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A Quizlet for Edexcel S1
Terms in this set (78)
What is Stage 1 of the Statistical Model?
The recognition of a real-world problem.
What is Stage 2 of the Statistical Model?
A statistical model is devised.
What is Stage 3 of the Statistical Model?
Model used to make predictions.
What is Stage 4 of the Statistical Model?
Data is collected.
What is Stage 5 of the Statistical Model?
Comparisons between predictions and observations.
What is Stage 6 of the Statistical Model?
Statistical tests are used to check how well the model describes the real-world problem.
What is Stage 7 of the Statistical Model?
Model is refined.
What is a quantitative variable?
A variable associated with numerical observations.
What is a qualitative variable?
A variable associated with non-numerical observations.
What is continuous data?
Data that can take any value on a given range. e.g. height, weight, length etc.
What is discrete data?
Data that can only take specific values. e.g. shoe size, number of people, colour.
What is the formula for Mean from a Frequency Table?
What are the steps in calculating the Mean from a Frequency Table?
1) Add a column for midpoints, x.
2) Multiply the frequencies by midpoints and add to the fx column.
3) Add up the fx column.
4) Divide the sum of the fx column by the total frequency.
How is the Interquartile Range calculated?
Upper Quartile - Lower Quartile
What is the formula for Standard Deviation for a list of numbers?
What are the steps in calculating the Standard Deviation for a list of numbers?
1. Add up all the values of x, this is ∑x
2. Square all the values and add up, this is ∑x²
3. Count the number of values, this is n.
4. Substitute all these values into the formula.
What is the formula for Standard Deviation for a Frequency Table?
What are the steps in calculating the Standard Deviation from a Frequency Table?
1. Calculate the mean.
2. Square all the midpoints and multiply by the frequency. Add up all these values, this is ∑ƒx².
3. Divide ∑ƒx² by the total frequency and subtract the mean squared.
4. Square root.
How is the standard deviation found if you know the variance?
Square root it.
How is the variance found if you know the standard deviation?
Square it.
What does P(A∩B) look like on a Venn Diagram?
What does P(A∪B) look like on a Venn Diagram?
What is the formula for Linear Interpolation?
How is the standardised z calculated?
What is the formula for Var(X)
E(X²) - E(X)²
How is PMCC affected by coding?
It is not affected by coding.
How do you calculate the position of the median for discrete data/list of data?
1. Work out n ÷ 2
2. Round up to nearest whole number if decimal.
3. Round up to next 0.5 if whole number.
How do you calculate the position of the median for grouped data/histograms.
1. Work out n ÷ 2
What is the independent variable also known as?
Explanatory variable
What is the dependent variable also known as?
Response variable
What axis should the independent variable be plotted on?
x-axis
What axis should the dependent variable be plotted on?
y-axis
When PMCC is calculated, what does the answer mean?
It should be between -1 and 1.
If it is negative, there is a negative correlation.
If it is positive, there is a positive correlation.
If it is very close to 0, there is no correlation.
What is Q₀
The lowest value
What is Q₁
The lower quartile
What is Q₂
The Median
What is Q₃
The upper quartile
What is Q₄
The highest value
A box plot should have lines drawn where?
At lowest value, lower quartile, median, upper quartile and highest value.
Unless there is an outlier, and an X is drawn there and the line should be drawn at the next largest/smallest.
What is the formula for Sxx?
This is found in the formula booklet.
What are the steps in calculating Sxx?
1. Square all the values and add this up. This is ∑x²
2. Add up all the values, this is ∑x
3. Square ∑x and divide by the number of values.
4. Subtract that answer from ∑x²
How is an outlier found?
Work out 1.5 x Interquartile Range.
Add this to upper quartile and also subtract it from lower quartile.
Those values are the boundaries for outliers.
What is the formula for Sxy?
This is found in the formula booklet.
What are the steps in calculating Sxy?
1. Multiply each pair of x and y and add these up. That is ∑xy.
2. Add up all the x values and all the y values and multiply these.
3. Divde that answer by n and subtract from ∑xy.
What is the equation of a regression line?
y = a + bx, where a is the y-intercept and b is the gradient.
How is a calculated for the equation of a regression line, y = a + bx.
This is found in the formula booklet.
How is b calculated for the equation of a regression line, y = a + bx.
This is found in the formula booklet.
What is the formula for PMCC?
This is found in the formula booklet.
What are the steps in calculating PMCC?
1. Calculate Sxy, Sxx and Syy
2. Multiply Sxx by Syy and square root.
3. Divide Sxy by that answer.
What is the underlying feature of each bar of a histogram?
The area is proportional to the frequency.
How do you find the height of a bar of a histogram?
For the bar given, find the area and divide by the number of people to find the cm² per person. Use this to calculate the area for the frequency for the group in question. Then work out the height.
What is P(A')
The complement of A.... or "A not happening."
It is found by 1 - P(A)
When does P(A) x P(B) = P(A∩B)?
For independent events.
If two events of independent, what does this mean?
That the outcome of one, does not affect the outcome of the other.
If two events are mutually exclusive, what does this mean?
They cannot happen at the same time.
What does P(A)P(B|A) =
P(A∩B)
What does P(A∪B) equal?
P(A) + P(B) - P(A∩B)
What does P(A∩B) equal?
P(A) + P(B) - P(A∪B)
How is the mean affected by coding?
By the same as the coding.
How is the standard deviation affected by coding?
Adding and subtracting has no affect on the standard deviation.
Multiplying and dividing does affect the standard deviation.
How is variance affected by coding?
Adding and subtracting has no affect on the variance.
Multiplying the numbers by k, means the variance will be multiplied by k².
Dividing the numbers by k, means the variance will be divided by k²
How is E(X) calculated?
Multiply all the x values by the probabilities.
Then add up.
How is E(X) affected by the coding E(aX+b)?
aE(X) + b
How is Var(X) affected by the coding Var(aX+b)?
a²Var(X)
How is E(X²) calculated?
By rearranging Var(X) = E(X²) - E(X)²
How is the class width calculated?
Upper bound minus lower bound.
Be careful if they groups are not 'touching.'
How is the PMCC affected by coding?
The PMCC is not affected by coding
What does a symmetrical distribution look like?
What does a distribution with a positive skew look like?
What does a distribution with a negative skew look like?
How can you show a distribution has a symmetrical skew?
Q₂-Q₁ = Q₃ - Q₂
or
Median = Mean
How can you show a distribution has a positive skew?
Q₂-Q₁ < Q₃ - Q₂
or
Median < Mean
How can you show a distribution has a negative skew?
Q₂-Q₁ > Q₃ - Q₂
or
Median > Mean
What is the P(A|B)?
What does a venn diagram look like for mutually exclusive events?
What does P(A∪B) equal for mutually exclusive events?
P(A) + P(B)
Why is extrapolation bad?
You are estimating a value outside the range of the data. Values estimated can be unreliable.
For a normal distribution X∼N(4,9)
What is the mean? What is the standard deviation?
The mean is 4.
The standard deviation is 3.
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