Question

The following are the ages of 13 mathematics teachers in a school district.

29, 32, 33, 33, 35, 41, 42, 43, 44, 51, 53, 56, 58

Notice that the ages are ordered from least to greatest.
Give the median, lower quartile, and upper quartile for the data set.

Answer 1

Median = 42
LQ = 33
UQ = 52

Explanation:

median is given by the term that divides the groups in two equally quantities. In this case is (n+1)/2 = (13+1)/2 = 14/2 = 7

the 7th term is: 42
(notice this means 6 values are below 42 and 6 values are above 42, the definition of a median)

the first (lower) quartile is given then by the (n+1)/4 value

(13+1)/4=3.5, this is the half between 3th and 4th terms.

since the term is the same (3th value is 33 and 4th value is 33)

LQ=33
(25% of the values are below 33)

for the upper quartile the value represents the top 75%, this is given by

3(13+1)/4 = 10.5

this is the half between 10th and 11th terms

(51+53)/2=52

(25% of the values are above 52)