Question

The following questions are asked by students after a unit on mean, median, and mode. Respond as if you were responding to your student. Use correct grammar, spelling and punctuation and be thorough in your responses.

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

Dear student, please comment in the case of any doubt and I would love to clarify it.

1)

The median average is the middle number in a set of data when the data has been written in ascending size order.

If there is an even number of items of data, there will be two numbers in the middle. The median is the number that is halfway between these two numbers.

To find the median, put all numbers into ascending order and work into the middle by crossing off numbers at each end.

If there are a lot of items of data, add 1 to the number of items of data and then divide by 2 to find which item of data will be the median. This works when it is an odd number but when it is an even number you will get a decimal answer such as 7.5. The median will be halfway between the 7th and 8th items.

2)

If the mean income of 10 people is $10,000, then the total income will be $100,000. And if one person gets a raise of $10,000, then the sum will be $110,000 and the mean will be 110000/10, which is $11000. Here, the mean increased by $1,000.

There will be no change in mode or median here.

3)

Here, percentiles can be used. We can use the PERCENTILE function in excel here. If 80 is what Tom scored and the mean is also 80, then he must have scored more than 50 percent of the students in class.