12.30 Finding the standard deviation. The level of various substances in the blood influences our health. Here are measurements of the level of phosphate in the blood of a patient, in milligrams of phosphate per deciliter of blood, made on six consecutive visits to a clinic:
| 5.6 | 5.2 | 4.6 | 4.9 | 5.7 | 6.4 |
A graph of only six observations gives little information, so we proceed to compute the mean and standard deviation.
(a) Find the mean from its definition. That is, find the sum of the six observations and divide by 6.
(b) Find the standard deviation from its definition. That is, find the distance of each observation from the mean, square the distances, then calculate the standard deviation. Example 4 shows the method.
(c) Now enter the data into your calculator and use the mean and standard deviation keys to obtain and . Do the results agree with your hand calculations?