Measures

Different Measure in Statistics

Measures of Central Tendency

Mean - Gives average/expected value of distribution. Mean may get disturbed in presence of outlier i.e. it may not be good measure of central tendency in presence of outliers.

Median - It is robust to outliers. Middle point when numbers are arranged in increasing order. It doesn't take every point into account when calculating.

Mode - Most frequent value in the data. Gives the most popular value or fashionable value. Like in a normal distribution is unimodal data as it has one peaks. Now if a distribution have two peaks i.e. two modes, it is called bimodal data. It is useful when you have large number of data points as it will have large number of popular values.

When $mean \neq median$ , data is said to be skewed. Otherwise it is said to have zero skew. Skewedness tells if data if data is symmetric around mean or not. If it is symmetric then $skew=0$ .

Measures of Spread

Range - $largest - smallest$ . Shows distance between two extremes. Takes only two extreme point in consideration hence less information is retained/used.

Interquartile Range (IQR)- Range spread in middle 50% of data.

Standard Deviation - Average amount we expect a point to differ(or deviate) from the mean. It takes every point in calculate

Mean and Variance are both EXPECTATIONS.

Variance Second Moment - The variance is the second moment, which can be used to tell how reliable the first expectation is. So if variance is high, we can say the mean which is first moment is not much reliable because data have large variance.

Skewness Third Moment - It is the measure of skewness in data. Skewness tell if there is more extreme values on one side of mean. If more values are smaller than mean then skewness is negative and positive for vice-versa.

Now Skewness(third momemnt) can be used to tell how reliable the variance is.

Kurtosis Fourth Moment - Tell how much the data resembles to a normal distribution.