Q: Is chi-square distribution symmetrical about mean value?

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The Mean is the average of a given set of values. The Median is the value that has the same number of smaller values than the number of higher values, it is in the middle of them. In a symmetrical distribution the Mean is equal to the Median. In an asymmetrical distribution they have different value.

The mode is the most probable value. Often, you determine the mode by plotting the experimental probability distribution, and finding the peak value. The mode is not necessarily the same as the mean nor the median, unless the distribution is symmetrical.

mean deviation is minimum

Your distribution is unimodal and symmetrical.

Skewness is a measure of the asymmetry in a distribution. In a non-symmetrical distribution, skewness can be calculated using a formula that considers the deviation of each data point from the mean. A positive skewness indicates a longer tail on the right side of the distribution, while a negative skewness indicates a longer tail on the left side.

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for symmetrical distributions your mean equals the median. that is one of the properties of the symmetrical distribution.

No they are not the same in a unimodal symmetrical distribution and they will never be

The Mean is the average of a given set of values. The Median is the value that has the same number of smaller values than the number of higher values, it is in the middle of them. In a symmetrical distribution the Mean is equal to the Median. In an asymmetrical distribution they have different value.

Yes, and they WILL be if the distribution is symmetrical.

The mode is the most probable value. Often, you determine the mode by plotting the experimental probability distribution, and finding the peak value. The mode is not necessarily the same as the mean nor the median, unless the distribution is symmetrical.

The median and mode.

mean deviation is minimum

Normal distribution is a perfectly symmetrical bell-shaped normal distribution. The bell curve is used to find the median, mean and mode of a function.

No. They are equal only if the distribution is symmetrical.

yes it is true

Your distribution is unimodal and symmetrical.

Generally, when the median is greater than the mean it is because the distribution is skewed to the left. This results in outliers or values further below the median than above the median which results in a lower mean value than median value. When a distribution is skewed left, it is generally not very symmetrical or normally distributed.