Question

36, 38, 38, 37, 35, 40, 41, 39 Mean Median Mode - Range Variance - Standard Deviation

Answer 1

Mean = 38

Median = 38

Mode = 38

Range = 6

The variance is
`\sigma^(2) = 4`

The standard deviation is
`\sigma = 2`

Explanation:

The mean is the sum of the values divided by the number of values. There are 8 values, so:

`M = (36+38+38+37+35+40+41+39)/(8) = (304)/(8) = 38`

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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:

`\sigma^(2) = (1)/(N)\sum_(k=1)^(N) (x_(k) - M)^(2)`

where
`x_(k)` 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
`\sigma^(2) = 4`.

The standard deviation
`\sigma` is the square root of the variance, so in our problem
`\sigma = √(4) = 2`.