Frequency table or grouped data (Edexcel GCSE Statistics): Flashcards
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What is the key difference when calculating SD from frequency tables?
What is the key difference when calculating SD from frequency tables?
Weight each value by its frequency in calculations.
Name the two formulas for standard deviation in frequency tables.
Name the two formulas for standard deviation in frequency tables.
Formula 1: Σf(x−x̄)²/Σf; Formula 2: √(Σfx²/Σf - (Σfx/Σf)²)
How do you find the mean (x̄) from a frequency table?
How do you find the mean (x̄) from a frequency table?
x̄ = Σfx / Σf, sum of fx divided by total frequency.
Describe the step to find (x - x̄) in SD calculation.
Describe the step to find (x - x̄) in SD calculation.
Subtract the mean from each x-value in the table.
How does spread relate to a large SD value?
How does spread relate to a large SD value?
Large SD indicates more data spread from the mean.
How does SD respond to increasing data spread?
How does SD respond to increasing data spread?
SD increases as data spread out more from the mean.
Std dev from Σf(x-x̄)²=24 and Σf=25
Std dev from Σf(x-x̄)²=24 and Σf=25
σ = √(24/25) = √0.96 = 0.98 goals
Find SD: Σf=25 Σfx=45 Σfx²=105
Find SD: Σf=25 Σfx=45 Σfx²=105
SD=√(105/25−(45/25)²)=√0.96=0.98
Compute mean from frequency table: Σfx=45, Σf=25
Compute mean from frequency table: Σfx=45, Σf=25
x̄ = Σfx/Σf = 45/25 = 1.8
Calculate SD: Σf(x−x̄)²=24 and Σf=25
Calculate SD: Σf(x−x̄)²=24 and Σf=25
σ = √(24/25) = √0.96 = 0.98