Question

Example 2: Compute median, mean, spread and quartiles for data of Serum-cholesterol (measured in mg/100ml) given 120.82, 86.2, 124.2, 92.6, 95.19, 103.4, 95.3, 80.6, 84.3, 103.3. Is a value of spread independent from unit of variable (or it is dependent on it)?

From what I understand in the second part about the unit, an example would be "If I asked for height in centimeters instead of height in inches, would that change the spread?"

Answer 1

The first task is to compute the median and the quartiles. And, in order to compute the median and the quartiles, the data needs to be put into ascending order, as shown in the table below

Position	X (Asc. Order)
1	80.6
2	84.3
3	86.2
4	92.6
5	95.19
6	95.3
7	103.3
8	103.4
9	120.82
10	124.2

Since the sample size n=10 is even, we have that (n+1)/2 = (10+1)/2 = 5.5 is not an integer value, the median is computing by taking the average of the values at the positions 5th and 6th, as shown below

Quartiles

The quartiles are computed using the table with the data in ascending order

For Q1​ we have to compute the following position:

Since 2.75 is not an integer number, Q1​ is computed by interpolating between the values located in the 2nd and 3rd positions, as shown in the formula below

For Q3​ we have to compute the following position:

Since 8.25 is not an integer number, Q3​ is computed by interpolating between the values located in the 8th and 9th positions, as shown in the formula below

The interquartile range is therefore

MEAN AND VARIANCE

The sample size is n=10. 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
	120.82	14597.4724
	86.2	7430.44
	124.2	15425.64
	92.6	8574.76
	95.19	9061.1361
	103.4	10691.56
	95.3	9082.09
	80.6	6496.36
	84.3	7106.49
	103.3	10670.89
Sum =	985.91	99136.839

The sample mean is computed as follows:

Also, the sample variance is

Therefore, the sample standard deviation s is

The value of the spread is independent from the unit of the variable. Units are immaterial while dealing with the spread.