find the median for the data items in the frequency distribution.\nthe median is
find the median for the data items in the frequency distribution.\nthe median is
Answer
Explanation:
Step1: Calculate the total number of data items
The total number of data items ( n=\sum f). (n = 5+1+3+5+3+1+1+1=20)
Step2: Determine the position of the median
Since (n = 20) (an even number), the median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+1))th ordered data items. (\frac{n}{2}=\frac{20}{2} = 10) and (\frac{n}{2}+1=11)
Step3: Cumulative frequency
| Score (x) | Frequency (f) | Cumulative Frequency (cf) |
|---|---|---|
| 1 | 5 | 5 |
| 2 | 1 | 5 + 1=6 |
| 3 | 3 | 6+3 = 9 |
| 4 | 5 | 9 + 5=14 |
| 5 | 3 | 14+3 = 17 |
| 6 | 1 | 17+1=18 |
| 7 | 1 | 18+1=19 |
| 8 | 1 | 19+1=20 |
The 10th and 11th data items fall in the (x = 4) group (because (cf) for (x = 3) is 9 and (cf) for (x=4) is 14)
Answer:
(4)