. Here's how you can find the MAD for the given data set: 49, 55, 52, 46, 47, 42, 38.
1. Find the mean of the data set:
- Add up all the given numbers: 49 + 55 + 52 + 46 + 47 + 42 + 38 = 329.
- Divide the sum by the number of data points (in this case, 7): 329 ÷ 7 = 47.
- So, the mean of this data set is 47.
2. Find the absolute deviation of each data point from the mean:
- Subtract the mean from each data point and take the absolute value.
- For example, the absolute deviation of 49 from the mean (47) is |49 - 47| = 2.
- Repeat this step for all data points in the data set.
3. Find the average of these absolute deviations:
- Add up all the absolute deviations: 2 + 8 + 5 + 1 + 0 + 5 + 9 = 30.
- Divide the sum by the number of data points (in this case, 7): 30 ÷ 7 ≈ 4.2857.
- Round the answer to an appropriate number of decimal places.
Therefore, the Mean Absolute Deviation (MAD) of this data set is approximately 4.29.
Now let's move on to finding the distance of each number from the mean. The distance of a number from the mean is simply the absolute deviation of that number from the mean.
To find the distance of each number from the mean, you can follow the same steps as mentioned above to find the absolute deviation. Here's how to do it for the given data set:
1. Find the mean of the data set (as calculated previously): 47.
2. Subtract the mean from each data point and take the absolute value:
- For example, the distance of 49 from the mean (47) is |49 - 47| = 2.
- Repeat this step for all data points in the data set.
The distances from the mean for the given data set are as follows:
2, 8, 5, 1, 0, 5, 9.