Standard deviation is a measure of spread of numbers in a set of data from its mean value. Use our online standard deviation calculator to find the mean, variance and arithmetic standard deviation of the given numbers.
Formula for the sample standard deviation for a frequency distribution: sample standard deviation = s = √∑(x-x̅)²f/n-1 where n=∑f is the number of entries in the data set - REMEMBER: formulas for grouped data require you to multiply by the frequencies. Frquency distribution or grouped standard deviation calculator - step by step. On the group or range & frequency of data, provided with formula & solved example. In a class of students, 9 students scored 50 to 60, 7 students scored 61 to 70,.
Standard deviation is a measure of spread of numbers in a set of data from its mean value. Use our online standard deviation calculator to find the mean, variance and arithmetic standard deviation of the given numbers.
Formula :
Mean :Mean = Sum of X values / N(Number of Values)Variance : Variance = s2
Sample Standard Deviation :
Population SD :
In statistics, Standard Deviation (SD) is the measure of 'Dispersement' of the numbers in a set of data from its mean value. This is represented using the symbol σ (sigma). The formula for the Standard Deviation is square root of the Variance. Here is a free online arithmetic standard deviation calculator to help you solve your statistical questions. This can also be used as a measure of variability or volatility for the given set of data. Enter the set of values in the online SD calculator to calculate the mean, standard deviation, variance and population standard deviation.
Example:
Consider a set X = {5,10,15,20,25}
Step 1 :
Mean = Sum of X values / N(Number of values)
= (5+10+15+20+25) / 5
= 75 / 5
= 15 Hence Mean = 15
= (5+10+15+20+25) / 5
= 75 / 5
= 15 Hence Mean = 15
Step 2 :
To find the variance,
Subtract the mean from each of the x values,
5-15 = -10
10-15 = -5
15-15 = 0
20-15 = 5
25-15 = 10
Now square all the answers you have got from subtraction.
(-10)2 = 100
(-5)2 = 25
(0)2 = 0
(5)2 = 25
(10)2 = 100
Add all the Squared numbers,
100 + 25 + 0 + 25 + 100 = 250
Divide the sum of squares by (n-1)
250 / (5-1) = 250 / 4 = 62.5
Hence Variance = 62.5
Subtract the mean from each of the x values,
5-15 = -10
10-15 = -5
15-15 = 0
20-15 = 5
25-15 = 10
Now square all the answers you have got from subtraction.
(-10)2 = 100
(-5)2 = 25
(0)2 = 0
(5)2 = 25
(10)2 = 100
Add all the Squared numbers,
100 + 25 + 0 + 25 + 100 = 250
Divide the sum of squares by (n-1)
250 / (5-1) = 250 / 4 = 62.5
Hence Variance = 62.5
Step 3 :
Find the square root of variance,
√62.5 = 7.905
Hence Standard deviation is 7.905
To find minimum and maximum SD,
Minimum SD = Mean - SD
= 15 - 7.905
= 7.094
Maximum SD = Mean + SD
=15 + 7.905
= 22.906
√62.5 = 7.905
Hence Standard deviation is 7.905
To find minimum and maximum SD,
Minimum SD = Mean - SD
= 15 - 7.905
= 7.094
Maximum SD = Mean + SD
=15 + 7.905
= 22.906
Step 4 :
To find the population SD,
Divide the sum of squares found in step 2 by n
250 / 5 = 50
Find the square root of 50, √50 = 7.07
Divide the sum of squares found in step 2 by n
250 / 5 = 50
Find the square root of 50, √50 = 7.07
Related Calculators:
Top Calculators
Popular Calculators
Top Categories
Use this online frequency distribution calculator to find the number of observation within a given interval of time which is called as the frequency distribution.
Use this online frequency distribution calculator to find the number of observation within a given interval of time which is called as the frequency distribution.
Frequency: The frequency is the number of occurrence of a repeating event per unit time.
Frequency Distribution: Any collected data can be arranged in a meaningful form, so that any new emerging data can be easily seen. One of the most used methods to arrange the data is the frequency distribution. It is a statistical calculation represented either in tabular or graphical formats.
The factors that are needed to calculate it are the minimum, maximum, range and the total number of the data set. This frequency distribution calculator can find the distribution for the individual and group of data set. Also, it provides the distribution in the tabular format.
Frequency Distribution: Any collected data can be arranged in a meaningful form, so that any new emerging data can be easily seen. One of the most used methods to arrange the data is the frequency distribution. It is a statistical calculation represented either in tabular or graphical formats.
The factors that are needed to calculate it are the minimum, maximum, range and the total number of the data set. This frequency distribution calculator can find the distribution for the individual and group of data set. Also, it provides the distribution in the tabular format.