Standard deviation - Revision history

Velez105 at 04:57, 9 December 2025

2025-12-09T04:57:56Z

Casimir007 at 06:01, 14 November 2025

2025-11-14T06:01:26Z

Admin at 14:24, 20 April 2022

2022-04-20T14:24:00Z

Admin at 14:23, 20 April 2022

2022-04-20T14:23:11Z

Ciskowskid: /* Standard Deviation Formula */

2022-02-11T16:04:24Z

‎Standard Deviation Formula

Ciskowskid: /* Standard Deviation Formula */

2022-02-11T16:03:11Z

‎Standard Deviation Formula

Ciskowskid: /* Standard Deviation Formula */

2022-02-11T15:55:48Z

‎Standard Deviation Formula

Ciskowskid: /* Standard Deviation Formula */

2022-02-11T15:53:58Z

‎Standard Deviation Formula

Ciskowskid at 15:39, 11 February 2022

2022-02-11T15:39:08Z

Ciskowskid: /* Standard Deviation Formula */

2022-02-11T15:38:34Z

‎Standard Deviation Formula

← Older revision		Revision as of 04:57, 9 December 2025
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	''contributed by Casimir007''		''contributed by Casimir007''
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		+	[[Standard Deviation]]
		+	Standard deviation is a measure of the amount of variation or dispersion in a set of values. It tells you, on average, how much each data point deviates (differs) from the mean of the entire set.
		+	Low SD indicates that the data points are clustered closely around the mean (highly consistent).
		+	High SD indicates that the data points are spread out over a broader range (high variability).
		+	== Why Standard Deviation Matters ==
		+	SD is crucial because the mean alone can be misleading. It provides the necessary context to interpret the central value of a data set.
		+	Consistency: It measures the consistency or reliability of data. For example, two classes might have an average test score (mean) of 75, but the one with a lower SD has more consistent scores (clustered around 75), while the one with a higher SD has scores that are widely spread (many high and many low scores).
		+	Data Interpretation (Normal Distribution): For data that follows a normal distribution (bell curve), SD allows for quick interpretation using the Empirical Rule (68-95-99.7 Rule):
		+	Approximately 68% of the data falls within 1 SD of the mean.
		+	Approximately 95% falls within 2 SDs of the mean
		+	Outlier Identification: It helps determine what constitutes a "normal" range of values and thus identifies potential outliers (data points that are statistically far from the mean).
		+
		+	== Main Elements and Calculation Steps ==
		+	The Standard Deviation is the square root of the Variance. The calculation is based on four main elements:
		+	Element Symbol Description
		+	Individual Value xᵢ: Each data point in the set.
		+	Mean μ: The simple average of all data points.
		+	Number of Values N: The total count of data points.
		+	Summation Σ: The command to add up all results of an operation.
		+
		+	== Calculation Steps ==
		+	1. Calculate the Mean (μ): Add all the data points and divide by the total number of points (N).
		+	2. Find the Deviation and Square It: For each data point (xᵢ), subtract the mean (μ), and then square the result: (xᵢ - μ)². (Squaring ensures all values are positive and emphasizes larger deviations)
		+	3. Sum the Squared Deviations: Add up all the squared results from Step 2. This is called the Sum of Squares (Σ (xᵢ -μ)².
		+	4. Calculate the Variance: Divide the Sum of Squares by the total number of data points (N). For a sample standard deviation, divide by n -1, which is known as Bessel’s correction.
		+	5. Take the Square Root: Take the square root of the result from Step 4. This is the Standard Deviation (σ).
		+	[https://www.youtube.com/watch?v=hMs9OeyIqD8]
		+	‘ ‘contributed by Jerry Velez’ ’

