Formula and Execution

Average

It is the central value of the data that gives a picture of the whole data.

Formula: Average = (Sum of All Quantities/Total No of Quantities)

This formula is used to calculate the average of the data. Our online average calculator works with this formula. You simply have to substitute individual values in the sections named as #1, #2, #3,… in our calculator. Like, write your first value in #1, press tab, write your second value in #2, and carry further in this way. You can write up to 30 values. The calculator assumes the total numbers itself and gives you instant results.

Average Calculator

Whether you want to know if your average performance got any better from your last exam, or you want to know your dog’s favorite food, or you are just keen to know the average height of students in your class, all the things fall in the category of averages. However, the method used to arrive at the results may differ.

The mean, which is usually known as the average, in general, is calculated by our online average calculator.

Our simple to use online average calculator makes sure to provide you precise results for up to 3o values.

 

How to Calculate Average Using Calculator Beast’s Online Average Calculator

Using our online average calculator is as easy as ABC. It’s a snap! The average is simply the ratio of the sum of all the individual values of the data to the number of values of the data.

Our online average calculator can compute the average of 30 values in total. Just substitute the individual values in individual sections, our calculator depicts the total quantity itself and gives you results as quick as lightning.

The more you keep on inserting the values, the more you will see the result change.

Consider an example of the data consisting of Jim’s marks out of 100 in his individual subjects.

EnglishFrenchMathScienceGeography
8275889579

These are five subjects, so their average can be written as: (82+75+88+95+79)/5 = 419/5 = 83.8

The above calculations can be performed easily by our online average calculator. Just substitute the values individually in each section and get instant results. A screenshot can help you see the convenience of our calculator.

 

Concept of Average

The mean or the average is the most popular kind of average that is used to calculate a central value of the data. The average falls in the category of measures of central tendency in statistics. These measures are used to find out an estimated middle value of the data, around which the data fluctuates.

Like in the example provided above, the average of the marks calculated was 83.8, which means that Jim’s marks circles the value of 83.8, and his performance is estimated to 83.6%.

 

Formula for Average

Calculating the average is no rocket science. You just need to add up all the quantities and divide it by the total number of quantities to get the average. Mathematically it is written as,

 

X_bar = x1 + x2 + … + xn/n = 1/n Σxi

 

Where X_bar represents the average, n is the number of values in the data set, xi represents the individual values of the data, and Σ is the Greek letter sigma, and it is used for summing up all the quantities.

 

Example:

The number of bus passengers traveling on a certain route was recorded for 2 weeks, as shown below.

 

42, 45, 39, 41, 38, 37, 38, 43, 40, 36, 35, 32, 38, 36

Find the mean number of passengers

 

Solution:

To calculate the mean of the above data, we use the following formula:

 

Average = sum of values/number of values

Average = (42+ 45+ 39+ 41+ 38+ 37+ 38+ 43+ 40+ 36+ 35+ 32+38+ 36)/(14)

Average = 540/14 = 38.571 ≈ 39

 

Since the number of passengers cannot be in fraction form, we can round-off the value to the nearest whole figure to get the estimated number of passengers that travel each day.

The above problem took you some time to calculate it manually. With our user-friendly calculator, you just need to substitute the values in their respective sections to get quick results.

 

FAQs

1. What are the kinds of averages?

The kinds of averages vary for their uses. Different averages are used for different purposes. These averages are usually used for calculating a middle value of the data around with the data resonates.

 

  • The mean or average is the most common type of average that is calculated by summing up all the quantities of the data and dividing them by the total number of quantities as you saw above.
  • The median is the second popular kind of average that is the middle value of the set of values when they arranged in ascending order.
  • The mode is the most frequently occurred value of the data.
  • The range is the difference between the extreme values of the data i.e., the difference of the maximum and minimum value of the set of values.
  • And the mid-range is the arithmetic mean of the largest and the smallest values of any set.

 

2. What kind of average is appropriate for what kind of data?

The averages, mean, median, and mode, also known as the measures of central tendency are used widely in our daily life. Their usage is common from a normal household to calculating the statistics of this mighty earth. They give us an estimate of the value of a very large data.

All the averages, though, give us a measure of the central value of the data, their usage varies from data to data.

The mean is usually used when the data is symmetric, or in other words, the data is evenly spread and does not have any extreme values. Like if you want to calculate the average money you spend on food every month, you will go for mean as your average because all the values of data would be lying close to a single value.

The median, on the other hand, is good with handling the data, which has extreme values. Like if a firm wishes to calculate the average salary of their employees, they would use the median to find the average because their data contains extreme values. A janitor’s salary would be a lot lesser than the salary of their director. While most of the employees’ salary would lie between the two extremes. So the best average to be used here is the median.

