Chapter 2E Flashcards
(16 cards)
When Should Standard Deviation Not Be Used?
When Should Standard Deviation Not Be Used?
Standard deviation should not be used with data that has a non-normal distribution or when the data contains extreme outliers. It works best when the data is symmetric and does not have too many unusual values. It also doesn’t work well with categorical or non-numeric data.
Why and When Is Standard Deviation Used?
Standard deviation is used whenever we want to describe how consistent or spread out data is. It is very commonly used in school performance data, scientific experiments, finance, and any area where variation matters. Unlike variance, standard deviation is easier to explain because its unit matches the data.
What Does Standard Deviation Tell Us?
What Does Standard Deviation Tell Us?
If the standard deviation is small, the data values are close to the mean. If it is large, the values are spread out. For example, if a test has a mean score of 70 and a standard deviation of 2, most students scored between 68 and 72. But if the standard deviation were 15, students’ scores would be spread out much more widely.
How is Standard Deviation Calculated?
How is Standard Deviation Calculated?
The formula is just the square root of the variance:
* For population:
σ = √[(Σ(x − μ)²) ÷ N]
* For sample:
s = √[(Σ(x − x̄)²) ÷ (n − 1)]
This tells you, on average, how far the data values are from the mean. Unlike variance, this is in the same unit as your data, so it is more useful when interpreting your results.
What is Standard Deviation?
What is Standard Deviation?
Standard deviation is the square root of the variance. It also measures the spread of data around the mean, but it gives the answer in the same units as the original data. This makes it easier to understand and compare directly with the mean.
Where Should Variance Not Be Used Alone?
Where Should Variance Not Be Used Alone?
Variance should not be used when you want a measure of spread that is in the same unit as the data (like kilograms, metres, or points). Also, if your data has extreme outliers, variance might give a distorted picture since it reacts strongly to values far from the mean.
Why and When Is Variance Used?
Why and When Is Variance Used?
Variance is used when you want to measure spread in a mathematical way that is sensitive to every value in the data set. It is especially useful when comparing how different groups vary. It is also part of many statistical techniques like hypothesis testing, ANOVA (analysis of variance), and regression analysis. However, because of the squared units, variance is usually not the final value reported—standard deviation is used instead.
What Does the Variance Tell Us?
A higher variance means more spread or inconsistency in the data. A lower variance means the data is more consistent and closer to the mean. But because variance is in squared units, it’s not easy to interpret directly. For example, if the data is in kilograms, the variance will be in square kilograms, which isn’t a real-world unit.
What is Variance?
What is Variance?
Variance is a measure of how spread out the data values are around the mean. If the values in a data set are all close to the mean, the variance will be small. If the values are very spread out, the variance will be large. It gives a numeric answer to the question: “How far are the numbers, on average, from the mean?”
How to calculate the interpercentile range
How to calculate the interpercentile range
To calculate the interpercentile range, subtract the lower chosen percentile from the higher chosen percentile.
For example: interpercentile range = 90th percentile minus 10th percentile
How is Variance Calculated?
The formula for variance is this:
* For a population (true whole set):
σ² = (Σ(x − μ)²) ÷ N
* For a sample (a selection from a larger group):
s² = (Σ(x − x̄)²) ÷ (n − 1)
Where:
* σ² is population variance, s² is sample variance
* x means each individual data point
* μ is the population mean, x̄ is the sample mean
* N is the total number in the population, n is the number in the sample
You square the difference from the mean so that negative and positive differences don’t cancel each other out. Squaring also gives more weight to values that are far from the mean.
How to calculate the interquartile range (IQR)
How to calculate the interquartile range (IQR)
To calculate the interquartile range, subtract the lower quartile (Q1) from the upper quartile (Q3).
IQR = Q3 minus Q1
Interpercentile Range
Interpercentile Range
The interpercentile range is the difference between two selected percentiles. It shows the spread of a specific portion of the data between those percentiles. A common example is the 90th percentile minus the 10th percentile.
Interquartile Range (IQR)
Interquartile Range (IQR)
The interquartile range is the difference between the upper quartile and the lower quartile. It measures the spread of the middle 50 percent of the data. It is not affected much by extreme values.
How to calculate the range
How to calculate the range
To calculate the range, subtract the smallest value from the largest value in the data set.
Range
Range
The range is the difference between the largest and smallest values in a data set. It gives a basic idea of how wide the data is spread. It is easy to calculate but can be affected by extreme values.
