In stat, lower/upper fourth is the same as lower/upper quartile. Right?

Question

Anyway, I need a little help in understanding a certain problem.

data 1: 10, 20, 25, 28, 31, 35, 37, 38, 38, 39, 39, 42, 46

data 2: 23, 39, 40, 41, 43, 47, 51, 58, 63, 66, 67, 69, 72

For data 1,
sample mean = 52.23
median = 51
standard deviation = 14.86
upper fourth (or quartile?) = 66
lower fourth (or quartile?) = 41

For data 2,
mean = 32.92
median = 37
SD = 9.93
upper fourth (or quartile?) = 39
lower fourth (or quartile?) = 28

The solutions manual and my TI-83 Plus calculator agrees with me on all those answers except the lower/upper fourths (or quartiles?).

For data 1, my calculator says:
upper quartile = 66.5
lower quartile = 40.5

For data 2, calc says:
upper quartile = 39
lower quartile = 26.5

To find fourths (or quartiles?), I generally understand about splitting your samples in one half of the lower values and the other half of higher values, and then find the median in each of those halves.

Also read about including the median in both halves if the number of samples is odd.

Can someone explain or elaborate?

Answer 1

First, your data 1 and 2 sets are reversed when you do your computations.

If you look at your data 2 parameters, the median and mean are pretty divergent. This suggests that the baseline assumption of your calculations, the normal distribution, may not apply.

You may want to check the calculator handbook to see if the formula it is using to calculate quartiles is the same as yours.