00:01
For this problem, a sample of 100 cars was drawn, and the number of occupants in each car was recorded, and the results were presented.
00:09
For the first question, we had to calculate the mean number of occupants.
00:15
So calculate the mean number of occupants, we need to construct a frequency distribution table and were presented with the occupants, we label it as x, and the number of cars we label it as f or the frequency.
00:31
To calculate the mean, we need to compute f of the frequency.
00:34
X that is simply f times x so the mean is equal to the mean or x bar is equal to the sum of f of x divided by the sum of f so we have 152 divided by 100 that is equal to 1 .52 that is equal to 1 .52 and the b says you are to find the sample standard deviation on the standard deviation is equal to the square root of the expression sum of f times x minus x bar squared divided by the sum of f so then we need these two additional columns so we calculate x minus x bar squared or sometimes called a deviation that is simply the x value minus the mean that is x minus x bar and then we square the results and we do for the of the numbers and then for this column we multiply the frequency by the deviation squared then we get this column and then we sum this up and that gives us 86 .96.
02:06
So we have sum of f times the deviation squared is given us 86 .96 divided by since you are finding sample standard deviation we need to subtract one from the denominator so you have sigma f so this gives us 100 minus 1.
02:38
We have square root of 86 .96 divided by 99 and that is equal to 0 .94.
02:59
For c we have to find a sample median, sample median number of occupants.
03:06
And then the median is giving us the median position, the position average we can identify the median is giving us sum of f divided by 2 th therefore we have 100 divided by 2 that is equal to 50th position this means that the median number of occupant can be located in a 50th position so we go to the cumulative frequency column that is simply the frequency to compute this we begin with the first frequency and then we add next frequency to it so 70 plus 15 90s us 85 and then we add 10 to it that use as 95 95 plus 3 that is 98 and 98 plus 2 and use us 100 we come to the accumulative frequency column and we locate the 50 position and that can be found in this range so we locate the x value that corresponds to this and that is 1 therefore our median is equal to 1.
04:32
The next question we are to compute the first and third quartile of the number of occupant.
04:41
And the first quartile or q1 is equal to one fourth of the sum of frequencies, that is equal to 1 over 4 times 100, which gives us 25 or 25 position.
05:10
So this means that the first quartile can also be located on the 25th position.
05:14
So we go back to the occulative frequency table and we locate the 25th position.
05:22
That is also in this ring and the x that corresponds to it is 1.
05:27
So q1 is equal to 1.
05:43
Now we need to find q3 or the third quartile.
05:48
That is given us 3 over 4 times zigma f is div over 4 times 100.
06:00
That is 75th position.
06:02
So we need to take a look at the qualitative frequency column.
06:12
We look at the 75th position.
06:15
The 70, we've grown 70.
06:18
So the 70th position can be found in this range...