## Story

*
It was a Saturday
A family of the Dad, Mom, Daughter, Son
The two children are in middle school.
The Dad and Mom were reviewing the notes of their children
The children were reading books.
All of them were in the living room at home.
*

**Dad:** Elijah

**Son:** Yes, Dad

**Dad:** Esther

**Daughter:** Yes, Dad

**Dad:** A philanthropist wanted to buy shoes for the motherless and fatherless children at an orphanage.

There were $300$ children at the orphanage.

He arrived at the orphanage and asked for a shoe size.

What shoe size should the director recommend?

**Son:** He asked for just a shoe size...

Rather than shoe sizes?

**Dad:** Yes. Do you not think it is cumbersome to ask for the shoe sizes of $300$ children?

**Son:** But, if he really wanted to help, why would he not help "all" of them?

Typically, all of them would not have the same shoe size.

So, why not just make everyone happy by providing each one with the shoe that fits him/her?

**Dad:** I understand.

But, let's assume he just wanted a shoe size.

What shoe size should the director give?

**Son:** But, Dad; why would he want to do that?

**Dad:** Answering questions with questions...typical of a *Nigerian*

Just answer my question or say you do not know the answer.

Rather than answering it with a question

**Son:** I have your gene, Dad ☺

**Dad:** Whatever...

But, I want you to think about it... while I ask your sister

Esther, what shoe size would the director recommend?

**Daughter:** I think Elijah made a point.

Why would the philanthropist choose to buy shoes of only one size?

One size certainly does not fit all.

**Mom:** Listen my children.

Your Dad is indirectly asking you about what you learned in school last week.

He wants you to see the connection/application of what you learned.

**Daughter:** Okay, Mom. I get it.

The director can measure the shoe sizes of the $300$ children.

Find the sum.

And divide by $300$

That is known as the **Mean or Average**

**Dad:** Correct! Proud of you, Daddy's girl! ☺

**Son:** The second way would be the arrange all those measured shoe sizes in order ...

Preferably in ascending order

Because it is an even sample size, there would be two sizes in the middle.

So, find the average of those two sizes.

That measure is the **Median**

**Mom:** Perfect! Mummy's boy! ☺

But, why would you arrange the sizes in ascending order?

What about descending order?

Would it not give the same result?

**Daughter:** Mom, guess what? ☺

That was the same question Elijah asked Mr. C in the class ☺

**Mom:** What did he say?

**Son:** He said that it is normal to start from the kindergarten up to the $12^{th}$ grade...

Rather than from the $12^{th}$ grade to the kindergarten

**Dad:** Wow, that is an "okay" answer. Is that the only reason?

**Daughter:** He also said that when we study the **Quartiles**, we must have to arrange it
in ascending order.

So, it is better to just learn to arrange the data in ascending order.

**Dad:** That is correct.

What other ways do we have?

**Daughter:** The director can find the most popular shoe size

**Dad:** What do you mean by "most popular"?

**Daughter:** By "most popular", I mean the shoe size that most of the children wear

**Dad:** Okay, but I am looking for a term... a statistics term...

**Son:** It means the shoe size with the highest frequency.

**Dad:** and the measure is called the ...

**Daughter:** **Mode**

**Dad:** Wow, my children are wonderful! Thank GOD!

**Mom:** Our children...

**Dad:** Yes, GOD gave us intelligent children.

**Mom:** What is the remaining measure of center?

**Son:** It's my turn this time.

The fourth measure is the **Midrange**

The director can take the average of the minimum shoe size and the maximum shoe size.

**Mom and Dad:** That is correct!

**Dad:** These are called the **Measures of Center**

**Mom:** or the **Measures of Central Tendency**

**Dad:** because they tend towards the "center" of the data set

**Mom:** and the center is seen as a representative of the whole.

**Dad:** The mean or average is the most used.

Although each of these measure has it's advantages and disadvantages

**Mom:** The midrange is also an average.

**Dad:** And if the sample size is an even number, the median is also an average.

**Daughter:** Thank You, Dad! Thank You, Mom!

**Son:** Thank You, Mom! Thank You, Dad!

**Dad and Mom:** You are most welcome!!!