In the process of studying mathematics, students get acquainted with the concept of the arithmetic mean. In the future, in statistics and some other sciences, students are faced with the calculation of others. What can they be and how do they differ from each other?
Averages: Meaning and Differences
Not always accurate indicators give an understanding of the situation. In order to assess this or that situation, it is sometimes necessary to analyze a huge number of figures. And then averages come to the rescue. They allow you to assess the situation in general.
Because the mean is heavily affected by data skewers and outliers, the median is the preferred measure of central tendency for a skewed distribution. For example, it is generally accepted that the median is better than the average for calculating a typical salary. The best way understand it from an example. Please see a few typical salaries for regular jobs.
Well, in this particular case, the means and medians give the same numbers. Agree, the median gives a better idea of what people usually earn, because it is not affected so much by abnormal salaries. There are several ways to get the mean or the average of the data set.
Since school days, many adults remember the existence of the arithmetic mean. It is very easy to calculate - the sum of a sequence of n terms is divisible by n. That is, if you need to calculate the arithmetic mean in the sequence of values 27, 22, 34 and 37, then you need to solve the expression (27 + 22 + 34 + 37) / 4, since 4 values \u200b\u200bare used in the calculations. In this case, the desired value will be equal to 30.
The mean for a particular column can be retrieved by selecting "Statistics: Descriptive Statistics: Column Statistics" from the "Origin" menu. The average value for each selected column is placed in a separate cell in the "Average" column. To get the average of a number of rows of data in a worksheet, select Statistics: Descriptive Statistics: Row Statistics.
Mean value using mean function
Average value for a piece of data
You can get statistics for a selected part of a line, line symbol, scatter, or column using the statistics gadget. The average amount of data for a group of data. Keywords: simple math, descriptive statistics, mean, column statistics, row statistics, averaging curves.Often, as part of the school course, the geometric mean is also studied. The calculation of this value is based on extracting the root of the nth degree from the product of n terms. If we take the same numbers: 27, 22, 34 and 37, then the result of the calculations will be 29.4.
The harmonic mean in a general education school is usually not the subject of study. However, it is used quite often. This value is the reciprocal of the arithmetic mean and is calculated as a quotient of n - the number of values and the sum 1/a 1 +1/a 2 +...+1/a n . If we again take the same for calculation, then the harmonic will be 29.6.
Step 3: Press the "Enter" key to display the average value. Choose a place to withdraw. Most statistics teachers recommend a graphing calculator for statistics. Watch the video or read the next steps. Enter data in one column.
Enter one number per cell. Step 3: Change the range in step 2 to reflect the actual data. When calculating the average annual earnings per share, you need to know the starting price, the ending price, the dividends paid, and the duration for which the share was held. You can calculate the price manually, or you can use the program spreadsheets to customize the formula. This allows you to fiddle around with the data so you can see how small changes can make a difference.
Weighted Average: Features
However, all of the above values may not be used everywhere. For example, in statistics, when calculating some, the "weight" of each number used in calculations plays an important role. The results are more revealing and correct because they take into account more information. This group of values is collectively referred to as the "weighted average". They are not passed at school, so it is worth dwelling on them in more detail.
If you have held shares for 3 years, enter. But it has certain features - one who does not respect them easily gets the wrong result. Below you will learn how to avoid mistakes and how to easily calculate weighted averages using a matrix formula.
Calculate the arithmetic mean
Text, truth values, or empty cells are ignored. Figure 1 illustrates this with an example. The semi-annual analysis table shown on the left contains the relevant cost values.
Maintain zero value
Example 2 contains the same values as in example 1, with the difference that zero has been entered here for the missing June value.First of all, it is worth explaining what is meant by the "weight" of a particular value. The easiest way to explain this is to specific example. The body temperature of each patient is measured twice a day in the hospital. Of the 100 patients in different departments of the hospital, 44 will have a normal temperature - 36.6 degrees. Another 30 will have an increased value - 37.2, 14 - 38, 7 - 38.5, 3 - 39, and the remaining two - 40. And if we take the arithmetic mean, then this value in general for the hospital will be over 38 degrees! But almost half of the patients have absolutely And here it would be more correct to use the weighted average, and the "weight" of each value will be the number of people. In this case, the result of the calculation will be 37.25 degrees. The difference is obvious.
