Overview of variance and Standard deviation.pptx
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This document provides an overview of variance and standard deviation. It defines variance as the average squared deviation from the mean of a data set, and is used to calculate standard deviation. Standard deviation measures how dispersed the data is from the mean - the higher the standard deviation, the more spread out the data. It gives the formulas for calculating variance using summation notation, and standard deviation as the square root of variance. An example is shown finding the variance and standard deviation of 5 test scores.
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Variance and standard deviation
This document discusses variance and standard deviation. It defines variance as the average squared deviation from the mean of a data set. Standard deviation measures how spread out numbers are from the mean and is calculated by taking the square root of the variance. The document provides step-by-step instructions for calculating both variance and standard deviation, including examples using test score data.
Variance & standard deviation
This document defines variance and standard deviation and provides formulas and examples to calculate them. It states that variance is the average squared deviation from the mean and measures how far data points are from the average. Standard deviation tells how clustered data is around the mean and is the square root of the variance. It provides step-by-step instructions to find variance and standard deviation, including calculating the mean, deviations from the mean, summing the squared deviations, and taking the square root. Worked examples are shown to find the variance and standard deviation of students' test scores and people's heights in a room.
Standard deviation & variance
The document discusses standard deviation and variance. It defines standard deviation as a measure of how spread out numbers are from the average. A low standard deviation means the numbers are close to the average, while a high one means they are more spread out. The document provides formulas for calculating variance using summation notation and standard deviation as the square root of variance. It includes an example of calculating standard deviation from a set of test scores.
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This document discusses measures of dispersion, specifically standard deviation and quartile deviation. It defines standard deviation as a measure of how closely values are clustered around the mean. Standard deviation is calculated by taking the square root of the average of the squared deviations from the mean. Quartile deviation is defined as half the difference between the third quartile (Q3) and first quartile (Q1), which divide a data set into four equal parts. The document provides examples of calculating standard deviation and quartile deviation for both individual and grouped data sets. It also discusses the merits, demerits, and uses of these statistical measures.
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The document discusses how to calculate variance and standard deviation. It provides the formulas and steps to find variance as the average squared deviation from the mean. Standard deviation is defined as the square root of variance and measures how dispersed data are from the mean, with a larger standard deviation indicating more variation. Examples are worked through to demonstrate calculating variance and standard deviation for different data sets.
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The document discusses variance and standard deviation. It defines variance as the average squared deviation from the mean of a data set. It provides the step-by-step process to calculate variance which includes finding the mean, deviations from the mean, squaring the deviations, summing the squares, and dividing by the number of data points. Standard deviation is defined as the square root of the variance and measures how spread out numbers are from the mean. Examples are provided to demonstrate calculating variance and standard deviation.
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This document defines variance and standard deviation, which are measures of how spread out numbers are in a data set from the mean. It explains how to calculate variance by finding the mean, subtracting it from each value, squaring the deviations, summing them and dividing by the number of items. Standard deviation is the square root of variance and measures how far data points on average lie from the mean, with a higher value indicating more dispersion from the mean. Formulas for calculating both are provided.
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This document discusses variance and standard deviation. It defines variance as the average squared deviation from the mean of a data set. Standard deviation measures how spread out numbers are from the mean and is calculated by taking the square root of the variance. The document provides step-by-step instructions for calculating both variance and standard deviation, including examples using test score data.
Variance & standard deviation
This document defines variance and standard deviation and provides formulas and examples to calculate them. It states that variance is the average squared deviation from the mean and measures how far data points are from the average. Standard deviation tells how clustered data is around the mean and is the square root of the variance. It provides step-by-step instructions to find variance and standard deviation, including calculating the mean, deviations from the mean, summing the squared deviations, and taking the square root. Worked examples are shown to find the variance and standard deviation of students' test scores and people's heights in a room.
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The document discusses variance and standard deviation. It defines variance as the average squared deviation from the mean of a data set. It provides the step-by-step process to calculate variance which includes finding the mean, deviations from the mean, squaring the deviations, summing the squares, and dividing by the number of data points. Standard deviation is defined as the square root of the variance and measures how spread out numbers are from the mean. Examples are provided to demonstrate calculating variance and standard deviation.
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This document defines variance and standard deviation, which are measures of how spread out numbers are in a data set from the mean. It explains how to calculate variance by finding the mean, subtracting it from each value, squaring the deviations, summing them and dividing by the number of items. Standard deviation is the square root of variance and measures how far data points on average lie from the mean, with a higher value indicating more dispersion from the mean. Formulas for calculating both are provided.
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- 1. Overview of variance and Standard deviation
- 2. VARIANCE: Variance is the average squared deviation from the mean of a set of data. It is used to find the standard deviation. Find the mean of the data. (Mean is the average so add up the values and divide by the number of items.) Subtract the mean from each value- the result is called the deviation from the mean. Square each deviations of the mean. Find the sum of the squares. Divide the total by the number of items.
- 3. VARIANCE FORMULA: The variance formula includes the Sigma Notation, 𝚺 which represents the sum of all the items to the right of Sigma. (𝑥 − µ) n 2 Mean is represented by µ and n is the number of items.
- 4. Standard deviation shows the variation in data. If the data is close together, the standard deviation will be small. If the data is spread out, the standard deviation will be large. Standard Deviation is often denoted by the lowercase Greek letter sigma (σ). STANDARD DEVIATION:
- 5. STANDRAD DEVIATION: Find the variance. a) Find the mean of the data. b) Subtract the mean from each value. c) Square each deviation of the mean. d) Find the sum of the squares. e) Divide the total by the number of items. Take the square root of the variance.
- 6. STANDARD DEVIATION FORMULA: The standard deviation formula can be represented using Sigma Notation: σ= 𝚺 (x−µ) n 2 The standard deviation formula is the square root of the variance.
- 8. FIND THE VARIANCE AND STANDARD DEVIATION The math test scores of five students are: 92,88,80,68 and 52. 1. Find the mean: (92+88+80+68+52)/5 = 76 2. Find the deviation from the mean: 92-76=16 88-76=12 80-76=4 68-76=-8 52-76=-24
- 9. 3. Square the deviation from the mean: (16)2 =256 (12)2 = 144 (4)2 =16 (-8)2=64 (-24)2=576 4. Find the sum of the squares of the deviation from the mean: 256+144+16+64+576= 1056 5. Divide by the number of data items to find the variance: 1056/5= 211.2 6. Find the square of the variance: 211. 2 = 14.53 Thus the standard deviation of the test scores is 14.53.
- 10. Conclusion: As we have seen, standard deviation measures the dispersion of data. The greater the value of the standard deviation, the further the data tend to be dispersed from the mean.
- 11. THANK YOU