Answer: To find the standard deviation of a population, we need to first calculate the mean (or average) of the data. The mean is found by adding up all the values in the data set and dividing by the total number of values. In this case, the ages of the 5 doctors are 53, 36, 36, 44, and 31, so the mean is (53 + 36 + 36 + 44 + 31) / 5 = 200 / 5 = 40.
Next, we need to find the difference between each value in the data set and the mean. These differences are called the "deviations" of the data. In this case, the deviations are 53 - 40 = 13, 36 - 40 = -4, 36 - 40 = -4, 44 - 40 = 4, and 31 - 40 = -9.
To find the standard deviation, we need to square each deviation (to make all the values positive), add them up, and divide by the total number of values. This gives us:
(13² + (-4)² + (-4)² + 4² + (-9)²) / 5 = (169 + 16 + 16 + 16 + 81) / 5 = 282 / 5 = 56.4
Finally, we need to take the square root of the result to find the standard deviation. The square root of 56.4 is 7.5, so the standard deviation of the population is 7.5. To round this to two decimal places, we would express it as 7.50.
Therefore, the standard deviation of the population is 7.50. This means that the ages of the doctors at the local clinic vary from the mean by about 7.50 years on average.