00:01
These data values represent scores on a chemistry quiz out of a possible 20 points.
00:08
And in problem number one, we want to calculate the sample mean.
00:12
Sample mean is x bar equals sum of x divided by n.
00:19
So that means we're going to add up all of the pieces of data and get 110 and divide by the fact that there were 10 pieces of data.
00:28
So our mean would be 11.
00:32
The other part of problem number one is to calculate the sample standard deviation.
00:38
And sample standard deviation, the formula is s equals the square root of the sum of x minus x bar squared divided by n minus 1.
00:55
And our square root is the entire quantity under that radical.
01:04
So my suggestion to do that would be to create a table.
01:13
We'll put all of our pieces of data down the side.
01:16
So we have 16, 14, 1, 8, 12, 12, 9, 10, 15, and 13.
01:28
And we need to talk about the deviation from average.
01:35
So 16 is above the average by 5.
01:40
So if i do 16 minus 11, i'll get 5.
01:43
14 is above the average by 3.
01:47
One is well below the average.
01:50
So it's going to be 10 below, thus it's going to be negative.
01:54
8 is below average by negative 3.
01:59
12 is above average by 1, 9 is below average by 2, 10 is below average by 1, 15 is above average by 4, and 13 is above average by 2.
02:14
Now, if i were to average those values, those deviations, i would end up with 0 because the deviations always sum up to 0.
02:24
So it's kind of meaningless data.
02:26
So what we'll do is we'll square each of those pieces of data.
02:33
And later, we're going to undo the square by doing this square root in our formula.
02:39
So if i square five, i get 25.
02:41
If i square three, i get nine.
02:44
If i square one or a 10, i get 100.
02:47
Squaring a negative three, i get nine.
02:49
If i square one, i still get one.
02:51
If i square negative two, it's a four.
02:54
If i square a negative one, i get one.
02:56
If i square four, i get 16, and the square of two is four.
03:02
So now the formula calls for you to add up that column.
03:07
So when i add up that column, i get 170.
03:15
And then i want to divide that by one lower than the sample size.
03:21
So i'm dividing it by 10 minus 1 or 9.
03:24
And when i do that, i get a standard deviation of 4 .34 -6134 -4937.
03:41
Now, your problem did not specify how you should round your answer, so i'm going to leave it all there, and then you could either refer to your instructions in your textbook or your professor or teacher as to how to display your final answer.
03:58
For question number two, you need to calculate the range.
04:05
And range, we're using the capital letter r, is maximum minus minimum...