**– Ages of all the people at some league game.**

**– No. of siblings all of your classmates**

**– Heart rates of college-age male students**

**– No. of times each face shows up in a hundred tosses of a die**

The aim of this question is to understand the **different statistical properties of data**.

For example, whether the data is **uniform, uni-modal or bi-modal, **whether **symmetric or skewed,** etc.

When a **distribution of data is plotted**, its peak represents the average value of that sample. **If there is only one peak** (average value), then the distribution is called **unimodal**. **If there are two distinct peaks**, then the distribution is called **bimodal**. If there is **no distinct peak** and all data values are equally likely, then the distribution is called **uniform**.

If the n**egative and positive tails** of the distribution are of **equal length**, then the data is said to be **symmetric.** If they are **not equal**, it’s called **skewed**.

## Expert Answer

Part (a): **Ages of all the people at some league game.**

Since a league game may be attended by people from all age groups with **equal likelihood**, we can conclude that their ages will form a **uniform distribution**. By definition, **all uniform distributions are symmetric**, so their ages will also be symmetric.

Part (b):** No. of siblings all of your classmates**

Most people have zero, one, or two siblings. Therefore **we could expect one clear peak** for the distribution of no. of siblings in any population group. Therefore it’s **uni-modal**. Also, we can note that the **tail of this distribution is more extended** towards the higher no. of siblings compared to the lower ones, so this distribution is also **skewed**.

Part (c): **Heart rates of college-age male students**

All heart rate values will **vary around some average value**, so we can expect **a single clear peak**. Therefore, the distribution is **uni-modal**. Since there is an equal likelihood of heart rate falling slightly below or above this average value, the distribution is also **symmetric**.

Part (d):** No. of times each face shows up in a hundred tosses of a die**

If the die is fair, every face has an **equal likelihood** of showing up, so the distribution will be **uniform and symmetric**.

## Numerical Result

– The distribution of **ages of all the people at some league game** would be **uniform and symmetric.**

– The distribution of n**o. of siblings of all of your classmates** would be **uni-modal and skewed**.

– The distribution of **heart rates of college-age male students** would be **uni-modal and symmetric.**

– The distribution of **no. of times each face shows up** in a hundred tosses of a die would be **uniform and symmetric.**

## Example

Would you expect the distribution of **heights of adult humans** to be uniform, unimodal, bimodal, symmetric, or skewed?

We know that there are **two distinct types of adult humans** with different average heights i.e. men and women. Therefore the distribution would have **two distinct peaks** and the data would be **bimodal**. There is an **equal likelihood** that the height of a man or a woman may fall below or above their respective average heights. So the data distribution would also be **symmetric**.