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Ultimate AS Statistics True False Quiz (Set 1)

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  • Opportunity sampling is unbiased
    False – It is prone to bias because it depends on who is available.
  • The expected value of a discrete random variable is its mean
    True – It's the long-run average.
  • The standard deviation measures the average deviation from the mean
    True – It's a common measure of spread.
  • In a binomial distribution, the number of trials must be fixed
    True – That’s part of the definition.
  • Using a large sample eliminates all bias
    False – It reduces random error but doesn’t prevent systematic bias.
  • A binomial variable can take any real value
    False – It takes whole numbers between 0 and n.
  • A skewed distribution has mean = median = mode
    False – That’s true for a symmetric distribution, not skewed ones.
  • Histograms display grouped continuous data using frequency
    False – Histograms use frequency density, not frequency.
  • A fair six-sided die has a probability of 1/3 of rolling an even number
    True – Even numbers are 2, 4, 6 → 3 outcomes.
  • The range is always smaller than the interquartile range
    False – The range is usually larger as it covers the entire spread.
  • A frequency polygon is a graph of grouped data using lines instead of bars
    True – It's a line graph joining midpoints.
  • If a spinner has 3 equal sections, the probability of each is 1/3
    True – Equal sections mean equal probabilities.
  • The sample mean is a statistic
    True – A statistic is any calculated measure based on sample data.
  • If events A and B are independent, P(A and B) = P(A) + P(B)
    False – For independence: P(A and B) = P(A) × P(B).
  • In a probability distribution, the sum of all probabilities must equal 1
    True – That’s a key requirement.
  • The probability of a certain event is 1
    True – A certain event has a probability of 1.
  • Stratified sampling involves dividing the population into groups and sampling proportionally
    True – That’s the definition.
  • The probability of success in a binomial distribution must stay constant
    True – It’s required for binomial assumptions.
  • In a binomial distribution B(n, p), the variance is given by np(1 – p)
    True – That’s the standard formula.
  • If all values in a data set are increased by 5, the variance stays the same
    True – Adding a constant doesn’t change spread.
  • The interquartile range is affected by extreme values
    False – It’s resistant to outliers as it focuses on the middle 50%.
  • Probability trees are useful for showing dependent events
    True – They help visualise conditional probabilities.
  • Discrete data can only take specific values
    True – Like shoe sizes, test scores, etc.
  • Continuous data can take any value in a given range
    True – Like time, weight, etc.
  • The binomial distribution is used when there are more than two outcomes
    False – It applies to two outcomes only (success/failure).
  • A sample always gives the exact same results as a census
    False – A sample involves variation and can differ from the true population.
  • The complement of event A is the event that A does not occur
    True – Denoted as A′.
  • P(A or B) = P(A) + P(B) for any events A and B
    False – Only if they’re mutually exclusive. Otherwise subtract the overlap.
  • In statistics, a model is used to represent real-life data more simply
    True – Statistical models simplify reality.
  • Cumulative frequency diagrams are useful for estimating medians
    True – They're used to estimate median, quartiles, etc.
  • The median is always halfway between the smallest and largest value
    False – The median is the middle value when data is ordered, not necessarily the midpoint.
  • A simple random sample gives every member of the population an equal chance
    True – Key characteristic of simple random sampling.
  • The mean is affected by extreme values
    True – Outliers can significantly influence the mean.
  • The probability of an impossible event is 0
    True – That defines an impossible outcome.
  • Box plots can show outliers
    True – They indicate outliers with separate marks.
  • The interquartile range is a measure of spread
    True – It shows the range of the middle 50% of the data.
  • The median is less affected by outliers than the mean
    True – It’s more robust for skewed data.
  • A positively skewed distribution has a longer tail on the left
    False – It has a longer tail on the right.
  • A census collects data from a sample
    False – A census gathers data from the entire population.
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