Find the median of the data $ 11, 16, 33, 15, 51, 19, 71, 75, 21, 17 $.

Question

Examoogle · Accepted Answer

The correct answer is Option A: 20. Count the total number of items ($n$), arrange them in ascending order, and pick the middle value (or average the two middle values if $n$ is even).

Step-by-Step Solution & Concepts:
Shortcut Trick: Count the total number of items ($n$), arrange them in ascending order, and pick the middle value (or average the two middle values if $n$ is even).

Formula Used: $$	ext{Median} = \begin{cases} \left(\frac{n}{2}ight)^{	ext{th}} 	ext{ term} & 	ext{if } n 	ext{ is odd} \ \frac{\left(\frac{n}{2}ight)^{	ext{th}} 	ext{ term} + \left(\frac{n}{2} + 1ight)^{	ext{th}} 	ext{ term}}{2} & 	ext{if } n 	ext{ is even} \end{cases}$$

Given: Data values: 11, 16, 33, 15, 51, 19, 71, 75, 21, 17

Steps: Count the number of observations: Count the total number of given values in the dataset: $n = 10$.. Arrange the data in ascending order: Sort the given numbers from smallest to largest: $11, 15, 16, 17, 19, 21, 33, 51, 71, 75$.. Apply median formula for even $n$: Since $n = 10$ is even, the median is the average of the $\left(\frac{n}{2}ight)^{	ext{th}}$ and $\left(\frac{n}{2} + 1ight)^{	ext{th}}$ terms, which are the 5th and 6th terms.. Calculate final median: Compute the average of 19 and 21: $$	ext{Median} = \frac{19 + 21}{2} = \frac{40}{2} = 20$$

Answer: A is correct because the median of the given dataset after arranging in ascending order and taking the average of the 5th and 6th terms equals 20.

Exam Tip: For grouped frequency distributions, the median is calculated using the cumulative frequency distribution and the formula $	ext{Median} = L + \left(\frac{\frac{n}{2} - cf}{f}ight) 	imes h$.

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Discussion (0)

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)