Question

A random sample of 8 adults aged 30 years were asked how much they spent on medical costs in the year 2009. Using the following data, compute the sample mean, the sample standard deviation, the sample median, and the first and third quartiles. 300 140 5600 520 470 700 640 1200

Answer 1

Mean and standard deviation

The sample size is n=8. The provided sample data along with the data required to compute the sample mean and sample variance are shown in the table below:

	X	X2
	300	90000
	140	19600
	5600	31360000
	520	270400
	470	220900
	700	490000
	640	409600
	1200	1440000
Sum =	9570	34300500

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

Median and quartiles

These are the sample data that have been provided with:

Position	X (Asc. Order)
1	140
2	300
3	470
4	520
5	640
6	700
7	1200
8	5600

Now the position of the first quartile Q1​ is:

Since is not an integer number, the first quartile ​ is computed by interpolating between the values located in the 2nd and 3rd positions, as shown in the formula below:

Since the sample size n=8 is even, we have that is not an integer value, so the median is computed directly by finding the average of the values located at positions 4th and 5th, which is:

Now the position of the third quartile Q3​ is:

Since is not an integer number, the third quartile ​ is computed by interpolating between the values located in the 6th and 7th positions, as shown in the formula below:

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