Tutorial Playlist
68 Lessons1. Excel Tutorial
2. Excel Worksheet for Practice
3. Google Sheets Vs. Excel
4. Excel Shortcut Keys
5. Excel Keyboard Shortcuts
6. Excel AutoSum Shortcut
7. Redo Shortcut in Excel
8. Charts in Excel
9. Pivot Charts in Excel
10. Excel Sum Formula
11. Excel Percentage Formula
12. Excel Age Calculation Formula
13. Excel Range Formula
14. Round Off Formula in Excel
15. VLOOKUP Formula in Excel
16. Excel Transpose Formula
17. Average Equation in Excel
18. How to Use DATEDIF Formula in Excel
19. IRR Formula in Excel
20. Standard Deviation Formula
Now Reading
21. Excel Age Calculation Formula
22. Excel MAX Function
23. Excel LEFT Function
24. Excel RIGHT Function
25. Trim Function In Excel
26. LookUp function in Excel
27. Columns in Excel
28. How To Sort Data In Excel
29. How To Freeze Panes in Excel
30. Page Setup in Excel
31. How to Recover an Unsaved Excel File
32. Concatenate in Excel
33. Count In Excel
34. IF Condition In Excel
35. H LOOK UP in Excel
36. How Do You Move Columns in Excel
37. Split Cells in Excel
38. Remove Blank Rows in Excel
39. How To Lock Cells in Excel
40. Data Validation in Excel
41. How to Insert Checkbox in Excel
42. How To Highlight Duplicates in Excel
43. Fill Series in Excel
44. How to Create Excel Drop-Down List
45. What-If Analysis in Excel
46. How to Use SUMIFS Function in Excel
47. INDIRECT Function in Excel
48. Pivot Table in Excel
49. Slicers in Excel
50. How to Create a Dashboard in Excel
51. Excel Data Cleaning
52. Data Analysis In Excel
53. Goal Seek in Excel
54. Solver in Excel
55. Power Query in Excel
56. Macros In Excel
57. How To Make Graph in Excel
58. How To Make Histogram In Excel
59. How To Convert PDF to Excel Without Software
60. Barcode Font For Excel
61. Gantt Chart in Excel
62. Excel RANK function
63. AND Function in Excel
64. How to Calculate NPV
65. Format Painter in Excel
66. Count Colored Cells in Excel
67. Amortization Schedule in Excel
68. Master Cell References in Excel
As a former retail chain employee, I understand the challenges of managing excessive data. This one time, I was looking over customer wait times and noticed that the long queues desperately needed a rescue. The standard deviation formula helped me in those days of distress.
I opened my system, entered a few formulas, and voila, suddenly, I knew the numbers even better.
In this tutorial, I’ll cover a range of topics related to equation for standard deviation. Learn from an expert and see how you can ease up data analysis in the flick of a finger.
Now that I've established the solution to all my data problems let me tell you about the one-stop solution standard deviation offers.
The standard deviation formula is a statistical function meant to produce an average and tell you how far each data point falls from the average value in your dataset. But how does it achieve this complexity?
Source: Math is Fun
σ = √(Σ(x̅ - xi)² / (n - 1))
Let me give you a breakdown of the standard deviation formula Excel often works on:
The standard deviation formula illustrated in steps:
Step 1: Find the difference between each data point and the average value.
Step 2: Square those differences to understand both the positive and negative variations.
Step 3: Add all the squared differences.
Step 4: Divide the sum by n-1. (Here, N accounts for the total data points.)
There are two Excel formulas for use — population standard deviation and sample standard deviation.
You can extract the population standard deviation variance formula by taking the square root of the average of the squared deviations of each value from the population mean (µ), divided by the total population size (N.)
Formula for the population standard deviation
σ = √(Σ(x̅ - xi)² / (n - 1))
where
σ = population standard deviation symbol
x̄ = population mean
xi = terms presented in the data
n = the total number of observations
The sample standard deviation formula calculates how spread out your data is by finding the square root of the average squared distance from the mean.
