Question 1

A student’s marks in five subjects are 25, 26, 27, 28, and 29. In this data set, which measure(s) of central tendency is 27?

Accepted Answer

Introduction / Context: We compare the mean, median, and mode for a small, ordered data set. Given Data / Assumptions: Data: 25, 26, 27, 28, 29 (distinct values). All observations have equal weight. Concept / Approach: Median is the middle value in ordered data; mean is the arithmetic average; mode is the most frequent value. Step-by-Step Solution: Median = middle of five numbers = 27.Mean = (25 + 26 + 27 + 28 + 29) / 5 = 135 / 5 = 27.Mode: none (all values occur once), so 27 is not the mode. Verification / Alternative check: Symmetry around 27 makes it both mean and median. Why Other Options Are Wrong: “Mode” or “Median and Mode” are incorrect because the distribution has no mode; “Median” alone omits the mean; “Mean” alone omits the median. Common Pitfalls: Assuming a mode exists just because a central number looks typical. Final Answer: Mean and Median

Question 2

Find the median of the data set: 2, 4, 6, 8, 10, 12, 14.

Accepted Answer

Introduction / Context: The median is the middle value in an ordered data set. For odd-sized samples, it is the central observation. Given Data / Assumptions: Ordered data (n = 7): 2, 4, 6, 8, 10, 12, 14. Concept / Approach: With 7 values, the 4th value is the median. Step-by-Step Solution: Indexing from 1: the 4th value is 8. Verification / Alternative check: Equal number of observations on either side (three below and three above). Why Other Options Are Wrong: 6 and 10 are adjacent but not central; 9.5 would be the median for an even-sized data set between 9 and 10, not applicable here. Common Pitfalls: Confusing mean and median; the mean here is also 8 but that is coincidental due to symmetry. Final Answer: 8

Statistics Questions