Question
If a, b and c are the median, mode and range,
respectively of the data: 8, 5, 4, 3, 2, 7, 3, 10, 9, 17, 12, 3, 8, 4, then what is the value of (3a-2b+c)?Solution
Arranging the data in ascending order, we have: 2, 3, 3, 3, 4, 4, 5, 7, 8, 8, 9, 10, 12, 17 The median is the middle value of the data. Since there are 14 values, the median is the average of the 7th and 8th values: Median = (5+7)/2 = 6 The mode is the value that appears most frequently in the data. In this case, the value 3 appears three times, which is more than any other value. Therefore, the mode is 3. The range is the difference between the largest and smallest values in the data. In this case, the smallest value is 2 and the largest value is 17. Therefore, the range is: Range = Largest value - smallest value = 17 - 2 = 15 Now, we can substitute the values of a, b, and c into the given expression: 3a - 2b + c = 3(6) - 2(3) + 15 = 18 - 6 + 15 = 27 Therefore, the value of (3a-2b+c) is 27.
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