the mean wages is 75/day and SD wages is 5/day for a group of 1000 person and same is 60 and 4.5 for group of 1500 person.what is mean and standard deviation in total?
To find the mean and standard deviation for the total wages, we need to calculate the total wages for each group and then combine them.
Let's start with the first group of 1000 people:
Mean wages:
Mean = (mean wages) * (number of people)
Mean = 75 * 1000
Mean = 75,000/day
Standard deviation:
Standard deviation = (SD wages) * (square root of the number of people)
Standard deviation = 5 * √1000
Standard deviation = 5 * 31.62
Standard deviation = 158.11/day (rounded to two decimal places)
Now, let's move on to the second group of 1500 people:
Mean wages:
Mean = (mean wages) * (number of people)
Mean = 60 * 1500
Mean = 90,000/day
Standard deviation:
Standard deviation = (SD wages) * (square root of the number of people)
Standard deviation = 4.5 * √1500
Standard deviation = 4.5 * 38.73
Standard deviation = 174.28/day (rounded to two decimal places)
To find the total mean and standard deviation, we add up the mean wages and sum the variances of each group:
Total mean = mean of group 1 + mean of group 2
Total mean = 75,000/day + 90,000/day
Total mean = 165,000/day
Total standard deviation = square root [(variance of group 1) + (variance of group 2)]
Total standard deviation = √[(158.11/day)^2 + (174.28/day)^2]
Total standard deviation = √(24,989.52/day^2 + 30,348.94/day^2)
Total standard deviation = √55,338.46/day^2
Total standard deviation = 235.03/day (rounded to two decimal places)
Therefore, the total mean wages is 165,000/day and the total standard deviation is 235.03/day.