Answer:
a) Mean = 20.23 million dollars.
b) Median = 14.1 million dollars.
c) Mode = non-existent for this distribution.
d) Midrange = 22.65 million dollars.
- Given that these are the top 10 salaries, do we know anything about the salaries of TV personalities in general?
Answer - Since the sample values are the 10 highest, they give almost no information about the salaries of TV personalities in general.
- Are such top 10 lists valuable for gaining insight into the larger population?
Answer - No, because such top 10 lists represent an extreme subset of the population rather than the larger population.
Explanation:
The question is incomplete, the top 10 salary data, in millions of dollars, was obtained online to be
8.3, 9.2, 9.8, 12.1, 13.5, 14.7, 26.5, 34.7, 36.5, 37
a) Mean
The mean is the sum of variables divided by the number of variables
x = each variable
N = number of variables = 10
Mean = (Σx)/N
Σx = 8.3+9.2+9.8+12.1+13.5+14.7+26.5+34.7+36.5+37 = 202.3
Mean = (202.3/10) = 20.23 million dollars
b) Median
The median is the variable that falls at the middle of the distribution when all the variables are arranged in ascending or descending order. For an odd-numbered dataset, it is simply the middle number, but for an even-numbered dataset, it is the average of the two middle numbers.
The distribution, arranged in ascending order is 8.3, 9.2, 9.8, 12.1, 13.5, 14.7, 26.5, 34.7, 36.5, 37
The two middle numbers are 13.5 and 14.7
Median = (13.5+14.7)/2 = 14.1 million dollars
c) Mode
The mode is the variable that occurs the most in a distribution. It is the variable with the highest frequency in the distribution.
For this distribution of the top 10 salaries for TV personalities, all the variables occur only once, with no variable appearing more often than another. Hence, there is no more for this distribution.
d) Midrange
The midrange is the average of the highest and lowest variables in a distribution. It is the midpoint of the range, hence, it is arithmetic mean of the highest and lowest variables of the distribution.
Highest value = 37
Lowest value = 8.3
Midrange = (37+8.3)/2 = 22.65 million dollars
Given that these are the top 10 salaries, do we know anything about the salaries of TV personalities in general?
Since the sample values are the 10 highest, they give almost no information about the salaries of TV personalities in general. For all we know, the top 10 highest salaries can be very far away from the day if the distribution, or the rest of the distribution can just be the same number over and over again, no way to know that from just the data of the top 10 salaries for TV personalities.
Are such top 10 lists valuable for gaining insight into the larger population?
No, because such top 10 lists represent an extreme subset of the population rather than the larger population
Hope this Helps!!!