Respuesta :
Answer:
Mean = 38
Median = 38
Mode = 38
Range = 6
The variance is [tex]\sigma^{2} = 4[/tex]
The standard deviation is [tex]\sigma = 2[/tex]
Step-by-step explanation:
The mean is the sum of the values divided by the number of values. There are 8 values, so:
[tex]M = \frac{36+38+38+37+35+40+41+39}{8} = \frac{304}{8} = 38[/tex]
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To find the median, the first step is to order the data set, so we have
35, 36,37,38,38,39,40,41
When n is even, as in this exercise, the median is the average of the values at the positions n/2 and (n+1)/2. Here, the value at position n/2, which is position 4, is 38. The value at position 5 is 38 to. The average between this values is (38+38)/2 = 38. So the median 38.
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The mode is the value that appears the most at the data set. 38 appears 2 times, while the other values appear once. So 38 is the mode.
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The range of a set is the result of the subtraction of the highest value by the lowest value of the set.
So, in this set:
Range = 41 - 35 = 6
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The variance of a N-cardinality set is given by the following formula:
[tex]\sigma^{2} = \frac{1}{N}\sum_{k=1}^{N} (x_{k} - M)^{2}[/tex]
where [tex]x_{k}[/tex] is the element at the position k of the set and M is the mean of the set.
In our problem, we have that the variance is [tex]\sigma^{2} = 4[/tex].
The standard deviation [tex]\sigma[/tex] is the square root of the variance, so in our problem [tex]\sigma = \sqrt{4} = 2[/tex].
