Using empirical formula, calculate the mode for the following data.
17, 20, 21, 18, 25, 28, 24, 22, 16, 24, 25, 24
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 25.
Data in ascending order: 16, 17, 18, 20, 21, 22, 24, 24, 24, 25, 25, 28
Sum = 16 + 17 + 18 + 20 + 21 + 22 + 24 + 24 + 24 + 25 + 25 + 28 = 264
Number of values = 12
Mean = 264 / 12 = 22
There are 12 values (an even number), and the median is the average of the two middle values.
The middle values are the 6th and 7th values in the ordered list.
6th value = 22 and 7th value = 24
Median = (22 + 24)/2 = 46/2 = 23
Empirical formula: Mode = 3Median - 2Mean
Mode = 3 × 23 - 2 × 22 = 69 - 44 = 25
Therefore, the mode is 25.