माध्य

In statistics, the mean is one of the measures of central tendency, other than the mode and median. Mean is the average of the given set of values. It denotes the equal distribution of values for a given data set. The mean, median and mode are the three commonly used measures of central tendency.

To calculate the mean, we need to add the total values given in a datasheet and divide the sum by the total number of values.

Definition

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Mean = Sum of all the observations / Total number of observations

Example:

What is the mean of 2, 4, 6, 8 and 10 ?

Mean = Sum of all the observations / Total number of observations

Mean = ${\frac {2+4+6+8+10}{5}}=6$

Mean Formula

The mean formula in statistics for a set is defined as the sum of the observations divided by the total number of observations. But the formula is different if the data is grouped (i.e., if the data is segregated as categories).

• Mean formula of grouped data Grouped data is a set of given data that has been bundled together in categories. For a mean of grouped data, a frequency distribution table is created, which shows the frequencies of the given data set. We can calculate the mean of the given data using the following methods:
  1. Direct Method
  2. Assumed Mean Method
  3. Step Deviation Method
• Mean formula of ungrouped data

Ungrouped data is the raw data gathered from an experiment or study. In other words, an ungrouped set of data is basically a list of numbers. To find the mean of ungrouped data, we simply calculate the sum of all collected observations and divide by the total number of the observations. Follow the below-given steps to find the mean of a given set of data,

1. Note down the given set of data whose mean is to be calculated.
2. Apply any of the following formulas based on the type of information available.
3. ${\frac {x_{1}+x_{2}+x_{3}+...+x_{n}}{n}}$ where $x_{1},x_{2},x_{3},...,x_{n}$ are $n$ observations.

Example: The heights of five students are $161,130,145,156,162$ inches respectively. Find the mean height of the students.

Solution: To find: the mean height of the students.

The heights of five students = $161,130,145,156,162$ inches (given)

Sum of the heights of five students = $(161+130+145+156+162)=754$

Using mean formula,

The mean height of the students is $150.8$ inches. सांख्यिकी में, बहुलक और माध्यिका के अलावा, माध्य केंद्रीय प्रवृत्ति के मापों में से एक है। माध्य दिए गए मानों के समुच्चय का औसत है। यह दिए गए दत्त(डेटा) समुच्चय के लिए मानों के समान वितरण को दर्शाता है। माध्य, माध्यिका और बहुलक केंद्रीय प्रवृत्ति के तीन सामान्यतः उपयोग किए जाने वाले माप हैं।

माध्य की गणना करने के लिए, हमें आंकड़ा पत्र (डेटाशीट) में दिए गए कुल मानों को जोड़ना होगा और योग को मानों की कुल संख्या से विभाजित करना होगा।

परिभाषा

माध्य दी गई संख्याओं का औसत है और इसकी गणना दी गई संख्याओं के योग को संख्याओं की कुल संख्या से विभाजित करके की जाती है।

माध्य = सभी प्रेक्षणों का योग / प्रेक्षणों की कुल संख्या

उदाहरण:

2, 4, 6, 8 और 10 का माध्य क्या है?

माध्य = सभी प्रेक्षणों का योग / प्रेक्षणों की कुल संख्या

माध्य = ${\frac {2+4+6+8+10}{5}}=6$