00:01
Here in this question we are giving a data as 10, 8, 12, 15, 13, 11, 6 and 5.
00:14
So first of all, we have to arrange this data into the ascending order.
00:18
So our least value is 5, then we have 6 after that 8, 9, 10, then 11, after that 12, 13 and 15.
00:28
This is the ascending order of the data.
00:33
And here we can see our number of term n, 1, 2, 3, 4, 6, 7 and 8.
00:40
Total number of terms are 8 here.
00:43
And as for the question, our first solution is asking for the point estimate of the population mean.
00:48
So we need to find the population mean for the question.
00:56
And so for the population mean, the formula is sum of all observation.
01:03
Divided by number of observations.
01:11
So here the sum will be as 5 plus 6 plus 8 plus 10 plus 11 plus 12 plus 13 plus 15 divided by 8 and the value will be equal to when we add all the observations here this will be equal to mean x is equal to 80 by 8.
01:40
This is equal to 10.
01:42
Our value for mean is equal to 10.
01:46
This is our first solution of the question.
01:49
Now let's move on to the part b.
01:52
In part 2, here the question is asking for the standard deviation.
02:01
So for finding a standard deviation, what we need to do here? first of all, as we have done with the value of summation of x, which was some of all observations, that is, is 80 and now we will find our value the value for summation of x squares so if we square all the terms given into the data first so this will be as we are having our terms as 5 to the whole square added by 6 to the whole square added by 8 to the whole square then we have 10 whole square after that 11 whole square 12 whole square 13 whole square and lastly 15 whole square so our value will be computed as equal to 8884 for summation of x square and therefore the standard deviation standard deviation is here as 884 will be calculated as s is equal to square root of by the formula 884 minus 80 by 8 to the whole square divided by number of terms n minus 1 so 8 minus 1.
03:35
So our value will be equal to 8, 8, 8, 4 and the square of 10 will be as equal to 800 and divided by 7.
03:49
So here we will get our value as equal to root 12 .84 divided by 7 is root 12 and value of 12 is 3 .46.
04:04
So here we have our value for standard deviation as equal to 3 .46...