Answer:
a) 57
b) 19.476
c) 1.106 (rounded)
Explanation:
a) note: the very first step here is to find the number of people of age 21 which is found through subtraction. We have a total of 250 people, and we currently have data on 193 (64 + 60 + 69) people. This means there are (250 - 193 = 57) 57 remaining people of age 21.
The first thing we're trying to find here is the mean, which we sometimes refer to as the average, of this data set.
To find the mean, we add all values together and then divide by the number of values we've combined.
We could write out 18 + 18 + 18... sixty-four times, and then to the same thing for 19's, but that would take a while. So, we can find this value through multiplication (remember, multiplication is the same thing as repeated addition).
18 × 64 = 1152
19 × 60 = 1140
20 × 69 = 1380
21 × 57 = 1197 *see above
Now, we find the sum of our values added together:
Now, we know we have 250 values, so we will divide 4869 by 250:
4869 / 250 = 19.476
So, the mean of this sample is 19.476
Now, we are finding the standard deviation, which is found through the formula:
∑ (x - x^(line over x) ) ²
√ _______
n - 1
(this is hard to write on this website sorry)
find difference between each value and mean (that's what "x - x^(line over x)" is)
18 - 19.476 = -1.476
19 - 19.476 = -0.476
20 - 19.476 = 0.524
21 - 19.476 = 1.524
square each difference: (that's what " (x - x^(line over x))² " is)
now, we need to add up our squared values. But first, we must account for how many of each value there are
now, let's add up our squared values: (that's what "∑" is )
we now need to divide this number by n - 1 (we have 250 samples, so we need to divide by 250 - 1 (249) to find our variance)
now, we find our standard deviation by taking the square root of the variance that's what the "√" is )
we can round this number to:
1.106 (or any other rounded decimal place, I did it this way to match our previous answer)
So, the standard deviation of this set is 1.106 (rounded)
hope this helps! have a lovely day :)