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 1 3 6 6 1 3 1 1 the median is . (type an integer or a decimal.)

Explanation:

Step1: Calculate total frequency

$n=\sum f=1 + 3+6 + 6+1+3+1+1=22$

Step2: Determine position of median

Since $n = 22$ (an even - numbered data set), the median is the average of the values at positions $\frac{n}{2}=11$ and $\frac{n}{2}+1 = 12$ when the data is arranged in ascending order.

Step3: Cumulative frequency

Score, $x$	Frequency, $f$	Cumulative Frequency, $cf$
2	3	1 + 3=4
3	6	4+6 = 10
4	6	10+6=16
5	1	16 + 1=17
6	3	17+3 = 20
7	1	20+1=21
8	1	21+1=22

The 11th and 12th ordered data values fall within the score of 4 (because the cumulative frequency up to score 3 is 10 and up to score 4 is 16).

Answer:

4