Answer:
Step-by-step explanation:
Mean is defined as the sum total of data divided by the total number of data.
[tex]\overline x = \frac{\sum Xi}{N}[/tex]
Xi are individual data
N is the total number of data = 5
Given the mean of the pulse rate = 65.4
a) Let the 5pulse rates be our data as shown: 57, 55, 62, 83 and y where y is the missing value. According to the formula:
[tex]65.4 = \frac{57+55+62+83+y}{5}[/tex]
[tex]65.4 = \frac{257+y}{5}\\ 257+y = 65.4*5\\257+y = 327\\y = 327-257\\y = 70[/tex]
The missing value is 70
b) Since the total list of numbers is n values with a specific known mean, if some of this values can be freely selected, the number of n values that can be freely assigned before the remaining values are determined is any values less than n i.e n-1 values.
From the formula for calculating mean:
[tex]\overline x = \frac{\sum Xi}{N}\\{\sum Xi} = N\overline x[/tex]
This shows that the sum of all the values is equal to the product of the total values and the mean value. Since we can freely choose n-1 values, then sum of the set of data can be written as [tex]\sum \sumx^{n-1} _i__=_1 Xi[/tex]
[tex]\sum \sumx^{n-1} _i__=_1 Xi \ =\ N \overline x[/tex]
The number of n values which is referred to the degree of freedom is n-1
