Question

Five pulse rates are randomly selected from a set of measurements. The five pulse rates have a mean of 74.6 beats per minute. Four of the pulse rates are 87​, 95​, 72​, and 53. 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 many of the n values can be freely assigned before the remaining values are​ determined? (The result is referred to as the number of degrees of​ freedom.) a. The missing value is how many beats per minute?

Answer 1

Answer

(a) We have mean value = 74.6

and given four values are 87, 95, 72 and 53

We know that mean = (sum of all values)/(total number of data values)

let x be the required value or unknown value.

So, we get

74.6 = (87+95+72+53+x)/5

74.6 = (307+x)/5

multiplying both sides by 5, we get

74.6*5 = (307+x)

373 = 307 +x

subtracting 307 on each side, we get

373-307=x

or, x = 66

So, required value is x = 66

(b) we know that we can assign one value and can freely select n-1 values with respect to the assigned value. So, we can say that we can freely select n-1 values before determining the remaining values.

Suppose we have 5 values and we have assigned 1st value, then we have n-1 = 5-1 = 4 values which can be selected freely.