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Average and Mean 

 

Average

The average is a numerical figure representing a vast amount of data. A classic example of average is, it is useful in assessing the performance of a class on a specific topic. The average value of a set is the sum of the values divided by the total number of respective values. In cases where values change, an average is also utilized. Deciding based on a single data or a huge number of data is sometimes challenging. The average value is therefore determined, and it allows all values to be represented in one value.

Application of Average

  • To figure out the future weather conditions of a place, the temperature values over a period of time are averaged. This is beneficial for conducting outdoor events like cricket matches and sports days.
  • Average is used to determine the salary of all the employees working in a particular company.
  • The age of various students is averaged to set the bar for the age limit for various competitive and home examinations.

Formula:

Average is the arithmetical mean; in simple terms, it is the summation of magnitudes of all items present in a collection to the number of items present in that particular collection.

Average = Summation of all items in a collection/ Total number of items

Steps to calculate Average

  • Counting the number of items: The first and foremost step is counting how many data items have been provided in the problem.
  • Adding the data: Next, perform basic arithmetic addition on all the data points provided.
  • Applying formula: The final values from steps one and two are substituted in the formula, and basic division is performed to find the average.

Mean

An average of two or more data items is defined as a mathematical average, known as Mean. It is used mostly in statistics and applies to any geometric distribution, binomial distribution, Poisson distribution, etc. In a more scientific and statistical meaning, mean is employed. The mean definition of a particular data set is the average for a certain number of data set. This is the sum of all data values divided by the total number of data values in any given data collection. There are three types of mean, namely Arithmetic mean, Geometric mean, and Harmonic mean.

Applications of Mean:

  • Mean along with the Mode and Median is used to measure the central tendency for a given set of data.
  • Mean is an active component in a probability distribution. Mean is measured by deducting the product of every value and probability, and then combining all these products in a probability distribution.
  • The root mean square or RMS value is beneficial to engineering and scientific studies involving negative terms in the collection.

Formula:

Similar to the formula of Average, the mean is calculated with the help of the formula mentioned below:

Mean = Summation of the provided data/ total amount of data

Mean is represented by the symbol containing the bar above it. For example, x̄.

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