GCSE Statistics flashcards
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32 cards. Read the term and the definition here. The deck at the top of this page is optional.
- Simple random sample
- A sample in which every member of the population has an equal chance of being selected and each selection is independent; a sampling frame listing the whole population is required.
- Systematic sample
- A sample taken by selecting every kth item from an ordered list after a random start, where k equals the population size divided by the sample size.
- Stratified sample
- The population is divided into groups called strata, and the number sampled from each stratum is proportional to its size, so the sample reflects the population's structure.
- Quota sampling
- An interviewer fills fixed target numbers of respondents in each subgroup. Selection inside each quota is not random, so the resulting sample may be biased.
- Capture-recapture estimate
- Estimated population size = (first sample size × second sample size) ÷ number of marked individuals found in the second sample. It assumes the population is closed and marks are not lost.
- Census
- A survey in which every member of the population is measured. It gives exact results but is expensive, slow and often impractical for large populations.
- Frequency density
- In a histogram with unequal class widths, frequency density = frequency ÷ class width, so the area of each bar is proportional to the frequency it represents.
- Cumulative frequency
- The running total of frequencies up to a given value. It is plotted against upper class boundaries to estimate the median, quartiles and interquartile range.
- Class mid-point
- The value halfway between the lower and upper boundaries of a class, calculated as (lower + upper) ÷ 2 and used to represent every value in the class when estimating a mean.
- Two-way table
- A table showing counts for two categorical variables, with row and column totals, allowing the distribution of one variable to be compared within categories of the other.
- Pie chart angle
- The sector angle for a category equals its frequency divided by the total frequency, then multiplied by 360 degrees; all sector angles add up to 360 degrees.
- Mean
- The sum of all values divided by the number of values. For grouped data, multiply each frequency by its class mid-point, sum these and divide by the total frequency.
- Median
- The middle value when the data are arranged in order. When the number of values is even, it is the mean of the two middle values.
- Interquartile range
- The upper quartile minus the lower quartile. It measures the spread of the middle 50% of the data and is not affected by extreme values.
- Standard deviation
- A measure of spread describing the typical distance of values from the mean. It uses every value but is strongly affected by outliers.
- Outlier test (1.5 × IQR)
- A value is treated as an outlier if it lies below lower quartile − 1.5 × interquartile range, or above upper quartile + 1.5 × interquartile range.
- Combined mean
- For two groups, the combined mean = (n₁ × mean₁ + n₂ × mean₂) ÷ (n₁ + n₂), where n₁ and n₂ are the numbers of values in each group.
- Line of best fit
- A straight line drawn through a scatter diagram that passes through the mean point of the data and has roughly equal numbers of points above and below it.
- Positive correlation
- A relationship in which the response variable tends to increase as the explanatory variable increases, so the points on the scatter diagram slope upwards from left to right.
- Extrapolation
- Using a line of best fit to predict a value outside the range of the observed data. It is unreliable because the relationship may not continue in the same way.
- Spearman's rank coefficient
- r_s = 1 − 6Σd² ÷ (n(n² − 1)), where d is the difference between the ranks of each pair and n is the number of pairs of data.
- Correlation and causation
- A strong correlation between two variables does not prove that changes in one cause changes in the other; a third variable may be influencing both.
- Trend
- The underlying long-term direction of a time series once short-term and seasonal fluctuations have been smoothed out, usually by means of a moving average.
- Seasonal variation
- A regular pattern in a time series that repeats over a fixed period, such as a year, measured as the difference between the actual value and the trend value.
- Centred moving average
- For an even number of points per cycle, the average of two consecutive moving averages. It lines up with an actual data point so seasonal components can be calculated.
- Time series forecast
- Predicted value = trend value for that period plus the mean seasonal component for that period. The forecast is only reliable for periods close to the data.
- Complement rule
- The probability that an event does not happen equals 1 minus the probability that it does happen, written P(not A) = 1 − P(A).
- Mutually exclusive events
- Events that cannot occur at the same time. For such events the addition rule applies: P(A or B) = P(A) + P(B).
- Independent events
- Events where the outcome of one does not change the probability of the other. For independent events, P(A and B) = P(A) × P(B).
- Relative frequency
- An estimate of probability obtained from data: the number of times an event occurred divided by the number of trials. It becomes more reliable as the number of trials increases.
- Expected frequency
- The number of times an event is expected to occur, calculated as the number of trials multiplied by the probability of the event happening.
- Conditional probability
- The probability of an event given that another event has already happened, written P(A | B), and calculated within the reduced set of possible outcomes.