Question

find the median for the data items in the given frequency distribution.
score, x: 1 2 3 4 5 6 7 8
frequency, f: 2 4 4 2 2 2 2 12
the median is
(type an integer or a decimal.)

Explanation:

Step1: Calculate total frequency

$n=\sum f=2 + 4+4 + 2+2+2+2+12=30$

Step2: Determine position of median

Since $n = 30$ (an even - numbered data set), the median is the average of the $\frac{n}{2}=15$th and $(\frac{n}{2}+1)=16$th ordered data values.

Step3: Calculate cumulative frequency

Score, $x$	Frequency, $f$	Cumulative Frequency
2	4	$2 + 4=6$
3	4	$6 + 4 = 10$
4	2	$10+2 = 12$
5	2	$12 + 2=14$
6	2	$14+2 = 16$
7	2	$16+2 = 18$
8	12	$18+12 = 30$

Step4: Identify median values

The 15th and 16th ordered data values fall within the score of 6.

Answer:

6