Formula for the sample standard formula
s = √(Σ (x̅ - xi)² / n-1)
where
s = sample standard deviation symbol
x̄ = population mean
xi = terms given in the data
n = the total number of observations
Feature | Population standard deviation | Sample deviation |
Formula | Σ (x̅ - xi)² / n (or Σ (x - μ)² / n for population) | √(Σ (x̅ - xi)² / n-1) |
Units | Squared units of the data (e.g., cm² for height) | Same units as the data (e.g., cm for height) |
Interpretation | It measures the average squared deviation from the mean and indicates the difference in data points and mean. (It does not reveal the difference (positive or negative.) | It indicates how spread out your data is relative to the mean. A higher standard deviation points towards data points being further away from the mean. This shows a greater spread. |
Where to Use | Coefficient of variation | Simpler to understand and interpret the spread of data in the original units. |
Relationship | Since squaring a number removes the negative sign, variance reflects the average squared distance from the mean, regardless of direction. | Standard deviation "undoes" the squaring done in variance, putting the answer back in the original units of the data. |
Example | Here’s a dataset of exam scores: {70, 80, 90, 100, 110}. The variance might be 100, indicating the scores deviate from the average (80) by an average of 10 squares. | The standard deviation would be 10. This is easier to interpret as scores typically deviate from the average by 10 points. |
Among the plethora of reasons, the two most vital are data availability and accuracy.
Let’s say you want to study everyone’s heights in your country. It is highly doubtful that you’ll have access to everyone’s data.
In this case, an equation for standard deviation (sample) may be of better use due to the availability of info on a subset of the population.
When it comes to accuracy, the population standard deviation paints a more accurate picture of the data. On the other hand, think of sample standard deviation as your friend who’s better at estimation.
Let’s assume that the exam scores are grouped by grades (A, B, C, D, F), with frequencies representing the number of students in each grade.
s = √(Σ f(x - x̅)² / N)
Example
Here are the steps to your standard dev calculator:
Step 1. Calculate the mean (x̅) considering frequencies and grade midpoints (e.g., midpoint of grade A).
Step 2. Find squared deviations (x - x̅)² for each grade.
Step 3. Multiply each squared deviation by its frequency (f).
Step 4. Add the products from step 3 (Σ f(x - x̅)²).
Step 5. Divide the sum by the total students (N) and take the square root.
When working with samples (a portion of the population), I use slightly different formulas. Here’s a quick overview of the three ways in which you can customize your output:
Method | Formula | Notation | Considerations |
Actual mean method | s² = Σ f(x - x̅)² / (n-1) | s² (sigma squared): Sample variance Σ (sigma): Summation f: Frequency x: Midpoint of each class x̅: Sample mean n: Total number of samples (sum of frequencies) | Calculates deviations from the actual sample mean and offers an unbiased estimate of the population. |
Assumed mean method (estimate) | s² ≈ Σ f(x - A)² / (n-1) | s² (sigma squared): Estimated sample variance Σ (sigma): Summation f: Frequency x: Midpoint of each class A: Assumed mean (chosen value within data range) n: Total number of samples | Less accurate than the actual mean method. |
Step deviation method (estimate) | s² ≈ (i² / 12) Σ f(d')² / (n-1) | s² (sigma squared): Estimated sample variance Σ (sigma): Summation f: Frequency d': Deviation from assumed mean in class widths i: Class width (difference between midpoints of adjacent classes) n: Total number of samples | Reduces the impact of choosing an assumed mean by using class widths. |
Alt text: Table showing a coffee shop’s wait time
Step 1. Calculate midpoints (m) for each class except the open-ended ones.
Step 2. Estimate frequency density (f_d) for each class (f / class width). Note that we can't calculate f_d for the open-ended class just yet.
Step 3. Calculate the sample mean (x̅) using midpoints and frequencies.
Step 4. Apply the equation for standard deviation for ungrouped data, using midpoints (m) and frequency densities (f_d) for classes 1-4 only using this formula:
s² ≈ Σ f_d (m - x̅)² / n
Step 5. Take the square root of the result for estimated standard deviation (s).
Step 6. Address the open-ended class. Assume a class width of 20-25 minutes for simplicity.
Step 7. Calculate f_d for this class (assumed to be 2 data points/minute).
A coin toss experiment is the easiest way to get things going for this method.
The goal is to find the standard deviation (σ) to understand the possible outcomes (heads or tails). The comparison happens with the average outcome (average of getting heads and tails).