You want to calculate the average, highest, and lowest sales for an estimate. First, click the cell where you want the result to appear and click the arrow on the Start button in the Edit group. Select Average, Max. Or Min.
How to find the arithmetic mean in Excel
This can lead to undesirable results in some calculations. Therefore, you must select cells that are relevant to this function. Apply these features now. To complete the following steps, open the workbook. Click the button with the arrow next to it.
In the case of weighted average calculations, the "weight" can be taken as the number of shipments, the number of people working on a given day, in general, anything that can be measured and affect the final result.
Varieties
The weighted average corresponds to the arithmetic average discussed at the beginning of the article. However, the first value, as already mentioned, also takes into account the weight of each number used in the calculations. In addition, there are also weighted geometric and harmonic values.
Arithmetic mean for an interval series
Click the button with the arrow next to it again. Now your result will look like this. If you want to compare your results with a sample solution, open the book. To do this, open the book. Compare the results with the file. If it's just two numbers, almost everyone in their head can calculate the average.
Calculation of the average value by condition
These situations involve calculating an average. The corresponding formula is actually simple. The sum is added from all values, which are then divided by the number of values. So if there were 20 students on Mondays, 26 on Tuesdays, and only 14 on Wednesdays, then the sum is 60, and since there are three values, it's divisible by three. We calculate this as an average of 20 students per lesson.
There is another interesting variety used in series of numbers. This is a weighted moving average. It is on its basis that trends are calculated. In addition to the values themselves and their weight, periodicity is also used there. And when calculating the average value at some point in time, values for previous time periods are also taken into account.
The result can be displayed in another cell. All you have to do is enter the values first. Then select the target cell and click on it. Now we can enter the corresponding function above or select it. We do it manually. So, source cell, colon, end cell. . This can also be done with a few mouse clicks.
- Select the target cell again.
- Click on the function symbol.
- Here you can enter the start and end cell values again.
Calculating all these values is not that difficult, but in practice, only the usual weighted average is usually used.
Calculation methods
In the age of computerization, there is no need to manually calculate the weighted average. However, it would be useful to know the calculation formula so that you can check and, if necessary, correct the results obtained.
Arithmetic weighted average
The classic example for calculating weighted averages is school notes made up of oral and written grades. For example, 60% of the oral grade could be included in the total score, while the written test was 40%. Written work can again be assessed differently - approximately 10 percent for the first test and 15 percent for the second and third.
You have entered descriptions and weights in two rows of the table. Below you enter the grades you gave the students in the tests and in the whirlpool. The normal, unweighted average in this case is "2.5", i.e. in the overall ranking at best 2 if not 3. The weighted average is the overall score of "1.7". And how do you calculate this weighted average? First, you must multiply the individual values by the appropriate weights. The sum is then divided by the sum of all weight fractions. In the case of weight proportions that generally lead to 100%, this division is not entirely clear.
It will be easiest to consider the calculation on a specific example.
It is necessary to find out what is the average wage at this enterprise, taking into account the number of workers receiving a particular salary.
So, the calculation of the weighted average is carried out using the following formula:
x = (a 1 *w 1 +a 2 *w 2 +...+a n *w n)/(w 1 +w 2 +...+w n)
For example, the calculation would be:
Through the use of absolute and relative references, this formula can be easily copied down to calculate total scores for other students. Now you would like to know how much you have paid on average per liter of fuel over time. Here it is important that you again divide the amount of product per liter and the amount of fuel by the total amount of fuel. Mean as mean and arithmetic mean is also used in terms of averages or averages. The table automatically calculates the values.
