Find the mean of the absolute differences between each number and the mean of these numbers 141, 330, 292, 198, 263, 224, 149, 121, 223, 125, 126, 48, 111, 327, 238
To find the mean of the absolute differences, we first need to find the mean of the given numbers:
(141+330+292+198+263+224+149+121+223+125+126+48+111+327+238) / 15 = 204.6
Next, we find the absolute difference between each number and the mean and add them up:
|141-204.6| + |330-204.6| + |292-204.6| + |198-204.6| + |263-204.6| + |224-204.6| + |149-204.6| + |121-204.6| + |223-204.6| + |125-204.6| + |126-204.6| + |48-204.6| + |111-204.6| + |327-204.6| + |238-204.6|
= 63.6 + 125.4 + 87.4 + 6.6 + 58.4 + 19.4 + 55.6 + 83.6 + 18.4 + 79.6 + 78.6 + 156.6 + 93.6 + 122.4 + 122.4 = 1151.2
Finally, we divide the sum by the number of numbers (15) to find the mean of the absolute differences:
1151.2 / 15 = 76.747.
Therefore, the mean of the absolute differences between each number and the mean of these numbers is approximately 76.747.
76.747 no the nearest 100
The nearest 100 to 76.747 is 100. Therefore, the mean of the absolute differences between each number and the mean of these numbers to the nearest 100 is 100.
To find the mean of the absolute differences between each number and the mean of the given numbers, follow these steps:
1. Find the mean of the given numbers:
- Add up all the numbers: 141 + 330 + 292 + 198 + 263 + 224 + 149 + 121 + 223 + 125 + 126 + 48 + 111 + 327 + 238 = 2928
- Divide the sum by the total number of numbers: 2928 / 15 = 195.2
- The mean of the given numbers is 195.2.
2. Find the absolute difference between each number and the mean:
- Subtract the mean from each number and take the absolute value (ignoring the sign):
|141 - 195.2| = 54.2
|330 - 195.2| = 134.8
|292 - 195.2| = 96.8
|198 - 195.2| = 2.8
|263 - 195.2| = 67.8
|224 - 195.2| = 28.8
|149 - 195.2| = 46.2
|121 - 195.2| = 74.2
|223 - 195.2| = 27.8
|125 - 195.2| = 70.2
|126 - 195.2| = 69.2
|48 - 195.2| = 147.2
|111 - 195.2| = 84.2
|327 - 195.2| = 131.8
|238 - 195.2| = 42.8
3. Find the mean of the absolute differences:
- Add up all the absolute differences: 54.2 + 134.8 + 96.8 + 2.8 + 67.8 + 28.8 + 46.2 + 74.2 + 27.8 + 70.2 + 69.2 + 147.2 + 84.2 + 131.8 + 42.8 = 1038.4
- Divide the sum by the total number of numbers: 1038.4 / 15 = 69.22666666666667 (rounded to 2 decimal places)
Therefore, the mean of the absolute differences between each number and the mean of the given numbers is approximately 69.23.