Question

Suppose you scored 81,00, 71, and 2 on your four exams in a mathematics course. Calculate the range and standard deviation of your exam scores. Round the mean to the nearest forth to calculate the standard devia The range of the same is (Simplify your newer) The standard deviation of the camerei Round to two decimal places ded) Enter your answerinch of the answer boxes

Answer 1

Range = 81

Standard deviation = 43.50

Explanation:

These scores in the mathematics course can form a set S:

S = {0,2,71,81}

Range:

The range of a set is the result of the subtraction between the highest and the lowest value of the set.

Here, the highest value is 81 and the lowest value is 0. So:

Range = 81-0 = 81.

Standard deviation:

The standard deviation
`\sigma` is given by the following formula:

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

where
`x_(k)` is the value at the position k of the set and M is the mean of the set and N is the cardinality of the set.

So, to know the standard deviation, we need to know the mean.

The mean of a set is the sum of the values of the set divided by the set cardinality. So, the mean M of our set is.

`M = (81 + 0 + 71 + 2)/(4) = 38.5`

The standard deviation is:

`\sigma = 43.50`