Question

find the median for the data items in the given frequency distribution.
the median is
(type an integer or a decimal.)

Explanation:

Step1: Calculate the total number of data items

We sum up the frequencies. $n=\sum f = 2 + 6+2 + 4+2 + 4+3 + 1=24$.

Step2: Determine the position of the median

Since $n = 24$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data values. $\frac{n}{2}=\frac{24}{2}=12$ and $\frac{n}{2}+1 = 13$.

Step3: Cumulative frequency calculation

Score ($x$)	Frequency ($f$)	Cumulative Frequency ($cf$)
2	6	$2 + 6=8$
3	2	$8+2 = 10$
4	4	$10 + 4=14$

The 12th and 13th data values fall within the score of 4 (because when $x = 4$, $cf$ goes from 10 to 14).

Answer:

$4$