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Descriptive Statistics
Watch comprehensive video reviews for Descriptive Statistics, designed for final exam preparation. Each video includes integrated problems you can solve alongside detailed solutions.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
Not your average video:
Interactive Problems: Solve problems alongside the video with step-by-step guidance and detailed solutions.
Exam Preparation: Complete unit reviews designed for final exam preparation with all key concepts covered systematically.
Expert Teaching: High-quality instruction from Perplex co-founder James Mullen with clear explanations, worked examples, and exam tips.
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SL 4.3
If we have a dataset with mean xˉ and standard deviation σ, then if we
add a constant +b to the dataset, the mean increases by b and the standard deviation does not change
scale the values by a (eg. a=2 to double all the values), then both the mean and the standard deviation are scaled by a.
Example
A dataset has a mean of 5 and a variance of 4. Each item is doubled, and then incremented by 3. Find the new mean and variance.
An original variance of 4 is a standard deviation of √4=2.
First we double the items: the mean becomes 10 and the standard deviation becomes 4.
Then we add 3: the mean becomes 13 and the standard deviation does not change.
Hence the new mean is 13 and the new variance is 41=16.
SL 4.3
If we have a dataset with mean xˉ and standard deviation σ, then if we
add a constant +b to the dataset, the mean increases by b and the standard deviation does not change
scale the values by a (eg. a=2 to double all the values), then both the mean and the standard deviation are scaled by a.
Example
A dataset has a mean of 5 and a variance of 4. Each item is doubled, and then incremented by 3. Find the new mean and variance.
An original variance of 4 is a standard deviation of √4=2.
First we double the items: the mean becomes 10 and the standard deviation becomes 4.
Then we add 3: the mean becomes 13 and the standard deviation does not change.
Hence the new mean is 13 and the new variance is 41=16.