In the following questions you are required to determine the

In the following questions, you are required to determine the various statistical de-scriptions for the provided data: 0, 1, 2, 4, 5, 5, 7, 10, 10, 12, 13, 17, 39. Determine the mean, variance (population), and standard deviation (population) of the data. (Round your results to 3 decimal places.) What is the interquartile range (IQR) of the data? Based on this range identify the possible outliers What is the mode of the data?

Solution

1)

0,1,2,4,5,5,7,10,10,12,13,17,39

Mean, variance(population) and standard deviation of data ( round 3 decimal places)

Mean is calculate by average of given data
Here :
Mean = (0+1+2+4+5+5+7+10+10+12+13+17+39)/13
Mean = 9.077

Variance : it is the average of sqaure differences from the mean.
1) First calculate mean which is done in above
2) Then do it for each number : take the difference of number and mean and then sqaure that result
3) Then take the avearge of the results we get for each number in part2)

Mean : 9.077
0 : 0-9.077 = -9.077
Square(-9.077) = 82.391929
1: 1-9.077 = -8.077
Square(-8.077) = 65.237929
2 : 2-9.077 = -7.077
Square(-7.077) = 50.083929
4: 4-9.077 = -5.077
Square(-5.077) = 25.775929
5: 5-9.077 = -4.077
Sqaure(-4.077) = 16.621929
5: 5-9.077 = -4.077
Sqaure(-4.077) = 16.621929
7: 7-9.077 = 2.077
Square(2.077) = 4.313929
10: 10-9.077 = 0.923
Sqaure(0.923) = 0.851929
10: 10-9.077 = 0.923
Sqaure(0.923) = 0.851929
12: 12-9.077 = 2.933
Sqaure(2.923) = 8.543929
13: 13-9.077= 3.923
Square(3.923) = 15.389929
17: 17- 9.077 = 7.923
Square(7.923) = 62.773929
39: 39-9.077 = 29.923
Square(29.923) = 895.385929

Average of above square results = ( 82.391929 + 65.237929+ 50.083929 + 25.775929 + 16.621929 + 16.621929+ 4.313929 + 0.851929 + 0.851929 + 8.543929+ 15.389929 + 62.773929 + 895.385929)/13
= 1243.893158085193/13
= 95.68408908347638
= 95.684 (round off to 3 places)

Standard deviation : Sqaure root of Variance

= sqaureroot of (95.684)
= 9.781824425099664
= 9.782 (round off to 3 places)

2)

Interquartile range breaks at 25% (or we can say at quarter) so with our data

0,1,2,4,5,5,7,10,10,12,13,17,39

Here 7 is the median

IQR = Q3 - Q1
Q1 is the first quarter(25%) is 4
Q3 is the third quarter (75%) is 10

IQR = 10-4
IQR = 6

3) As per definition mode of data is the value that occurs most oftenly.

Here we have data : 0,1,2,4,5,5,7,10,10,12,13,17,39

Now as per definition it would be either 5 0r 10