| Q.50 | The median of Y in the following data is ________. | |||||
|---|---|---|---|---|---|---|
| Serial number | 1 | 2 | 3 | 4 | 5 | 6 |
| Y | 22 | 12 | 10 | 14 | 16 | 20 |
Median of Y in the Data Set 22, 12, 10, 14, 16, 20 – Step by Step Solution
Understanding Median of Ungrouped Data
For ungrouped data, the median is the middle value of a data set arranged in ascending or descending order.
If the number of observations (n) is even, the median is the average of the n/2th
and (n/2 + 1)th terms of the ordered data.
Step‑by‑Step Solution
Given Y values: 22, 12, 10, 14, 16, 20
Step 1: Arrange data in ascending order
Ordered set: 10, 12, 14, 16, 20, 22
Step 2: Count the number of observations
Here, n = 6 (even number).
Step 3: Identify the middle positions
For even n, the middle positions are n/2 = 3 and n/2 + 1 = 4.
Step 4: Pick the 3rd and 4th terms in the ordered list
- 3rd term = 14
- 4th term = 16
Step 5: Find the average of these two middle terms
Median = (14 + 16) / 2 = 30 / 2 = 15
Therefore, the median of Y for the data 22, 12, 10, 14, 16, 20 is 15.
How This Appears in an MCQ
In competitive exams, such a question usually appears with options like:
| Option | Value | Explanation |
|---|---|---|
| A | 14 | This is the 3rd term of the ordered data, but for even n, the median is the average of the 3rd and 4th terms, so 14 alone is incorrect. |
| B | 15 | Correct; it is the average of 14 and 16, the two middle terms of the six ordered observations, giving the true median. |
| C | 16 | This is the 4th term of the ordered data; using only one middle term ignores the rule for even‑sized data sets. |
| D | 17 | This is a guessed central value or the average of non-middle terms and does not correspond to the actual median. |
Correct Answer: Option B (15)
Brief Introduction for SEO
Finding the median of Y in the following data is a common statistics problem for students preparing for school and competitive exams.
By correctly arranging the ungrouped data and applying the median formula for an even number of observations, learners strengthen
their understanding of measures of central tendency and improve exam performance.
