Which of the following sets of data has a median of 45, a range of 57, and a mode of 45? Is it (A) 67, 45, 26, 77, 20, and 45; (B) 26, 67, 20, 20, 20, and 45; (C) 26, 26, 45, 77, 20, and 76; (D) 26, 67, 20, 45, 44, and 77; or (E) 25, 67, 19, 45, 45, and 77?
As we are given the median, range, and mode of the data set, we can start with any one of these. The mode is the easiest to identify, so we’ll firstly look for those data sets that have a mode of 45. The mode is the most common or most frequently occurring value.
In data set (A), this is 45 as this value appears twice. The most common value in data set (B) is 20. As the mode is 20, this cannot be the correct answer. Data set (C) has a mode of 26, so this is also incorrect. There is no mode in data set (D) as all of the values appear once. Data set (E) has a mode of 45 as this appears twice and the other four values appear once. Both data set (A) and data set (E) have a mode of 45.
We are also told that the range of our data set is 57. And we calculate the range by subtracting the smallest number from the largest number. In data set (A), the largest number is 77, and the smallest number is 20. 77 minus 20 is equal to 57. This means that data set (A) does have a range of 57. Data set (E) also has a largest value of 77. However, it has a smallest value of 19. This means that the range is equal to 58. Data set (E) does, therefore, not satisfy all three of the criteria. This suggests that (A) is the correct answer. We do need to check that the median of this set of data is 45.
The median is the middle value of a data set where the numbers are written in ascending or descending order. We can find the middle value by crossing off the lowest and highest values. Repeating this gives us two middle values that are both 45. This means that the median of data set (A) is 45. The numbers 67, 45, 26, 77, 20, and 45 have a median of 45, a range of 57, and a mode of 45.