Question

1) A student asks , " Can a median number be a decimal? " How do you respond. Use the definition of median in your answer. 2) A student asks, " If the mean income of 10 people is $10,000 and one person gets a raise of $10,000, is the median, the mean, or the mode changed and , if so, by how much?" How would you respond? Be thorough and explain to the student why you respond like you do. 3) Suppose the class takes a test and the following averages are obtained: Mean = 80 Median = 90, and Mode = 70 Tom, who scored an 80, would like to know if he did better that half the class. What is your response? Be thorough and explain to the student why you respond like you do.

Answer 1

1. Yes, the median can be a decimal. The median of a data sample can be any value that separates the lower half of the data from the upper half of the data. In other words, it is the middlemost value of a data sample. Therefore, even for a data sample with all integers and even number of data points, the median can be a decimal value.

2. "If the mean income of 10 people is $10,000 and one person gets a raise of $10,000"

From the above given data it is not possible to say conclusively whether the median will change or not, or even if it does, by how much. If the increment occurs to any person who was already beyond the 6th smallest value in the dataset, then there will be no change in median.

The mean will definitely change. If previous mean is   = 10000 and n = 10.

New mean = ((10000 X 10) + 10000)/10 = 11000

Therefore the mean changed by (11000 - 10000) = 1000

It is not possible to say if the mode will change. To check whether the mode has changed it is necessary to see the data itself.

3. In this scenario it has to be said that Tom who scored 80 did not do better than half the class. This is so because the median = 90. As we know the median is the middlemost value in a data. Therefore half the class has scored 90 or above and Tom's marks is lower than the median value that means more than half the class has done better than him. In this case although the mean is equal to Tom's marks and the mode lesser than Tom's marks but they are not valid to check whether Tom did better than half the class.