**Ages of all the people at some league game.****No. of siblings of 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 theÂ **different statistical properties of data**. For example, whether the data isÂ **uniform, uni-modal or bi-modal,Â **whetherÂ **symmetric or skewed,**Â etc.

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

If the n**egative and positive tails**Â of the distribution are ofÂ **equal length**, then the data is said to beÂ **symmetric.**Â If they areÂ **not equal**,Â it’s calledÂ **skewed**.

## Expert Answer

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

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

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

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

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

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

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

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

## Numerical Result

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

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

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

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

## Example

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

We know that there areÂ **two distinct types of adult humans**Â with different average heights i.e. men and women. Therefore the distribution would haveÂ **two distinct peaks**Â and the data would beÂ **bimodal**. There is anÂ **equal likelihood**Â that the height of a man or a woman may fall below or above their respective average heights, so the data distribution would also beÂ **symmetric**.