# How do you know if a graph is symmetric?

Space and AstronomyA graph is symmetric with respect to a line **if reflecting the graph over that line leaves the graph unchanged**. This line is called an axis of symmetry of the graph. A graph is symmetric with respect to the x-axis if whenever a point is on the graph the point is also on the graph.

## How can you tell if a graph is symmetric or asymmetric?

**A graph is said to be symmetric about the x -axis if whenever (a,b) is on the graph then so is (a,−b)** . Here is a sketch of a graph that is symmetric about the x -axis. A graph is said to be symmetric about the y -axis if whenever (a,b) is on the graph then so is (−a,b) .

## How do you determine if a function is symmetric?

For a function to be symmetrical about the origin, you must **replace y with (-y) and x with (-x) and the resulting function must be equal to the original function**. So there is no symmetry about the origin, and the credited answer is “symmetry about the y-axis”.

## How do you know if a graph is symmetric with respect to the origin?

Mathwords: Symmetric with Respect to the Origin. Describes a graph that looks the same upside down or right side up. Formally, a graph is symmetric with respect to the origin **if it is unchanged when reflected across both the x-axis and y-axis**.

## How do you check if a graph is symmetric about a line?

Video quote: *X-axis symmetry is that if you take the graph. And you fold it over the x-axis you're reflected over the x-axis. It will match up with itself so for example say for example your graph look like this.*

## How do you know if data is symmetric or skewed?

**A distribution is said to be symmetrical when the distribution on either side of the mean is a mirror image of the other**. In a symmetrical distribution, mean = median = mode. If a distribution is non-symmetrical, it is said to be skewed.

## What does symmetric graph mean in math?

A symmetric graph is **a graph that is both edge- and vertex-transitive** (Holton and Sheehan 1993, p. 209). However, care must be taken with this definition since arc-transitive or a 1-arc-transitive graphs are sometimes also known as symmetric graphs (Godsil and Royle 2001, p. 59).

## What is a symmetric bar graph?

A symmetric distribution is **one where the left and right hand sides of the distribution are roughly equally balanced around the mean**. The histogram below shows a typical symmetric distribution. For symmetric distributions, the mean is approximately equal to the median.

## What is an example of symmetric distribution?

**Standardized test scores** are an example of a symmetrical distribution. The mean, median, and mode of the data set will all occur at the same value.

## What does symmetrical data mean?

If the data are symmetric, **they have about the same shape on either side of the middle**. In other words, if you fold the histogram in half, it looks about the same on both sides. Histogram C in the figure shows an example of symmetric data. With symmetric data, the mean and median are close together.

## What is symmetry in statistics?

In statistics, a symmetric distribution is **a distribution in which the left and right sides mirror each other**. The most well-known symmetric distribution is the normal distribution, which has a distinct bell-shape.

## What does a symmetric dot plot look like?

Symmetric (bell shaped) – when graphed, **a vertical line drawn at the center will form mirror images, with the left half of the graph being the mirror image of the right half of the graph**. In the histogram and dot plot, this shape is referred to as being a “bell shape” or a “mound”.

## What are the rules of symmetry?

**If a graph does not change when reflected over a line or rotated around a point, the graph is symmetric with respect to that line or point**. The following graph is symmetric with respect to the x-axis (y = 0). Note that if (x, y) is a point on the graph, then (x, – y) is also a point on the graph.

## When a series is not symmetrical is called?

**Asymmetrical**. Step-by-step explanation: A distribution is asymmetric if it is not symmetric with zero skewness; in other words, it does not skew. An asymmetric distribution is either left-skewed or right-skewed. A left-skewed distribution, what is known as a negative distribution, has a longer left tail.

## How do you describe a symmetric distribution?

A symmetric distribution is **a type of distribution where the left side of the distribution mirrors the right side**. By definition, a symmetric distribution is never a skewed distribution.

## What is asymmetric data?

The term data asymmetry refers to **any occasion when there a disparity in access to data**. In all cases this results in the data steward being able to unlock more value than a contributor.

## Which of the following are characteristics of any symmetric distribution?

**Characteristics of symmetric distribution are:**

- In a symmetric distribution, the median, mean and mode are at the same position.
- The skewness or coefficient of skewness for a symmetric distribution will be zero.
- Symmetrical distribution originates if the values of variables occur at regular frequencies.

## What does it mean to say that the graph of the normal distribution is symmetric?

Normal distribution, also known as the Gaussian distribution, is a probability distribution that is symmetric about the mean, showing that **data near the mean are more frequent in occurrence than data far from the mean**. In graph form, normal distribution will appear as a bell curve.

## Why is my bell curve not symmetrical?

**Asymmetrical distribution occurs when the distribution of investment returns is not symmetric with zero skewness**. A negatively skewed distribution is known as left-skewed because it has a longer left tail on the graph. In contrast, a positively skewed distribution is called right-skewed and has a longer right tail.

## Is bell shaped the same as symmetrical?

A normal distribution is a true symmetric distribution of observed values. **When a histogram is constructed on values that are normally distributed, the shape of columns form a symmetrical bell shape**. This is why this distribution is also known as a ‘normal curve’ or ‘bell curve’.

## What is symmetric and bell shaped?

Video quote: *We haven't learned about it yet we won't learn about it till chapter 3. But it's called the normal distribution. So the shape is symmetric bell-shaped. But a specific distribution that has this*

## Which of the following is true for symmetric distribution?

When data is normally distributed, the mean, median and mode will all be the same: **mean = median = mode**.

## How do you tell if data is positively or negatively skewed?

Understanding Skewness

These taperings are known as “tails.” **Negative skew refers to a longer or fatter tail on the left side of the distribution, while positive skew refers to a longer or fatter tail on the right**. The mean of positively skewed data will be greater than the median.

## When each data class has the same frequency the distribution is symmetric True or false?

A data set can have the same mean, median, and mode. **When each data class has the same frequency, the distribution is symmetric**. false- …the distribution is UNIFORM.

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