Question

Five pulse rates are randomly selected from a set of measurements. The five pulse rates have a mean of 74.8 beats per minute. Four of the pulse rates are 91 , 79 , 70 , and 65.

A) Find the missing value.
B) Suppose that you need to create a list of n values that have a specific known mean. Some of the n values can be freely selected. How mary of the n values can be freely assigned before the remaining values are determined?

Answer 1

A) The missing value is 89. B) n - 1 values can be freely assigned.

Step-by-step explanation:

A) To find the missing value, we need to calculate the sum of the five pulse rates. The sum of the four given pulse rates is 285 (91 + 79 + 70 + 65). The mean of the five pulse rates is 74.8. Let's denote the missing value as x. So, we have the equation: (285 + x)/5 = 74.8. To solve for x, we can multiply both sides of the equation by 5 to get 285 + x = 374. Next, we subtract 285 from both sides to obtain x = 374 - 285. Therefore, the missing value is x = 89.

B) If we have a set of n values with a specific known mean and some of the values can be freely selected, the remaining values can be determined once we know the mean and the number of values being selected. This means that we can freely assign n - 1 values before the remaining values are determined.