Consider the following data:
7, 3, 9, 3, 12, 6, 3, 9
Consider the following statements about this data:
I. The mean is equal to the median.
II. The range is three times the mode.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both I and II
Write the 8 values in ascending order: 3, 3, 3, 6, 7, 9, 9, 12. The mean is the sum divided by 8, the median is the average of the 4th and 5th values, the mode is the most frequent value and the range is the largest minus the smallest value.
I. The mean is equal to the median. — Correct. The sum is \(3+3+3+6+7+9+9+12=52\), so the mean is \(52\div8=6.5\); the median is \((6+7)\div2=6.5\). Both are 6.5.
II. The range is three times the mode. — Correct. 3 appears three times, more than any other value, so the mode is 3; the range is \(12-3=9\), and \(9=3\times3\).