The Virginia Cooperative Extension reports that the mean weight of yearling Angus steers is 1152 pounds. Suppose that the standard deviation is 84 pounds. How many standard deviations from the mean would a steer weighing 1000 pounds be?

To find how many standard deviations a steer weighing 1000 pounds is from the mean, subtract the weight of the steer from the mean weight and divide by the standard deviation. The result, -1.81, shows that the steer is about 1.81 standard deviations below the mean.

Explanation:

In Statistics, one of the ways of understanding how far a data point is from the mean is with the standard deviation. A measure which is smaller than the mean falls on the left side of the mean in the distribution chart, hence would result in a negative deviation. To compute this, the weight of the steer (1000 pounds) is subtracted from the mean weight (1152 pounds) and then divided by the standard deviation (84 pounds): (1000 - 1152) / 84 = -1.81. Therefore, a steer weighing 1000 pounds is about 1.81 standard deviations below the mean.

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