Statistics

# What Is Symmetrical Distribution?

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## What Is Symmetrical Distribution?

A distribution is symmetrical if its two halves are mirror images of each other. This symmetry can be visualized by drawing a line down the middle of the distribution and looking at how the data on either side of the line resembles one another.

In a perfectly symmetrical distribution, every number would be the same on both sides of the line. However, in practice, most distributions are only partially symmetrical. This means that they have some symmetry but are not enough to be perfectly balanced.

There are a few reasons why a distribution might be symmetrical. One possibility is that the data was generated randomly. This could happen, for example, if you tossed a coin several times and recorded the results. Another option is that the data was developed by a process that is symmetrical. This could be, for example, the growth of a plant or the movement of water in a river.

There are also a few reasons why a distribution might not be symmetrical. One possibility is that the data was generated randomly but with some bias. This could happen, for example, if you repeatedly tossed a coin but only recorded the results when it came up heads. Another possibility is that the data was generated by a process that is not symmetrical in nature. This could be, for example, the growth of a tumor or the movement of traffic on a highway.

Whatever the cause, symmetrical distributions are interesting to study because they can tell us a lot about the underlying process that generated the data. In particular, they can help us to identify any patterns or biases that might be present.

## What is an example of symmetrical distribution?

One example of symmetrical distribution is the result of tossing a coin several times. If you throw a coin enough times, you will get a distribution that is symmetrical because it is generated randomly.

Another example is the growth of a plant. Plants grow in a symmetrical manner because they respond to environmental cues that are symmetrical in nature.

Finally, traffic on a highway can be thought of as symmetrical distribution because the movement of cars is governed by a set of rules that are symmetrical in nature.

## Symmetrical Distribution vs Skewed Distribution

A distribution is skewed if its two halves are not mirrored images of each other. This symmetry can be visualized by drawing a line down the middle of the distribution and looking at how the data on either side of the line differs from one another. In a perfectly symmetrical distribution, every number would be exactly the same on both sides of the line. However, in practice, most distributions are only partially symmetrical. This means that they have some symmetry but are not enough to be perfectly balanced.

There are a few reasons why a distribution might be skewed. One possibility is that the data was generated randomly but with some bias. This could happen, for example, if you repeatedly tossed a coin but only recorded the results when it came up heads. Another possibility is that the data was generated by a process that is not symmetrical in nature. This could be, for example, the growth of a tumor or the movement of traffic on a highway.

Whatever the cause, skewed distributions are interesting to study because they can tell us a lot about the underlying process that generated the data. In particular, they can help us to identify any patterns or biases that might be present.

## What is an example of a skewed distribution?

One example of a skewed distribution is the result of tossing a coin several times. If you toss a coin enough times, you will get a distribution that is skewed because it is generated randomly with a bias.

Another example is the growth of a tumor. Tumors grow in an asymmetrical manner because they respond to environmental cues that are asymmetrical in nature.

Finally, traffic on a highway can be thought of as a skewed distribution because the movement of cars is not governed by a set of rules that are symmetrical in nature.

## Symmetrical Distribution Quiz

What Is Symmetrical Distribution?

• A distribution is asymmetrical if its two halves are mirror images of each other
• A distribution is symmetrical if its two halves are not mirrored images of each other
• A distribution is symmetrical if its two halves are mirror images of each other
• A distribution is asymmetrical if its two halves are not mirrored images of each other

The empirical rule generally can be applied to…

• Bell-shaped distribution.
• Any distribution.
• Only continuous distribution.
• Any skewed distribution.

Symmetrical distribution will always have skewness equal to…

• Negative
• Positive
• Zero
• Approximately zero

For a normal distribution, the measure of Kurtosis equals to…

• Zero
• 3
• Positive number.
• Negative number

If the price of a kg of meat was Rs.40/- in 2000 and Rs.50/ in 2002, the simple price relative in…

• 125
• 100
• 80
• 50

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