Question

What is the difference between ordinal data and ratio data? What is the variance for problem number 3? #3 Identify the mode and median of the following data. Compute the mean, range and standard deviation as well. 3 place decimals please!! 18, 20, 19, 22, 20 25 Points – Mode, median and range are 3 points each, mean is 6 points, and standard deviation is 10 points

Answer 1

Solution:

An ordinal scale classifies values into distinct categories in which ranking is applied while ratio scale is an ordered scale in which the difference b/w the measurements involves a true zero point like height, weight, age and salary.
Mean = (18+20+19+22+20+25)/6 = 124/6 = 20.67
Lets sort data from smallest to largest
18,19,20,20,22,25
Median = (6+1)/2 = 3.5th Value
median = (20+20)/2 =20
Mode = 20 becuase its frequency is 2.
Range = (Largest - smallest) = (25-18) = 7
Variance = summation(Xi-Xbar)^2 / (n-1)

X	Xi-Xbar	(Xi-Xbar)^2
18	-2.66666666666667	7.11111111111112
20	-0.666666666666668	0.444444444444446
19	-1.66666666666667	2.77777777777778
22	1.33333333333333	1.77777777777777
20	-0.666666666666668	0.444444444444446
25	4.33333333333333	18.7777777777778
20.6666666666667
	Summation	31.3333333333333

Variance = (31.333)/5 = 6.27
Standard deviation = sqrt(variance) = sqrt(6.27) = 2.50