# Basic Statistics and Data Analysis

## Mode Measure of Central Tendency

The mode is the most frequent observation in the data set i.e. the value (number) that appears the most in data set. It is possible that there may be more than one mode or it may also be possible that there is no mode in a data set. Usually mode is used for categorical data (data belongs to nominal or ordinal scale) but it is not necessary. Mode can also be used for ordinal and ratio scale, but there should be some repeated value in the data set or data set can be classified in groups. If any of the data point don’t have same values (no repetition in data values) , then the mode of that data set will not exit or may not be meaningful. A data set having more than one mode is called multimode or multimodal.

Example 1: Consider the following data set showing the weight of child at age of 10 years: 33, 30, 23, 23, 32, 21, 23, 30, 30, 22, 25, 33, 23, 23, 25. We can found the mode by tabulating the given data in form of frequency distribution table, whose first column is the weight of child and second column is the number of times the weight appear in the data i.e frequency of the each weight in first column.

 Weight of 10 year child Frequency 22 1 23 5 25 2 30 3 32 1 33 2 Total 15

From above frequency distribution table we can easily found the most frequently occurring observation (data point), which will be the mode of data set. Therefore the mode of the given data set is 23, meaning that majority of the 10 year child have weight of 23kg. Note that for finding mode it is not necessary do make frequency distribution table, but it helps in finding the mode quickly and frequency table can also be used in further calculations such as percentage and cumulative percentage of each weight group.

Example 2: Consider we have information of person about his/her gender. Consider the M stands for male and F stands for Female. The sequence of person’s gender noted is as follows: F, F, M, F, F, M, M, M, M, F, M, F, M, F, M, M, M, F, F, M. The frequency distribution table of gender is

 Weight of 10 year child Frequency Male 11 Female 9 Total 25

The mode of gender data is male, showing that most frequent or majority of the people have male gender in this data set.

Mode can be found by simply sorting the data in ascending or descending order. Mode can also be found by counting the frequent value without sorting the data especially when data contains small number of observations, though it may be difficult in remembering the number of times which observation occurs. Note that mode is not affected by the extreme values (outliers or influential observations).

Mode is also a measure of central tendency, but the mode may not reflect the center of the data very well. For example the mean of data set in example 1, is 26.4kg while mode is of 23kg.

One should use mode measure of central tendency, if he/ she expect that data points will repeat or have some classification in it. For example in production process a product produced can be classified as defective or non-defective product. Similarly student grades can classified as A, B, C, D etc. For such kind of data one should use mode as a measure of central tendency instead of mean or median.

Example 3: Consider the following data. 3, 4, 7, 11, 15, 20, 23, 22, 26, 33, 25, 13. There is no mode of this data as each of the value occurs once. Grouping this data in some useful and meaningful form we can get mode of the data for example, the grouped frequency table is

 Group Values Frequency 0 to 9 3, 4, 7 3 10 to 19 11, 13, 15 3 20 to 29 20, 22, 23, 25, 26 5 30 to 39 33 1 Total 12

From this table, we cannot find the most appearing value, but we can say that “20 to 29” is the group in which most of the observations occur. We can say that this group contains the mode which can be found by using mode formula for grouped data.

# Measure of Central Tendency

What is a measure of central tendency and what are the common measures of central tendency? Also when is the median preferred over the mean?

A is the single numerical value considered most typical of the values of a quantitative variable. The most common measures of central tendency are the mode (i.e., the most frequently occurring number), the median (i.e., the middle point or fiftieth percentile), and the mean (i.e., the arithmetic average).

Median is preferred over the mean when the numbers are highly skewed (i.e., non-normally distributed).

# Basics Statistics

The two general rules are

1. If the mean is less than the median, the data are skewed to the left, and
2. If the mean is greater than the median, the data are skewed to the right.

Therefore, if the mean is much greater than the median the data are probably skewed to the right.