Question

Define the mean, median, and mode. Identify the strengths and weaknesses of each.

I know the definitions of each but I am having a hard to putting them into words not from "google"

i am needing help defining them without using google. i know what they are but am havubg trouble putting into words

Answer 1

Mean

It is defined as the sum of all observations divided by the number of observations. It is a measure of central tendency which balances the data.

Strengths:

Most commonly used statistic because it is calculated by using all the observations.

No matter which distribution does the data X belong, but the sample mean is always normally distributed for large sample sizes ( n> 30 ).

It is used to obtain the standard deviation, the most common measure of dispersion.

Weakness:

Mean is sensitive to extreme values. Especially when sample size is small.

Sometimes mean is a value which does not even appear in the data.

Median

Median is the center most observation of the dataset.

Strengths:

Not affected by extreme values as it focusses only on the center.

It is easy to compute and comprehend.

Weakness:

The calculation of median does not take in to account all values of the data, hence not a good representation of the entire dataset.

Not useful for further mathematical calculation, hence not used in statistical tests generally.

For even no. Of observations, median is the average of two middlemost data values, which results in a value that does not really belong to the dataset.

Mode

Mode is the data point which occurs most frequently in the dataset.

Strengths:

Easy to calculate.

It is the only measure of central tendency, that can be used for data measured in a nominal scale.

Not affected by extreme values or outliers.

Weakness:

Does not take in to account all the datasets for its calculation, hence not a good representation of the dataset.

Not used for further statistical analysis