Statistical Mean

In Mathematics in the branch of Statistics, the expression for the mathematical mean of a statistical distribution is the mathematical average of all the terms in the data. To calculate this, we add up the values of the terms given and divide the sum by the number of terms in the data. This expression is also called the
Arithmetic Mean.


While solving word problems, we come across problems like, Scott drove from Bloomington to Chicago driving at 6 different speeds on the same freeway; 63mph, 72mph,42mph, 53mph, 67mph, 59mph. how do we calculate the Mean driving speed? It is very simple, we know that Arithmetic Mean is the regular average, so we just add up the different speeds and divide the sum by the number of different speeds given. Let us see the steps involved,
 The Mean driving speed = total sum of driving speeds /total number of speeds
Total sum of driving speeds = 63+72+56+68+59+48 =366
Total number of different speeds = 6
So, Mean driving speed = 366/6 = 61mph


Definition of Mean Or Definition Mean
To define mean, let us first learn about average in mathematics. Given a data of values, the average would be the total sum of the values divided by the total number of values given in the data. This in statistics is called the Mean or Arithmetic Mean. So, Definition of Mean is the average of the values given in a data.
Mean Formula
The Arithmetic Mean is the regular average of the values given in a data.
So, Mean Formula = Total sum of the values/Total number of values

Example: A student took 8 tests in a subject in one marking period. What is the mean test score?
                88, 75, 82, 90, 86, 78, 94, 87
Solution:  Number of tests = 8
  Sum of the marks =88+75+82+90+86+78+94+87= 680
   Mean = sum of the marks/number of tests
= 680/8 = 85

Sample Mean Formula
The sample mean in statistics, branch of Mathematics is the sum of all observed outcomes from the sample divided by the total number of events (Arithmetic Average). It is denoted by the symbol x with a (bar) above it. The Sample Mean formula is as follows:
X (bar) = (1/n) (x1+x2+x3………xn)

Example: At a car rental shop data was collected on the number of rentals on each of 10 consecutive Saturdays.  50, 44, 96, 38, 39, 40,50,46,47,42. Find the Sample Mean of the rentals.
Solution:   n = 10
Sigma(rentals) = 50+44+96+38+39+40+50+46+47+42=492
X(bar) =sigma(rentals)/n
            = 492/10
            = 49.2 is the Sample mean

Decimal Numbers

Decimals:
The Number system that we follow is called base 10 number system. In this system, we have numbers between 0 and 9, which defines every other number.  Fractional part of a number can be expressed as decimals.
What is a decimal?
Decimal is way of representing a fraction without numerator and denominator. The period or decimal point signifies that the number following it is fractional part. Decimal number can be either greater than or lesser than one. In case of decimal numbers, which are less than one, the leading number is zero.
Example:
39/10 = 3.9 [Decimal number greater than one]
79/100 = 0.79 [Decimal number less than one]
Decimal Place value:
In numbers, position of a number decides its value.
For example in counting number 345, the 3 represents three hundreds, 4 represents four tens and 5 represents 5 units. Similarly, in decimal numbers also, we have place value
Naming decimals:
One tenths = 1/10
One hundredths = 1/100
In 0.7, there are seven tenths.
In 0.79, there are seventy nine hundredths
In 0.798, there are seven hundred and ninety eight thousandths.
Decimal to fraction:
Let us learn how to convert a decimal into fraction.
Step 1: Find the number digits after the decimal point
Step 2: Write the number without the decimal point in the numerator
Step 3: in denominator write 1, followed by as many zeros as the number of digits after the decimal point in the given number
Example: Convert 0.347 into a fraction
Step 1: Number of digits after the decimal point is 3
Step 2: Numerator = 347
Step 3: Denominator = 1000
Hence, the fraction is 347/1000
Decimal to percent:
Let us learn how to convert a decimal number into a percentage.
To convert decimal to percent, multiply the decimal number by 100 and add % sign.
In other words, shift the decimal point to the right and add % sign.
Example: Convert 0.95 into percentage.
0.95 x 100 = 95%
Convert 0.895 into percentage.
0.895 x 100 = 89.5%
Rounding decimals:
Reducing the number of digits without any appreciable change in its value is called Rounding off.  You need to know how many digits you would like to have after the decimal point to round off.
It involves two steps.
Step 1: Decide the number of digits that want to keep in a decimal number.
Step 2: Increase by 1 if the next digit is greater than or equal to 5.
Step 3: Leave it, as it is if the next digit is less than 5.
Example:
Round off 0.789 to nearest hundredths.
0.789 is rounded off to 0.79, as the next digit 9 is greater than 5.
Round off 0.5674 to nearest thousandths.
0.5674 is rounded off to 0.567, as the next digit 4 is less than 5.