The median for the given set of six ordered data values is 26.5. What is the missing value? 7 12 21 ______ 41 50

Verified step by step guidance

1. Identify the position of the median in an ordered data set with an even number of values. Since there are 6 values, the median is the average of the 3rd and 4th values.
2. Write the formula for the median in this case: \(\text{Median} = \frac{\text{3rd value} + \text{4th value}}{2}\).
3. Substitute the known median value and the known 3rd value into the formula: \$26.5 = \frac{21 + x}{2}\(, where \)x$ is the missing 4th value.
4. Multiply both sides of the equation by 2 to eliminate the denominator: \$2 \times 26.5 = 21 + x$.
5. Solve for \(x\) by subtracting 21 from both sides: \(x = 2 \times 26.5 - 21\).

Key Concepts

Median of a Data Set

The median is the middle value of an ordered data set. For an even number of values, it is the average of the two middle numbers. Understanding how to find the median helps identify the missing value when the median is given.

Ordered Data

Data must be arranged in ascending or descending order before finding the median. This ensures the middle values are correctly identified, which is essential for solving problems involving medians.

Solving for an Unknown Value

When a data set contains a missing value, algebraic methods can be used to find it by setting up an equation based on known statistics, such as the median, and solving for the unknown.