Answer :
Final answer:
To find the arithmetic mean, multiply each age by the corresponding frequency and divide the sum by the total number of employees. To calculate the standard deviation, subtract the arithmetic mean from each age, square it, multiply by the corresponding frequency, and take the square root of the sum divided by the total number of employees.
Explanation:
To calculate the arithmetic mean, we multiply each age by the corresponding frequency and then divide the sum by the total number of employees. For the given data:
(50-55): 25 employees
(45-50): 30 employees
(40-45): 40 employees
(35-40): 45 employees
(30-35): 80 employees
(25-30): 110 employees
(20-25): 170 employees
We need to find the weighted sum of the ages.
(50-55)x25 + (45-50)x30 + (40-45)x40 + (35-40)x45 + (30-35)x80 + (25-30)x110 + (20-25)x170
Then divide the sum by the total number of employees:
(50-55)x25 + (45-50)x30 + (40-45)x40 + (35-40)x45 + (30-35)x80 + (25-30)x110 + (20-25)x170) / (25+30+40+45+80+110+170) =
The arithmetic mean is the calculated value.
To calculate the standard deviation, we first subtract the arithmetic mean from each age value, square the differences, multiply each squared difference by the corresponding frequency, and then take the square root of the sum of these values divided by the total number of employees. We can follow the same steps with the given data to calculate the standard deviation.
Learn more about Calculating Arithmetic Mean and Standard Deviation here:
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