MBA Math Sample Exercise

Statistics: Variance

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Exercise

Unit sales for new product ABC have varied in the first seven months of this year as follows:

Month	Jan	Feb	Mar	Apr	May	Jun	Jul
Unit Sales	428	391	459	161	410	367	466

What is the (population) variance of the data?

Solution

Solution Commentary

(2:43)

Manual Solution

The variance is a measure of dispersion from the mean. Specifically, it is the average of the squared difference from the mean.

First, we compute the mean:
Mean = (428 + 391 + 459 + 161 + 410 + 367 + 466)/7
Mean = 383.143

Now we can compute the variance from the values and mean.
Variance = ((428 - 383.143)² + (391 - 383.143)² + (459 - 383.143)² + (161 - 383.143)² + (410 - 383.143)² + (367 - 383.143)² + (466 - 383.143)²)/7

Variance = 9,289 (rounded to the nearest integer)

Excel Solution

Peter Regan teaches decision science courses at Dartmouth’s Tuck School and Duke’s Fuqua School. He also teaches pre-term quantitative skills courses at Tuck and Cornell’s Johnson School. He created the MBA Math self-paced, online pre-MBA quantitative skills course covering finance, accounting, economics, statistics, and spreadsheets.