Statistical Formula

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What is Meant by Statistics?

Let’s know what do is meant by statistics. Statistics is the study of the collection, analysis, interpretation, presentation, and organization of large data. The statistical theory defines a statistic as a function of the sample data where the function itself is independent of the sample’s distribution.

Therefore, Statistics is associated with collecting, classifying, arranging and presenting the numerical data related in some context. It also allows us to interpret many results from it and forecast many possibilities for further applications. Using statistics, we can find various measures of central tendencies and the deviation of different values from the center.

We already have discussed what is statistics. In this article, we are going to discuss median formula, mean formula, what is mean in statistics, what is median in maths, what is variance in statistics, mode formula in statistics, mean statistics formula.


Measures of Central Tendency:

The central tendency of any data set can be measured by any one of the following ways.

  • Mean

  • Median

  • Mode

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What is Mean in Statistics?

We can define mean as the sum of all the values of the variable divided by the total number of values.

Mean Statistics Formula = \[\frac{\text{sum of all elements}}{\text{Total number of elements}}\]

The importance of mean lies in its ability that mean can represent the whole dataset with a single value.


What is the Median in Maths?

The median of a set of data values can be defined as the middle value of the data set when all the values have been arranged in ascending order.  

Median is calculated as

Where n is equal to the number of values in the data. If the number of values in the data set is even ( can be divided by 2), then the median is known to be the average of the two middle values.

Median Formula = (\[\frac{n}{2}\])th observation for odd number of observations

So, if a set consists of an odd number of values, then the middle value will be the median of the set. On the other hand, if the set consists of an even number of sets, then the median will be the average of the two middle values.

Thus, the median may be used to separate a set of data into two parts. To find the median of a set, we need to arrange the elements of the set in increasing order. Then find the middle value.


Mode:

The mode of statistical data is the value of that variable which has the maximum frequency. There are various different uses of mean, the median mode in daily life.

For example, 5,6,4,5,8,5

The number 5 occurs 3 times(Maximum number of times) in the list, therefore the number 5 is the Mode.


Variance:

We may want to measure the deviation of a set of data from their mean value. The variance for any given particular dataset will always give a positive value. Variance can be used in the calculation of Standard Deviation, the concept of variance is a very important concept of statistics.


Standard Deviation:

The standard deviation is defined as the square rooting of the variance of the data.

Questions to be Solved:

Question 1: Find the mode of the set S = 1,2,3,3,3,3,3,4,4,4,5,5,6,7.

Solution: Here 3 occurs maximum 5 times. Therefore 3 is the mode.


Question 2: Find the mean, median, mode, and range for the following list of values given below:

13, 18, 13, 13, 13, 16, 14, 21, 13

The mean is known as the usual average, so we will add and then divide the sum by the number of elements:

(13 + 18 + 13 + 13 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 14.8

Note that the mean, in this case, does not occur as any value from the original list. 

You should not assume that the mean of the given numbers will be one of your original numbers on the list.

The median is the middle value in the original list of numbers.

To find the median first we have to rewrite the list in numerical order:

13, 13, 13, 13, 13, 14, 16, 18, 21

We know that there are nine numbers in the original list, so the middle one in the original list will be the (9)/ 2 = 9 /2  that gives 4.5 that is the 5th number:

13, 13, 13, 13, 13, 14, 16, 18, 21

So the median is 13.

The mode can be defined as the number that is repeated more often than any other, so 13 is the mode from the original list.

The largest value in the original list is 21, and the smallest value in the original list is 13, so the range we get is 21 – 13 = 8.

Mean of the list    = 14.8

Median of the list = 14

Mode of the list    = 13

Range of the list   = 8

Note: The formula for the place to find the median in the original list is equal to "([the number of data points in the original list] + 1) ÷ 2", but you don’t need the formula. You can just count in from both ends of the original list until you meet in the middle if you prefer, especially if your original list is short. Either way, it will work.

FAQ (Frequently Asked Questions)

Question 1: What are the Formulas of Statistics?

Answer: The symbol 'σ' represents the population standard deviation. The term 'sqrt' in Mathematics is used in this statistical formula denoting the square root. The term 'Σ ( Xi – μ )2' is generally used in the statistical formula so as to represent the sum of the squared deviations of the scores from their population mean.

Question 2: What is the Statistical Formula for Mean?

Answer: The formula to find the sample mean is: = ( Σ xi ) / n. All that formula is saying is to add up all of the numbers present in your data set ( Σ means “add up” and xi means “all the numbers in the data set).

Question 3: What is Mean Median and Mode in Statistics and What are the Applications of Central Tendency?

Answer: 'Mean, Median, and Mode' are the three different types of averages used in statistics. Mean is defined as the average, where we add numbers and simply divide by the total number of numbers. Median can be defined as the middle value in the list of data. The mode can be defined as the number that occurs most frequently. 

Here are the uses of central tendency -

  • Central tendency helps to compress a data set to a single value which represents all the values in the data. 

  • It, therefore, helps to work with a larger set of grouped or ungrouped data.