The total sum of the population in the first sample is greater than the second, hence the first sample is a better representation.
The formula for calculating the mean of numbers is expressed according to to the formula;
[tex]\overline x=\frac{\sum x}{n} \\[/tex]
n is the total sample space
[tex]\overline x[/tex] is the mean of the samples
[tex]\sum x[/tex] is the sum of the variables
If the mean number of tickets sold by five drama club members was 16, then;
[tex]16=\frac{\sum x}5}\\\sum x = 16 \times 5\\\sum x_1 = 80[/tex]
If she took ten random samples from the entire drama club of 75 students with a mean number of 22.5, hence;
[tex]\sum x_2 = 75[/tex]
Since the total sum of the population in the first sample is greater than the second, hence the first sample is a better representation.
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