To calculate the mean absolute deviation of
1,2,3,4,5,6,7
, we start by finding the mean;
(1+2+3+4+5+6+7) =28/7
= 4
. Next, we determine the absolute differences of each data point from the mean (x-μ)
= -3,-2,-1,0,1,2,3
. The absolute values are 3,2,1,0,1,2,3
. Now we compute the mean of these absolute differences,
3+2+1+0+1+2+3 = 12
= 12/7
= 1.7143
. Thus, the mean is 4, and the Mean absolute deviation comes out to be 1.7143
Set A's standard deviation exceeds that of Set B. To explain, standard deviation reflects variation within data sets. Generally, a dataset with a narrower range will exhibit a smaller standard deviation. For Set A, the range is 25-1 = 24, while for Set B, it's 18-8 = 10. Given that Set A's range is bigger, we would anticipate its standard deviation to also be larger. Standard deviation is calculated as the square root of the average of the squared deviations from the mean. In Set A, the deviations are ±12, ±11, ±10, whereas Set B's deviations are ±5, ±3, ±1. We can reasonably conclude that the value for Set A will be greater without computing the RMS difference. Thus, Set A's standard deviation is larger compared to Set B.
<span>As the restaurant owner,
The likelihood of hiring Jun is 0.7 => p(J)
The likelihood of hiring Deron stands at 0.4 => p(D)
The chance of hiring at least one of them is 0.9 => p(J or D)
We can formulate the probability equation:
p(J or D) = p(J) + p(D) - p(J and D) => 0.9 = 0.7 + 0.4 - p(J and D)
p(J and D) = 1.1 - 0.9 = 0.2
Thus, the probability that both Jun and Deron are hired is 0.2.</span>