The mode is used for the nominal data. This can be understood by the example that if an ice-cream parlor wants to know of the flavor which is most liked by their customers, they will use mode to find the average, as it is the most repeated value of the data.

 

3. What are the properties of the mean?

Some of the properties of the mean are:

  • Mean uses all the values of the set of data.
  • Mean gives the closest central value of the data when all three averages i.e., mean, median, and mode, are computed.
  • Median and mode are values from the data, while the mean is unique and not necessarily a value from the data.
  • The sum of differences between the individual values of data and the mean of the data is always zero. Suppose, mean of a data is (x_bar) and the individual values are represented by x1,x2,…,xn, then the above property can be written mathematically as:

(x1 - x_bar) + (x2 - x_bar) +…+ (xn – x_bar) = 0

  • If the mean of a given data is (x_bar) and each value in the data is either increased or decreased by a quantity z, the mean will increase or decrease by the same quantity.

 

If (x1 + z), (x2 + z), … , (xn + z), then (x_bar + z)

If (x1 - z), (x2 - z), … , (xn - z), then (x_bar - z)

 

  • If each value of the data is multiplied by a nonzero number z, then the mean of that data is also multiplied by the same nonzero number z.
  • Mean is used to compute other statistical values like variance.
  • Mean serves to be of great assistance when two sets of data are compared.
  • Extreme values of the data have a great impact on the mean.

 

4. How can average be misleading? How much can a zero drop your grade?

We know that average is the central value of the data around which the data is dispersed. Average or mean is the most common type of average used widely because its value is based on all observations. But a bigger demerit of the average is that it is extremely affected by the extreme values.

It can be understood by the simple example of a student’s obtained marks. Suppose his marks in 5 subjects are as follows.

EnglishFrenchMathScienceGeography
807487820

Now to calculate the average of his marks, we divide the sum of quantities by the total number of quantities:

 

Average = (80 + 7+87 +82 + 0) / 5 = 323/5 = 64.6

 

The average of his marks, as we can see, is not near to the average we obtained from the mean formula. The zero, in this case, is the extreme value that has dramatically affected the result.

Now consider using the median as the measure to calculate the average in this case. The data arranged in ascending order is 0, 74, 80, 82, 87. We can see from this arrangement that the middle value of the data is 80, which seems a way better figure than the mean.

For the above reason, the average can be misleading, especially when extreme values exist in the data, and it can also be seen from the above example that how much a zero can put an impact on your grade!

 

5. What are outliers?

The extreme values of the data are known as outliers. Their presence can impact the result when you calculate the average. Like in the example in the above FAQ, zero is the outlier.

 

6. What is the weighted average?

Weighted average or weighted arithmetic mean is similar to the arithmetic mean, except that each value in the data is not weighted equally. Some values contribute more than the others.

The simple example is your credit hours. Some courses at your institute are weighted at 3 credit hours while others are weighted at 4 credit hours. The method to calculate their mean is a bit different than calculating the normal mean.

You can use our Weighted Average Calculator for that and learn more about the topic.

 

Interesting Facts on Averages

  • An average human heart pumps 7500 liters of blood in a single day and 250 million liters of blood in an average lifetime.
  • One-third of an average human life is spent in sleep.
  • Statistics show that you laugh 10 times a day on average!
  • On average, a person consumes 200 liters of water a day just to flush their wastage while he uses the toilet 6 times a day on average.
  • Throughout his lifespan, an average person uses up to 12 kg of toothpaste.
  • Your mini tongue has 10,000 taste buds on average.
  • An average human produces around 2400 liters of saliva in their lifetime.
  • Got long shiny hair? By the end of your life, you must’ve consumed around 500 to 600 shampoo bottles.
  • A human spends around 11 years of life watching TV. Amazed, aren’t you?
  • The average time for a person to fall asleep in just 7 minutes!
  • 1460 dreams a year is what an average human sees. I bet you don’t remember most of them!
  • Your beautiful silk tie is made up of 110 silkworm cocoons on average.
  • You will be shocked by this one! You eat around 35 tons of food on average in your life.
  • An average person knows around 5000-6000 words.
  • An average person sheds around 1.5 pounds of skin each year, and in a lifetime, the skin replaces around 900 times.
  • Do you love to exercise? Well, then Mazel tov! You have a chance of living an average of six years more than non-joggers.
  • An average person walks as much as miles in his life that would take to walk twice around the world!
  • The average age of an American president is estimated to be 54 years.
  • Now this one’s is funny right here. An average man spends around a year of his life staring at women.
  • And you know what an average woman does in a year of her life? She spends that in deciding what to wear.