Step 1. Calculate the mean (μ): μ = Σ (x * P(x)) = (1 * 0.6) + (0 * 0.4) = 0.6 (average outcome)
Step 2. Calculate squared deviations from the mean: (x - μ)² = [(1 - 0.6)²] + [(0 - 0.6)²] = 0.16 + 0.36
Step 3. Multiply deviations by probabilities: (x - μ)² * P(x) = (0.16 * 0.6) + (0.36 * 0.4) = 0.096 + 0.144
Step 4. Sum the products using: Σ ((x - μ)² * P(x)) = 0.24
By applying the standard deviation formula, here’s your outcome:
σ = √(Σ ((x - μ)² * P(x))) = √(0.24) ≈ 0.49 (rounded)
Here’s another example: roll a fair six-sided die. The random variable (X) represents the number rolled (1 to 6).
Step 1. Define probabilities (each number has a 1/6 chance).
Step 2. Calculate the mean (average outcome, μ = (1 + 2 + ... + 6) / 6 = 3.5).
Step 3. Find squared deviations from the mean for each outcome.
Step 4. Calculate the variance (σ²) considering probabilities (Σ shows summation).
Step 5. Standard deviation (SD) is the square root of the variance (SD = √σ²).
Learning the standard deviation formula might appear challenging. However, given the right methods, it can yield accurate (and estimated) results. To learn more about such formulas to ease up your task, visit upGrad.
With upGrad’s numerous courses, you can find one that best suits your objectives.
Take the first step today! Register for a course.
1. How do I calculate standard deviation?
The method for calculating the standard deviation will depend on whether you’re working with grouped or ungrouped data. To calculate standard division in Excel, use this formula - s = √(Σ (x̅ - xi)² / n-1). In case it is an entire population, use this formula - σ = √(Σ(x̅ - xi)² / (n - 1))
2. What is the standard deviation type formula?
The standard deviation type formula is usually σ = √(Σ(x̅ - xi)² / (n - 1)) for a large group of data and s = √(Σ (x̅ - xi)² / n-1) for sample data.
3. What do you mean by standard deviation?
The Excel standard deviation function allows for calculating the square root of the variant about a dataset.
4. What is Q in the standard deviation formula?
In binomial distribution, the letter ‘Q’ represents the probability of failure. The standard deviation formula for this would be σ = √npq with n standing for the total number of trials, p for the probability of success, and q for the probability of failure.
5. What is the standard deviation of 5 5 9 9 9 10 5 10 10?
For the dataset of 5, 5, 9, 9, 9, 10, 5, 10, 10, the population standard deviation is 2.29.
6. What are 2 standard deviations?
The two types of standard deviations are population standard deviation and sample standard deviation. The former is used for a large dataset, whereas the latter is more useful for a defined subset of data.
7. What is the 5 sigma rule?
The 5 sigma rule is a statistical concept particularly used in hypothesis testing to determine the likelihood of a random chance.
8. What is 1 sigma?
With relation to statistics, 1 sigma (σ) explains one standard deviation from the mean (average) of a distribution. It refers to how spread out the data is in comparison to the average value.
9. What is the 3 sigma limit?
The 3-sigma limit, also known as the 3-sigma rule or the empirical rule, is a statistical concept used primarily for normal distributions (bell-shaped curves). The three determiners are normal distribution, mean, and standard deviation (σ).
Devesh
Passionate about Transforming Data into Actionable Insights through Analytics, with over 3+ years of experience working in Data Analytics, Data V…Read More
Talk to our experts. We’re available 24/7.
Indian Nationals
1800 210 2020
Foreign Nationals
+918045604032
upGrad does not grant credit; credits are granted, accepted or transferred at the sole discretion of the relevant educational institution offering the diploma or degree. We advise you to enquire further regarding the suitability of this program for your academic, professional requirements and job prospects before enrolling. upGrad does not make any representations regarding the recognition or equivalence of the credits or credentials awarded, unless otherwise expressly stated. Success depends on individual qualifications, experience, and efforts in seeking employment.
upGrad does not grant credit; credits are granted, accepted or transferred at the sole discretion of the relevant educational institution offering the diploma or degree. We advise you to enquire further regarding the suitability of this program for your academic, professional requirements and job prospects before enr...