Measures of Central Tendency are statistical methods that summarize data by identifying a central point within that dataset. Common measures include Arithmetic Mean, Median, and Mode.

Arithmetic Mean is the sum of all observations divided by the number of observations. It is usually denoted by X and calculated as X = ΣX / N.

The Median is the middle value in a dataset sorted in ascending order. For N items, if N is odd, it's the (N+1)/2 th item; if N is even, it's the average of the N/2 th and (N/2 + 1) th items.

Mode is the value that appears most frequently in a dataset. A dataset may have one mode (unimodal), more than one mode (bimodal or multimodal), or no mode.

The Median is preferred when data has outliers or is skewed, as it is not affected by extreme values, unlike the Mean.

For grouped data, use the formula: X = ΣfX / Σf, where f is frequency and X is the value of observations.

Choose an assumed mean, calculate deviations from it, find their sum, and then estimate the true mean as: X = A + (Σd/N).

It simplifies calculations by dividing deviations from the assumed mean by a common factor. The formula is X = A + (Σfd'/Σf) * c.

An outlier is a data point that differs significantly from other observations in a dataset. It can skew the Mean, making the Median a more reliable measure.

Median is a positional value separating the higher half from the lower half, while Mode is the most frequently occurring value in a dataset.

A Discrete Series consists of distinct values or observations, often represented in a frequency distribution.

A Continuous Series consists of data divided into intervals or ranges, with class intervals used to calculate averages.

To calculate the median: Identify the cumulative frequency, find the class interval where the median lies, and use interpolation if necessary.

Typically, Me > Mi > Mo in a positively skewed distribution and Me < Mi < Mo in a negatively skewed distribution.

It is simple to calculate and incorporates all data points, providing a balanced central value.

For incomes of Rs 1600, 1500, 1400, 1525, 1625, and 1630, the Mean is (1600+1500+1400+1525+1625+1630)/6 = Rs 1547.

The median remains unaffected by outliers, providing a better central tendency indicator in skewed datasets.

Mode is used for categorical data or when identifying the most frequent occurrences is necessary.