Question

Pick any 5 different two digit numbers and calculate mean, median, standard deviation, range, 25th and outlier if any.

Answer 1

Since we know that

Where n is the number of data points
Now

and n = 5
This implies that

b) Since we know that
Median for a list of even number of data point is the mean of 2 middle most values if we sort the list in increasing order while for a list of odd number it is the middle most value if the list is sorted in increasing order.
Since our list have odd number of data points, this implies that
Median = 47.0
c) Since we know that

d) Since we know that
The range is the difference between the largest and smallest values in a set of values.
This implies that
Range = 92.0-16.0
Range = 76.0
e) Since we know that
The lower quartile(Q1) is the median of the lower half of the data set while upper quartile(Q3) is the median of the upper half of the data set.
Also, median for a list of even number of data point is the mean of 2 middle most values if we sort the list in increasing order while for a list of odd number it is the middle most value if the list is sorted in increasing order.
Since our list have odd number of data points, this implies that
Median = 47.0
Lower half of our list is [16.0, 34.0]
Since our lower half list have even number of data points, this implies that
Q1 = 25.0
Upper half of our list is [84.0, 92.0]
Since our upper half list have even number of data points, this implies that
Q3 = 88.0
Interquartile range is equal to the distance between quartile 1(Q1) and quartile 3(Q3).
IQR = Q3 - Q2
IQR = 88.0-25.0
IQR = 63.0
Since we know that the outliers are those points in the data set which are either less than 1.5 times the IQR from Quartile 1 or more than 1.5 times the IQR from Quartile 3
Therefore fthere are no outlers

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