The formular (N + 1)/2 is used to determine the

Analyze the question The question asks what statistical measure is found using the formula (N + 1)/2, where N is the number of observations.

Explain the concept The formula (N + 1)/2 gives the position of the middle value in an ordered data set. That middle value is the median.

• Mean = ΣX / N (sum of values divided by the number of values)
• Mode = the value that occurs most frequently
• Standard deviation = √[Σ(X − mean)² / N], which measures spread
• Median = the middle value, located at the (N + 1)/2 th position after arranging the data in order

Show the solution

Example 1 (N is odd): Data: 3, 5, 7, 9, 11

• N = 5
• Position = (5 + 1)/2 = 3rd position
• Median = 7

Example 2 (N is even): Data: 2, 4, 6, 8

• N = 4
• Position = (4 + 1)/2 = 2.5th position
• The median is the average of the 2nd and 3rd values = (4 + 6)/2 = 5

In both cases the formula points to the middle of the ordered data, which is the median. The mean, mode and standard deviation do not use this positional formula.

Identify the answer The correct option is A. median.

Exam tip Remember: "Median = Middle = (N + 1)/2 position." Note that the formula gives the position, not the value itself. Also, always arrange the data in order (ascending or descending) before using it.