The lowest value of a set of observations is 4.5, and their range is 10.9. The arithmetic mean is found to be 19.9, and the median is found to be 15.6. Which of the following statements is correct?

Correct option is C

Correct Option (C): Both arithmetic mean and median are wrong.
​Solution: ​
1. Range: The range is the difference between the highest and lowest values in the data set. It is given as 10.9, and the lowest value is 4.5. Therefore, the highest value should be:
    * Highest value = Lowest value + Range = 4.5+10.9 = 15.4
2. Arithmetic Mean: The arithmetic mean is the sum of all observations divided by the number of observations.
    * Given Mean = 19.9 , But the highest value is 15.4, and the lowest value is 4.5, which would generally result in a mean much lower than 19.9. This suggests that the reported mean of 19.9 is incorrect.
3. Median: The median is the middle value of a data set when the data is arranged in ascending order. Given that the median is reported as 15.6, it is reasonable because the median is likely between the lowest value (4.5) and the highest  value (15.4). This makes the median value of 15.6 incorrect.