Question

If the mode of the data 2, 4, 6, 7, 5, 6, 10, 6, 7, 2k + 1, 9, 7, 13 is 7, then the value of k is

• A. 7
• B. 3
• C. 4
• D. 2

Answer 1

The Correct Option is B

In the given data, the mode is the number that appears most frequently. The data consists of the following values: \[ 2, 4, 6, 7, 5, 6, 10, 6, 7, 2k+1, 9, 7, 13 \] The number 7 appears most frequently, and we are told that the mode is 7. To determine the value of \(k\), note that the term \(2k+1\) must not interfere with the frequency of 7. Thus, \(2k+1\) cannot be 7, otherwise it would alter the frequency. Now, to determine \(k\), we observe that the data must have at least 3 occurrences of 7 to make it the mode. Since there are already 3 sevens (7, 7, 7), we conclude that: \[ k = 3 \]

The correct option is (B): \(3\)