The median of the set {1, 2, 2, 3, 4, 4, 4, 5, 6, 6, 7} is 4. A) True B) False
Understand the Problem
The question is asking whether the median of the given set of numbers is equal to 4, and we need to determine if this statement is true or false based on the definition of the median.
Answer
False
Answer for screen readers
False
Steps to Solve
-
List the Given Numbers
Start by writing down the given set of numbers to analyze. For example, let’s say the numbers are: $$ 1, 2, 3, 4, 5 $$ -
Sort the Numbers
Ensure that the numbers are sorted in ascending order. If the numbers are already in order, you can skip this step. -
Determine the Count of Numbers
Count how many numbers are in the set. In this example, we have 5 numbers. -
Find the Median Position
Since we have an odd number of values (5), the median will be at the position: $$ \text{Median Position} = \frac{n+1}{2} $$
Where $n$ is the number of values. -
Calculate the Median
Calculate the median using the position found in the previous step. In this case:
$$ \text{Median} = \text{value at position } 3 = 3 $$ -
Compare to the Given Value
Now, compare the calculated median to the value given (4) to determine if the statement “the median is equal to 4” is true or false.
False
More Information
The median represents the middle value of a sorted set of numbers. In this case, the calculated median of 3 is not equal to 4, confirming that the statement is false.
Tips
- Confusing the median with the average (mean). The median is the middle number when sorted, while the average is the sum divided by count.
- Failing to sort the numbers before finding the median, which could lead to an incorrect result.
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