Question

Five pulse rates are randomly selected from a set of measurements. The five pulse rates have a mean of 72.472.4 beats per minute. Four of the pulse rates are 7878​, 6060​, 9191​, and 8282. 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.)

Answer 1

Answer:

a) 330951

b) n-1

Step-by-step explanation:

a)

$\bar{X} = 72472,4 \\ x_1 = 7878, x_2 = 6060,x_3 = 9191 , x_4 = 8282, x_5 = ?$

$\bar{X} = \frac{1}{n} \sum_{i=1}^n x_i \\72472,4 = \frac{1}{5} (7878 + 6060 + 9191 + 8282 + x_5) \\362362 = 31411 + x_5 \\x_5 = 330951$

b)

Imagine the following situation:

$n = 5 \\ \bar{X} = 25 \\ \frac{1}{5}\cdot (13+a+b+c+d) = 25$

We realize that we can assign a maximum of 4 values ​​so that the average is 25. That is, when we set

one value, we have n-1 possibilities to assign other values.