Question

12. The math department at a small school has 5 teachers. The ages of these teachers are 23, 34, 37, 42, and 58.Suppose you selected a random sample of 3 teachers and calculated the sample median.(a) List all 10 possible samples of size 3. Calculate the sample median for each sample.

Answer 1

Answer:

$\begin\\\begin{tabular}{|l|l|l|}No&Sample&Median\\01&58,42,37 &42\\02&58,42,34&42\\03&58,42,23& 42\\04&37,34,23 & 34\\05&58,37,34 & 37\\06&58,37,23 & 37\\07&58,34,23 &34\\08&42,37,34 &37\\09&42,37,23 &37\\10&42,34,23 &34\end$

Step-by-step explanation:

From the question we are told that

5 samples(23 34 37 42 58)

To select 3 random sample

a) Generally to find all 10 possible outcomes and there median we make a table

Therefore

L1

58,42,37  Median=42

L2

58,42,34  Median=42

L3

58,42,23  Median=42

L4

37,34,23  Median=34

L5

58,37,34  Median=37

L6

58,37,23  Median=37

L7

58,34,23  Median=34

L8

42,37,34  Median=37

L9

42,37,23  Median=37

L10

42,34,23  Median=34

$\begin\\\begin{tabular}{|l|l|l|}No&Sample&Median\\01&58,42,37 &42\\02&58,42,34&42\\03&58,42,23& 42\\04&37,34,23 & 34\\05&58,37,34 & 37\\06&58,37,23 & 37\\07&58,34,23 &34\\08&42,37,34 &37\\09&42,37,23 &37\\10&42,34,23 &34\end$