Standard deviation: formula in Excel
In the general case, the average value can be calculated by calculating from the sum of two numbers one more, which lies between the numbers. This can be done according to various procedures. This article explains the differences between arithmetic mean and median. After reading the post, you will understand why the arithmetic mean and median should always be considered in combination.
x = (32*20+33*35+34*14+40*6)/(20+35+14+6) = (640+1155+476+240)/75 = 33.48
Obviously, there is no particular difficulty in manually calculating the weighted average. The formula for calculating this value in one of the most popular applications with formulas - Excel - looks like the SUMPRODUCT (series of numbers; series of weights) / SUM (series of weights) function.
Arithmetic mean in excel. Excel spreadsheets, are the best suited for any calculations. Having studied Excel, you will be able to solve problems in chemistry, physics, mathematics, geometry, biology, statistics, economics and many others. We do not even think about what a powerful tool is on our computers, which means we do not use it to its full potential. Many parents think that a computer is just an expensive toy. But in vain! Of course, in order for the child to really study on it, you yourself need to learn how to work on it, and then teach the child. Well, this is another topic, but today I want to talk with you about how to find the arithmetic mean in Excel.
Mean
In other respects, the mean as well as the median are important metrics for evaluating the values of an observation. The mean in the classical sense is described as the arithmetic mean. The arithmetic mean is the sum of all observation values divided by the number of observations.
Mathematical formula for calculating the average value. The mean is often used to make general statements about the actual situation. In the example below, the question might be: “What do employees in the accounting department earn on average?”. In detail, department employees receive the following salary in €.
How to find the arithmetic mean in Excel
We have already talked about fast in Excel, and today we will talk about the arithmetic mean.
Select a cell C12 and with the help Function Wizards write in it the formula for calculating the arithmetic mean. To do this, on the Standard toolbar, click on the button - Inserting a Function −fx (in the picture above, the red arrow is on top). A dialog box will open Function Master .
Now we have come to the conclusion that colloquially all employees earn around €000. In fact, 7 employees earn significantly less than €000. However, an employee even earned more than twice €000. Therefore, the significance of the average arithmetic value must be supplemented by a second measure.
Why should you always consider the mean combined with the median?
- With the sum of the function, we can calculate the sum of salaries.
- With the feature number, we can calculate the number of salaries.
- Subsequently, the amount of salaries is divided by the number of salaries.
- Select in the field Categories — Statistical ;
- In field Select function: AVERAGE ;
- Click the button OK .
The following window will open Arguments and Functions .
The arithmetic mean also has a second drawback. In the case of skewed datasets, this does not necessarily reflect the position of the majority of the data. These disadvantages are similar to medians. Thus, the median is considered a "robust" measure. The median is the value in the middle of a size-ordered set of data. It divides the number of values into two equal halves. As a first step in calculating the median, unordered data is transferred to ordered data.
Defining a Recorded Record
This results in the following data from the above example. There are two ways to calculate the median depending on whether there is an even number or an odd number of values. For an even number of values, the median is the average of the two mean values. Mathematical median formula.
In field Number1 you will see the entry S2:S11- the program itself determined the range of cells for which it is necessary find the arithmetic mean.
Click the button OK and in the cell C12 the arithmetic mean of the scores will appear.
Median calculates an odd number
An example of the median number is attached. For an odd number of values, the median is the mean. Mathematical formula for this. Let's add the fifth value of the original example. The above rules are then applied to an even and odd number of values. The median function is easier to use. Thus, the median of the data series is automatically obtained without prior sorting.
How to calculate the average of a column, row, or individual cells
You can also calculate the arithmetic mean or median online. To do this, you insert the existing values into the table at the following link in the Median median tab. You will automatically get the calculated values. As an addendum, once again the median and value for the original question.
It turns out that calculating the arithmetic mean in excel is not at all difficult. And I was always afraid of any formulas. Eh, not at that time we studied.