mean absolute deviation of the numbers 231,417,327,279,376,432,274,198,734,495,274,528,365,645,437
To find the mean absolute deviation, we first need to calculate the mean of these numbers:
(231 + 417 + 327 + 279 + 376 + 432 + 274 + 198 + 734 + 495 + 274 + 528 + 365 + 645 + 437) / 15 = 385
The mean is 385.
Next, we find the absolute deviation of each number from the mean. To do this, we subtract the mean from each number and take the absolute value:
|231 - 385| = 154
|417 - 385| = 32
|327 - 385| = 58
|279 - 385| = 106
|376 - 385| = 9
|432 - 385| = 47
|274 - 385| = 111
|198 - 385| = 187
|734 - 385| = 349
|495 - 385| = 110
|274 - 385| = 111
|528 - 385| = 143
|365 - 385| = 20
|645 - 385| = 260
|437 - 385| = 52
Now we add up all the absolute deviations and divide by the total number of numbers (15):
(154 + 32 + 58 + 106 + 9 + 47 + 111 + 187 + 349 + 110 + 111 + 143 + 20 + 260 + 52) / 15 = 120.27
The mean absolute deviation is approximately 120.27.
To find the mean absolute deviation, follow these steps:
Step 1: Find the mean (average) of the numbers.
Add up all the numbers:
231 + 417 + 327 + 279 + 376 + 432 + 274 + 198 + 734 + 495 + 274 + 528 + 365 + 645 + 437 = 5996
Divide the sum by the total count of numbers:
5996 / 15 = 399.73 (rounded to two decimal places)
Step 2: Find the deviation of each number from the mean.
Deviation = number - mean
For each number in the given list, subtract the mean (399.73 in this case) from the number:
231 - 399.73 = -168.73
417 - 399.73 = 17.27
327 - 399.73 = -72.73
279 - 399.73 = -120.73
376 - 399.73 = -23.73
432 - 399.73 = 32.27
274 - 399.73 = -125.73
198 - 399.73 = -201.73
734 - 399.73 = 334.27
495 - 399.73 = 95.27
274 - 399.73 = -125.73
528 - 399.73 = 128.27
365 - 399.73 = -34.73
645 - 399.73 = 245.27
437 - 399.73 = 37.27
Step 3: Find the absolute value of each deviation.
Take the absolute value of each deviation calculated in Step 2:
|-168.73| = 168.73
|17.27| = 17.27
|-72.73| = 72.73
|-120.73| = 120.73
|-23.73| = 23.73
|32.27| = 32.27
|-125.73| = 125.73
|-201.73| = 201.73
|334.27| = 334.27
|95.27| = 95.27
|-125.73| = 125.73
|128.27| = 128.27
|-34.73| = 34.73
|245.27| = 245.27
|37.27| = 37.27
Step 4: Find the mean of the absolute deviations.
Add up all the absolute deviations:
168.73 + 17.27 + 72.73 + 120.73 + 23.73 + 32.27 + 125.73 + 201.73 + 334.27 + 95.27 + 125.73 + 128.27 + 34.73 + 245.27 + 37.27 = 1879.11
Divide the sum by the total count of numbers:
1879.11 / 15 = 125.274 (rounded to three decimal places)
Therefore, the mean absolute deviation of the given numbers is approximately 125.274.