An average of statistical data is the value which is representative of the entire data. An average represents the entire data, its value lies somewhere in between two extremes. For this reason, statistics average is called Measure of Central Tendency. Now we discuss how we calculate statistical average: |

We have several types of statistics mean or Averages for several types of data Sets.

Arithmetic mean (AM):

It is also known as standard average. Its general formula is

K = 1 / n * ∑ (i = I to n) a

_{i}

Suppose we have small number of students, some are tall while majority of them is small in height. Since the majorities are small in height therefore the mean definitely come lower than the middle value.

For example: The arithmetic mean or statistical mean of 5 values is

(5 +10+15+20+25)/5 = 75/5 = 15

Geometric Mean:

The Geometric mean is the standard average of the data sets identified by their product not by their sum. Example: Growth Rate

The general formula of geometric mean

K = (∏ (i = 1 to n) ai)

^{1 / n}

For example the geometric mean of 6 values is

(1 * 2 * 3 * 4 * 5 * 6)

^{1 / 6}= 17

Hence 17 is the geometric mean of the above data set.

Harmonic Mean:

The harmonic mean is the average of data sets which are in relation to some unit. Example: Volume

The general formula of harmonic mean is

K = n * (∑ (I = 1 to n) 1/ai )

^{-1}

This was a brief description about mean statistics.

We say that mid-range in Statistics is the midway Point between the minimum and the maximum in a Set of data. It is calculated as: midrange = (maximum + minimum) / 2.

For any set of numerical data, we say that the mid range in statistics of the given data is the Arithmetic. Mid-range is the mid – extreme of the set of statistical data values. It is the arithmetical Mean of the maximum and the minimum values that exist in the data set. It only deals with the outer liners of the given data and does not deal with the data inside. If the largest value and the lowest value in the data are same, it results to zero. So in such cases it cannot be used in Data Analysis. The mid-range is very commonly used to estimate the values between given two values. It is a Measure of Central Tendency. In order to reduce the chances of choosing and selecting wrong figures from the large data in the formula, we should always first try to arrange the data in ascending or descending order and then proceed for calculating midrange statistics for the data.

In mathematics or Statistics, median is defined as the value separating the data Set or the Probability distribution into two halves, lower half and upper half. The median in statistics can be determined by placing all the Numbers in increasing order and picking up the middle value. If the number of values are even than the median is defined by the arithmetic Mean of the two middle values. The median in statistics is basically used in population evaluation and probability. It is not necessary that the statistics median should be present in the data set. It may also happen that the median value may exist in the data set for one or more than one time.

Suppose we have set (p, q, r) where p < q < r then the median is ‘q’ but if we have a set (p, q, r, s) where p < q < r < s then the median is mean of ‘q’ and ‘r’. The median statistics helps in minimizing the deviation of the Arithmetic Mean. The median of the following set 3, 2, 2, 2, 1, 13 is 2.

Here the median value 2 will minimize the mean of absolute deviation (1, 0, 0, 0, 1, 11) is 2.3. Thus we can generalize median statistics as a value which minimizes the value of ‘m’. E |K - m| is a median of variable ‘K’. The value of the median ‘m’ may not be properly defined, it may also happen that the median is not even defined.

While studying Statistics Mean, median and mode are the Basic Terms used in the statistics sampling of data. Mean is used to find the Average of the given data, Median is used to find the mid value of the given data and mode in statistics is used to find the value of the most occurring value in the given data.

Literal meaning of mode statistics is the most occurring value, which means to find the number in the given collection of data which is occurring maximum number of times. It can also be said as the data with highest frequency is called statistical mode.

To find the mode of the given data, we will first arrange the data in ascending order and then find the frequency of all the collected data. The data with the highest frequency will be called the mode. Example: find the mode of the given ages of the teachers in the school: 29, 35, 43, 28, 36,41, 35, 41, 35, 29, 30, 35

Now we first arrange the data in ascending order and get

28, 29, 29, 30, 35, 35, 35, 35, 36, 41, 41, 43

Here the frequency of 35 is maximum as 35 occurs 4 times. So we can say that 35 is the most occurring age.

So the mode is 35.