Question

Think about the following questions, and post your ideas or questions to the discussion forum.

1. How many siblings do you have? (You may make up a realistic number if you wish to keep your family information private.)
2. Which do you think is larger, the mean number of siblings of people in this class, or the median number of siblings? Why do you think so?
3. How would you verify your answer to #2? What questions would you need to ask?
4. Why would the mean and median differ?
5. Under what circumstances would the mean be bigger? Give a specific instance in this case. Under what circumstances would the median be bigger? Again give a specific instance in this case.

Answer 1

(a)

Question:

How many siblings do you have?

3

(b)

Question:

Which do you think is larger, the mean number of siblings of people in this class, or the median number of siblings? Why do you think so?

The mean number of siblings of people in this class, will be larger than the the median number of siblings because the distribution of number of siblings of people in this class is right skewed, because most of the people in this class,are having smaller number of siblings but some people in this class,are having larger number of siblings.

(c)

Question:

How would you verify your answer to #2? What questions would you need to ask?

Our answer to #2 is verified by collecting data on siblings of people in this class from each student. The question to be asked is:"How many siblings do you have?"

(d)

Question:

Why would the mean and median differ?

The mean and median differ due to the variation in the distribution: negatively skewed, symmetrical or positively skewed.

(e)

Question:

Under what circumstances would the mean be bigger? Give a specific instance in this case.

The mean would be bigger than the median if the distribution is positively skewed. Specific instance is the distribution of income. Most people have low incomes but some people are very rich.

(f)

Question:

Under what circumstances would the median be bigger? Again give a specific instance in this case.

The median would be bigger than the mean if the distribution is negatively skewed. Specific instance is the distribution of marks obtained by students in an easy examination. Most students have high marks but some students will have low marks.