Question

Five puise rates are randomly selected from a set of measurements. The five pulise rates have a mean of 65.4 beats per minute.Four of the pulse raes are 82, 78, 56, and 61.

a. Find the missing value 

b. Suppose that you need to create a list of n values that have a speciic known mean Some of the n values can be freely selected How many of the n values can be freely assigned belore the remaining values are determined? (The result is neferred to as the number of degrees of fheedom.) 

a.The missng value is _______  beats per minute. 

Answer 1

Mean =      

$\bar{x} = \frac{\sum x_i}{n}$

We are given mean $\bar{x}$ = 65.4 , n = 5

So, Sum of 5 numbers = $\sum x_i = n*\bar{x}$ = 5*65.4 = 327

We are given four numbers.

Sum of 4 numbers = 82 + 76+ 55 + 61 = 274

So missing value = 327 - 274 = 53

b)

Whenever you have one group of n numbers, the degrees of freedom is equal to n - 1.

In the previous problem, we knew the values of n - 1 numbers (the 4 we were given) and using this information, we were able to find the 5th number.