Question

A dataset has the following observations:
5, 10, 10, 12 and 13.
Which of the following is true?

• A. Mean is equal to median, but not equal to mode.
• B. Mean is equal to mode, but not equal to median.
• C. Median = Mode = Mean
• D. Mode is equal to median, but not equal to mean.

Answer 1

The correct option is C Median = Mode = Mean

Dataset: 5, 10, 10, 12, 13.
(i) Sum of all observations = 5 + 10 + 10 + 12 + 13 = 50
Number of observations = 5
$\text{Mean}=\frac{\text{Sum of all observations}}{\text{Total number of observations}}=\frac{50}{5}=10$

(ii) When the data is arranged in ascending or descending order, the median of a dataset is the middlemost data point.
Dataset: 5, 10, 10, 12, 13.

Therefore, 10 is the median of the dataset.

(iii) Mode of a dataset is the most frequently occuring observation.
10 occurs twice in the dataset, and hence the mode equals 10.

$\therefore$ Mean = Median = Mode