Final Answer:
(a) the mean = $35,100.
(b) median = $25,500.
(c) mode = $24,000.
(d) midrange = $50,500.
Step-by-step explanation:
To find the different measures of central tendency and midrange for the given salaries, follow the steps below:
(a) Mean:
The mean of a set of numbers is calculated by adding all the numbers together and dividing by the count of numbers.
Add up all salaries: 26 + 62 + 23 + 22 + 29 + 25 + 24 + 79 + 24 + 27 = 351
Count the number of salaries, which is 10.
Divide the sum by the count: Mean = 351 / 10 = 35.1
So, the mean salary is $35,100.
(b) Median:
The median is the middle value of an ordered set of numbers. If there is an even number of values, the median is the average of the two middle numbers.
First, order the salaries from smallest to largest: 22, 23, 24, 24, 25, 26, 27, 29, 62, 79
Since there are 10 numbers, we'll take the average of the 5th and 6th numbers (the middle two values).
The 5th number is 25 and the 6th number is 26.
Average of the 5th and 6th number: Median = (25 + 26) / 2 = 25.5
So, the median salary is $25,500.
(c) Mode:
The mode is the number that appears most frequently in a set of numbers. If no number is repeated, then there is no mode.
Look for any numbers that are repeated in the set.
Looking at the ordered salaries, 24 is the number that appears more than once.
Since 24 appears twice and no other number does so, 24 is the mode.
So, the mode of the salaries is $24,000.
(d) Midrange:
The midrange is calculated by taking the average of the smallest and largest values in the set.
Identify the smallest and the largest salary: they are 22 and 79, respectively.
Calculate the midpoint between these two numbers:
Midrange = (22 + 79) / 2 = 101 / 2 = 50.5
So, the midrange of the salaries is $50,500.