Question

A product has a 4 week lead time. The standard deviation of demand for each of the week is given below. What is the standard deviation of demand over the lead time? (Answer to 2 decimal places) Week Standard deviation of demand 1 16 2 15 3 17 4 13

Answer 1

÷Answer:

Standard Deviation = 176.5

Explanation:

To calculate the standard deviation, calculate the mean score for the 4 standard deviation scores:

mean, m = Σx ÷ n

where Σx represents summation of each value = 162 + 153 + 317 + 413

= 1045

n = number of samples to be considered = 4

mean, m = 1045 ÷4

= 261.25

To calculate the standard deviation, use the formula below

SD =
`\sqrt{(Σ(x-m))/(n) ^(2) }`

where x = each value from the week lead time

m = mean = 261.25

n = the size = 4

The Standard deviation formula can be simplified further

when x = 162

`\sqrt{((x1-m))/(n) ^(2) }` = 49.625

when x = 153

`\sqrt{((x2-m))/(n) ^(2) }` = 23.125

when x = 317

`\sqrt{((x3-m))/(n) ^(2) }`= 27.875

when x = 413

`\sqrt{((x4-m))/(n) ^(2) }`= 75.875

Note that the above 4 equations can be lumped up into one giant equation by applying a big square root function instead of breaking it down

SD = 49.625 + 23.125 + 27.875 + 75.875

SD = 176.5