Question

For the data 6, 2, 9, 11, 3, 4, 9, 7, 13, 1, which of the following is true?

• A. \(\text{Median} < \text{Mean} < \text{Mode}\)
• B. \(\text{Mode} < \text{Mean} < \text{Median}\)
• C. \(\text{Mean} = \text{Median} < \text{Mode}\)
• D. \(\text{Mode} = \text{Median} < \text{Mean}\)

Answer 1

The Correct Option is C

First, arrange the data in ascending order: \[ 1, 2, 3, 4, 6, 7, 9, 9, 11, 13 \]
The Mode is the most frequent value in the dataset. Here, the mode is 9, as it appears twice.
The Median is the middle value when the data is arranged in order. Since there are 10 data points (even number), the median is the average of the 5th and 6th values: \[ \text{Median} = \frac{6 + 7}{2} = 6.5 \]
The Mean is the sum of all values divided by the number of values: \[ \text{Mean} = \frac{1 + 2 + 3 + 4 + 6 + 7 + 9 + 9 + 11 + 13}{10} = \frac{65}{10} = 6.5 \] Thus, the Mean = Median = Mode = 6.5.

The correct option is (C): \(\text{Mean} = \text{Median} < \text{Mode}\)