Answer:
f. age=16
g. age=17
Step-by-step explanation:
f. Mean is the sum of all the ages divided by the number of people. You need to make sure to account for the frequency of each age as well. Let x represent the other value that will make the mean 16.875. The number of people is sum of all the frequency values, plus one because you're adding a value (x).
mean=16.875= (12+13+14*3+15*3+16*2+17*3+18*5+19+20+21+22*2+x)/(1+1+3+3+2+3+5+1+1+1+2+1)
if you simplify that whole thing, you should get:
16.875=(x+389)/24
Now you need to solve for x.
Multiplying by 24 on both sides:
x+389=405
subtract 389 from both sides to get
x=16
That's the last value you need to add, another person who got their first job at 16.
g. If you listed all the ages out, making sure to account for the frequency of each age, the median would be the middle value, the one in the very center. Let's find it. Here's a complete list of all the ages:
12, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 20, 21, 22, 22
It's pretty boring, but what you do next is you cross values off from either end until you reach the center. (I'll use underline to show you because there is no strikethrough.)
12, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 20, 21, 22, 22
12, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 20, 21, 22, 22
12, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 20, 21, 22, 22
and so on, until you have:
12, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 18, 19, 20, 21, 22, 22
The median is 17 because it's the value at the very middle. If you were to add a value without changing the median, it would have to be 17. Let's look at what would happen then.
12, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 20, 21, 22, 22
You would have 2 values at the center instead of just one, because there's an even number of values now. To find the median, you have to find the mean of the two remaining points. The mean is (17+17)/2, which is just 17.
Hope this helps!