← Older revision		Revision as of 06:01, 14 November 2025
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	''contributed by David Ciskowski''		''contributed by David Ciskowski''
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		+
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		+	Standard deviation (SD) provides the amount of variation or the consistency of a dataset by giving the difference between the individual data points and the mean. In the case where the mean indicates the center of the point, standard deviation is employed to demonstrate how tight or loose the scores are around the mean. They may be combined to provide a more detailed picture of student or program performance. When SD is small, the scores are highly clustered, like the students have scored in a similar fashion. In order to give an example, where the mean score is 85 and the SD is 2, the majority of students fell within the range of 83-87.
		+	On the other hand, when SD is large, the scores are more dispersed, whereby some students are very far below or above the mean. The mean of two classes can be equal to 85, but one with a SD of 3 is more homogeneous than SD of 10. Two classes can be equal in terms of 85 average, but one with SD of 3 is more homogeneous than one with SD of 10. Variability in education assists teachers in interpreting the differences in achievement and consistency in teaching. When the SD in student performance is high, it may indicate that teaching methods are effective with one group of students and not with other students, which defines the necessity of differentiation.
		+	On the other hand, a small SD may indicate fair results or a ceiling effect in the design of the assessment. The SD is acquired in SPSS under Analyze - Descriptive Statistics - Descriptives. The data can be represented as visual tools like boxplots or histograms, which can be easier to interpret to determine the variability. Many inferential tests, including t-tests and ANOVA, are also based on the SD, as it has an effect on confidence intervals and effect sizes. Concisely, the standard deviation will convert numerical data into useful narratives on learning diversity, program consistency, and classroom equity.
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		+	''contributed by Casimir007''

← Older revision		Revision as of 14:24, 20 April 2022
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	[[File:Sample_Standard_Deviation_Formula.JPG]]		[[File:Sample_Standard_Deviation_Formula.JPG]]

		+	== Worked Example ==
	Here is a worked example for finding a '''''sample standard deviation''''' using a sample of 10 test scores:		Here is a worked example for finding a '''''sample standard deviation''''' using a sample of 10 test scores:

← Older revision		Revision as of 14:23, 20 April 2022
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	[[File:Worked_example_of_population_standard_deviation.JPG]]		[[File:Worked_example_of_population_standard_deviation.JPG]]

−	''~~Contributed~~ by David Ciskowski''	+	''contributed by David Ciskowski''

@@ Line 47: / Line 47: @@
 [[File:Sample_Standard_Deviation_Formula.JPG]]
-Here is a worked example for finding a sample standard deviation using a sample of 10 test scores:
+Here is a worked example for finding a '''''sample standard deviation''''' using a sample of 10 test scores:
 [[File:Worked_example_of_sample_standard_deviation.JPG]]
@@ Line 56: / Line 56: @@
 [[File:Population_Standard_Deviation_Formula.JPG]]
-Here is a work example for finding a population standard deviation using a population of 10 test scores (notice this is the same data and process as above, but with the slight difference of dividing by ''n'' instead of ''n-1''):
+Here is a work example for finding a '''''population standard deviation''''' using a population of 10 test scores (notice this is the same data and process as above, but with the slight difference of dividing by ''n'' instead of ''n-1''):
 [[File:Worked_example_of_population_standard_deviation.JPG]]
 ''Contributed by David Ciskowski''

← Older revision		Revision as of 16:03, 11 February 2022
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	The formula for a '''''population''''' standard deviation is:		The formula for a '''''population''''' standard deviation is:

		+	[[File:Population_Standard_Deviation_Formula.JPG]]

		+	Here is a work example for finding a population standard deviation using a population of 10 test scores (notice this is the same data and process as above, but with the slight difference of dividing by ''n'' instead of ''n-1''):
		+
		+	[[File:Worked_example_of_population_standard_deviation.JPG]]

	''Contributed by David Ciskowski''		''Contributed by David Ciskowski''

@@ Line 54: / Line 54: @@
 The formula for a '''''population''''' standard deviation is:
-[[File:Example.jpg]]
 ''Contributed by David Ciskowski''

@@ Line 43: / Line 43: @@
 == Standard Deviation Formula ==
-The formula for a sample standard deviation is:
+The formula for a '''''sample''''' standard deviation is:
 [[File:Sample_Standard_Deviation_Formula.JPG]]
@@ Line 50: / Line 50: @@
 [[File:Worked_example_of_sample_standard_deviation.JPG]]
 ''Contributed by David Ciskowski''

← Older revision		Revision as of 15:39, 11 February 2022
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	[[File:Worked_example_of_sample_standard_deviation.JPG]]		[[File:Worked_example_of_sample_standard_deviation.JPG]]
		+
		+	''Contributed by David Ciskowski''

← Older revision		Revision as of 15:38, 11 February 2022
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	Here is a worked example for finding a sample standard deviation using a sample of 10 test scores:		Here is a worked example for finding a sample standard deviation using a sample of 10 test scores:

−	[[File:Worked_example_of_sample_standard_deviation.~~jpg~~]]	+	[[File:Worked_example_of_sample_standard_deviation.JPG]]