Question

initial knowledge check
question 9
the following are the ages of 13 history teachers in a school district.
27, 28, 29, 31, 33, 35, 37, 40, 41, 43, 43, 50, 58
notice that the ages are ordered from least to greatest.
give the median, lower quartile, and upper quartile for the data set.
(a) median:
(b) lower quartile:
(c) upper quartile:

Explanation:

Step1: Find median position

For $n=13$ (odd), median position is $\frac{n+1}{2} = \frac{13+1}{2}=7$

Step2: Identify median value

7th value in ordered set: $37$

Step3: Split data for quartiles

Lower half: $27,28,29,31,33,35$; Upper half: $40,41,43,43,50,58$

Step4: Find lower quartile

Median of lower half: $\frac{29+31}{2}=30$

Step5: Find upper quartile

Median of upper half: $\frac{43+43}{2}=43$

Answer:

(a) Median: $37$
(b) Lower quartile: $30$
(c) Upper quartile: $43$