What is the overall mean number of hours worked by a group if the mean for 30 males is 6 hours and 20 females is 9 hours?

To find the overall mean number of hours worked by the group, we need to calculate the total hours worked by both males and females and then divide that total by the total number of individuals in the group.

First, calculate the total hours worked by the males. Since the mean hours worked by the 30 males is 6 hours, the total hours worked by them is:

Total hours for males = Mean hours × Number of males

= 6 hours × 30 males

= 180 hours.

Next, calculate the total hours worked by the females. Since the mean hours for the 20 females is 9 hours, the total hours worked by them is:

Total hours for females = Mean hours × Number of females

= 9 hours × 20 females

= 180 hours.

Now, combine the total hours from both groups:

Total hours worked by both males and females = Total hours for males + Total hours for females

= 180 hours + 180 hours

= 360 hours.

Next, we need to find the total number of individuals in the group:

Total individuals = Number of males + Number of females

= 30 males + 20 females

= 50 individuals.

Finally, to find the overall mean