Equations Flashcards
What does the capture-recapture method represent in ecology?
π = mN/n
Where π is the total population, π is the original marked, π is the new marked.
How is frequency density calculated in histograms?
Frequency density = frequency/class width
The area of the bar represents the frequency.
What is the formula for the mean (π₯Μ )?
Mean (π₯Μ ) = βπ₯/n
Where βπ₯ is the sum of all values and n is the number of values.
Define weighted mean.
Weighted mean = β(value Γ weight)
It accounts for the importance of different values.
What is the formula for standard deviation (not table)?
Standard deviation = β(βπ₯Β² - (n/n)Β²)
This formula calculates the spread of data points.
How do you calculate standard deviation for a frequency table?
Standard deviation = β(βπ(π₯βπ₯Μ )Β²)
Where π is frequency and π₯Μ is the mean.
What defines a small outlier?
Small outlier is less than LQ - (1.5 Γ IQR)
LQ is the lower quartile and IQR is the interquartile range.
What defines a large outlier?
Large outlier is greater than UQ + (1.5 Γ IQR)
UQ is the upper quartile.
In a positively skewed distribution, how are mean, median, and mode ordered?
mean > median > mode
This reflects the rightward tail of the distribution.
In a negatively skewed distribution, how are mean, median, and mode ordered?
mode > median > mean
This reflects the leftward tail of the distribution.
What is the formula for skewness?
Skew = 3(mean - median)
It quantifies the asymmetry of the distribution.
What does a box plot display?
Min, LQ, Median, UQ, Max
It summarizes the distribution of a dataset.
What is the equation of the line of best fit?
y = ax + b
Where a is the gradient and b is the y-intercept.
What does Spearmanβs rank correlation coefficient measure?
6βπΒ²/(π(πΒ² - 1))
It assesses the strength of association between two ranked variables.
How is seasonal variation at a point calculated?
Seasonal variation = actual value - trend value
This reflects the deviation from a trend.
What is the formula for expected frequency of event A?
Expected frequency A = P(A) Γ number of trials
This calculates how often an event is expected to occur.
How is risk of an event estimated?
Risk = number of trials with successful outcomes/total number of trials
This gives the likelihood of an event occurring.
What is the formula for mutually exclusive events A and B?
P(A βͺ B) = P(A) + P(B)
This applies when events cannot occur at the same time.
What is the general addition law for not mutually exclusive events?
P(A βͺ B) = P(A) + P(B) - P(A β© B)
This accounts for overlapping probabilities.
What is the formula for independent events A and B?
P(A β© B) = P(A) Γ P(B)
This applies to events where the occurrence of one does not affect the other.
What is conditional probability?
P(B|A) = P(A β© B)/P(A)
It is the probability of B given A has occurred.
What are index numbers calculated as?
Index numbers = (price/base year price) Γ 100
They measure relative changes in price levels.
What is the formula for weighted index numbers?
Weighted index numbers = (current weighted mean price/base year weighted mean price) Γ 100
It reflects the importance of different items in the index.
What does the normal distribution describe?
68% Β± one standard deviation, 95% Β± two standard deviations, 99.8% Β± three standard deviations
It indicates the spread of values around the mean.
What are warning limits in statistics?
Warning limits = ΞΌ Β± 2Ο
They signal potential issues in data.
What are action limits in statistics?
Action limits = ΞΌ Β± 3Ο
They indicate when corrective action is necessary.
What does the binomial distribution represent?
Binomial distribution = B(n, p)
It models the number of successes in n trials.
What is the mean of a binomial expansion?
Mean of binomial expansion = n Γ p
It determines the expected number of successes.
What does normal distribution N(ΞΌ, ΟΒ²) indicate?
Mean (ΞΌ) and variance (ΟΒ²)
It describes the parameters of the distribution.
How is variance calculated?
Variance = (standard deviation - Ο)Β²
It measures the spread of data points.
What is stated about GCSE statistics formulae?
Formulae in green boxes are given in the exam
Refer to your Revision Guide for all topics.
