find the median for the data items in the given frequency distribution. score, x 1 2 3 4 5 6 7 8 frequency…
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.)
Answer
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, $cf$ |
|---|---|---|
| 1 | 1 | 1 |
| 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