Z-score calculation formula with examples

Answer 1

In a certain city the mean price of a quart of milk is 63 cents and the standard deviation is 8 cents. The average price of a package of bacon is $1.80 and the standard deviation is 15 cents. If we pay $0.89 for a quart of milk and $2.19 for a package of bacon at a 24-hour convenience store, which is relatively more expensive? To answer this, we compute Z-scores for each:

Answer 2

The formula to calculate the z-score of a data point is: ( z = \frac{(x - \mu)}{\sigma} ), where (x) is the data point, (\mu) is the mean of the data set, and (\sigma) is the standard deviation. For example, if you have a data point of 85, a mean of 75, and a standard deviation of 5, the z-score would be ( z = \frac{(85 - 75)}{5} = 2 ). This means the data point is 2 standard deviations above the mean.