Answer:
a)
b)
c)
d)
e)
A possible outlier would be the value of 69 since its above the upper limti for the boxplot.
Step-by-step explanation:
For this case we have the following dataset:
55 56 44 43 44 56 60 62 57 45 36 38 50 69 65
A total of 15 observations
Part a
We calculate the mean with the following formula:
And for this case we got
For the median we ust need to order the data on increasing way like this:
36, 38,43,44,44,45,50,55,56,56,57,60,62,65,69
Since the number of observations is an odd number the median would be on the 8 position from the dataset ordered on this case:
Part b
In order to calculate the Q1 we need to select the following data:
36, 38,43,44,44,45,50,55
And the Q1 would be the average between the 4 and 5 positions like this:
And for the Q3 we select these values:
55,56,56,57,60,62,65,69
And the Q3 would be the average between the 4 and 5 positions like this:
Part c
The Range is defined as:
Part d
In order to calculate the sample variance we can use the following formula:
And if we replace we got:
And the deviation is just the square root of the variance:
Part e
For this case we need to find the lower and upper limits for the boxplot given by:
A possible outlier would be the value of 69 since its above the upper limti for the boxplot.