Question

You are conducting a study comparing two different treatments for post-surgical recovery. Group A, consisting of 10 patients from your clinic, will be given the current standard treatment. Group B, consisting of 10 different patients from your clinic, will be given a new experimental treatment. Both groups of patients have undergone the same surgery in the last month.

Table 1. Number of post-surgical recovery days reported by group.

Group A		Group B
3 days	5 days	8 days	5 days
10 days	10 days	10 days	6 days
10 days	13 days	10 days	7 days
8 days	3 days	7 days	6 days
4 days	4 days	5 days	6 days

Given this data, fill out the following chart. Show your work to receive full credit (10 points).

Group A	Group B
Mean:	Mean:
Median:	Median:
Mode:	Mode:
Range:	Range:
Standard deviation:	Standard deviation:

Now that you have completed these descriptive statistics, what conclusions would you draw about the differences between the two groups? (10 points) Hint: Compare the means, medians, modes, ranges, and standard deviations.

Answer 1

Solution:

Group A
Given data: 3, 10, 10, 8, 4, 5, 10, 13, 3, 4
Mean:
μ = 3 + 10 + 10 + 8 + 4 + 5 + 10 + 13 + 3 + 4/10 = 70/10 = 7

Median:
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
3 3 4 4 5 8 10 10 10 13   
As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:
Median = 5+8/2=6.5

Mode:
The mode of a set of data is the value in the set that occurs most often.
Ordering the data from least to greatest, we get:
3 3 4 4 5 8 10 10 10 13   
We see that the mode is 10 .

Range:
The range is the difference between the highest and lowest values in the data set.
Ordering the data from least to greatest, we get:
3 3 4 4 5 8 10 10 10 13   
The lowest value is 3.
The highest value is 13.
The range = 13 - 3 = 10.

Standard deviation:
σ = ⎷∑(xi-Xbar)^2/n−1 = ⎷118/10-1 ≈ 3.6209

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Group B
8, 10, 10, 7, 5, 5, 6, 7, 6, 6
Mean:
μ = 8 + 10 + 10 + 7 + 5 + 5 + 6 + 7 + 6 + 6/10 = 70/10 = 7

Median:
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
5 5 6 6 6 7 7 8 10 10   
As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:
Median = 6+7/2=6.5

Mode:
The mode of a set of data is the value in the set that occurs most often.
Ordering the data from least to greatest, we get:
5 5 6 6 6 7 7 8 10 10   
We see that the mode is 6 .

Range:
The range is the difference between the highest and lowest values in the data set.
Ordering the data from least to greatest, we get:
5 5 6 6 6 7 7 8 10 10   
The lowest value is 5.
The highest value is 10.
The range = 10 - 5 = 5.

Standard deviation:
σ = ⎷∑(xi-Xbar)^2/n−1 = ⎷30/10-1 ≈ 1.8257