OpenRevise

Flashcards · Maths

Statistics

80 cards from 5 lessons

  1. How do you calculate the mean?

    Add all the values and divide by the number of values.

  2. How do you find the median?

    Put the values in order and take the middle one, or the mean of the two middle values.

  3. What is the mode?

    The most common value.

  4. What is the range?

    The largest value minus the smallest value.

  5. Which average is affected most by an outlier?

    The mean.

  6. When is the mode the best average?

    For non-numerical data, such as the most popular colour.

  7. What does a smaller range tell you?

    The data is more consistent.

  8. How do you find the mean from a frequency table?

    \(\sum fx\) divided by \(\sum f\).

  9. How do you find the median from a frequency table of \(n\) values?

    Find the \(\dfrac{n + 1}{2}\)th value using cumulative frequencies.

  10. What is the mode in a frequency table?

    The value with the highest frequency.

  11. What is the mid-point of the class \(20 < w \leq 40\)?

    30.

  12. How do you estimate the mean of grouped data?

    Multiply each mid-point by its frequency, add up, and divide by the total frequency.

  13. Why is the mean of grouped data only an estimate?

    The exact values in each class are not known.

  14. Five numbers have a mean of 8. What is their total?

    40.

  15. What is the modal class?

    The class with the highest frequency.

  16. Why should you say "on average" in a comparison?

    The answer is about typical values, not every item.

  17. How do you calculate the angle for a sector of a pie chart?

    Frequency divided by total, multiplied by \(360^\circ\).

  18. How many degrees represent each person in a pie chart of 60 people?

    \(6^\circ\).

  19. How do you find a frequency from an angle?

    Angle divided by 360, multiplied by the total.

  20. What do the angles in a pie chart add up to?

    \(360^\circ\).

  21. What is a dual bar chart?

    A bar chart with two sets of bars side by side for comparing two groups.

  22. What is a stem-and-leaf diagram?

    A diagram that sorts data into stems and leaves while keeping every value.

  23. What must a stem-and-leaf diagram include?

    A key.

  24. How do you find the median from a stem-and-leaf diagram?

    Count to the middle value, or take the mean of the two middle values.

  25. What does the key \(2 \mid 3\) mean when the key says 23?

    The value is 23.

  26. Why should leaves be in order?

    It makes the median, quartiles and range easy to find.

  27. How can a bar chart be misleading?

    The vertical scale may not start at zero, or the bars may have uneven widths.

  28. Why is a 3D pie chart misleading?

    The 3D effect distorts the sizes of the sectors.

  29. What is the range of a data set with the highest value 45 and the lowest 12?

    33.

  30. How do you compare groups of different sizes?

    Use fractions or percentages rather than raw frequencies.

  31. What fraction of a pie chart is a \(90^\circ\) sector?

    \(\dfrac{1}{4}\).

  32. What percentage of a pie chart is a \(54^\circ\) sector?

    15%.

  33. What is a scatter graph?

    A graph that plots pairs of values to show whether two variables are related.

  34. What is positive correlation?

    As one variable increases, so does the other.

  35. What is negative correlation?

    As one variable increases, the other decreases.

  36. What does no correlation look like?

    Scattered points with no pattern.

  37. What is a line of best fit?

    A straight line through the middle of the points, showing the trend.

  38. How should you draw a line of best fit?

    With a ruler, with roughly equal numbers of points above and below and ignoring outliers.

  39. What is an outlier?

    A point that is far from the pattern of the others.

  40. What is interpolation?

    Estimating a value inside the range of the data.

  41. What is extrapolation?

    Estimating a value outside the range of the data.

  42. Why is extrapolation unreliable?

    The trend may not continue.

  43. Does correlation prove one thing causes another?

    No.

  44. What does the gradient of a line of best fit mean?

    The change in the vertical variable for each unit increase in the horizontal variable.

  45. What does the \(y\)-intercept of a line of best fit mean?

    The estimated value when the horizontal variable is zero.

  46. The line \(y = 4x + 8\) estimates the score for 12 hours of revision as?

    \(4 \times 12 + 8 = 56\).

  47. Why is a larger sample better?

    The line and correlation are more trustworthy.

  48. How should you describe correlation in an exam?

    Use the variable names, such as "as age increases, value decreases".

  49. What is cumulative frequency?

    A running total of frequencies.

  50. Where do you plot cumulative frequency points?

    At the upper boundary of each class.

  51. What is the first point on a cumulative frequency graph?

    The lowest value, with a cumulative frequency of 0.

  52. What is the median on a cumulative frequency graph of \(n\) values?

    The value at cumulative frequency \(\dfrac{n}{2}\).

  53. Where is the lower quartile?

    At cumulative frequency \(\dfrac{n}{4}\).

  54. Where is the upper quartile?

    At cumulative frequency \(\dfrac{3n}{4}\).

  55. What is the interquartile range?

    The upper quartile minus the lower quartile.

  56. Why is the interquartile range useful?

    It is not affected by extreme values.

  57. How do you find how many values are above 80 on a cumulative frequency graph?

    Read the cumulative frequency at 80 and subtract it from the total.

  58. What five numbers does a box plot show?

    Minimum, lower quartile, median, upper quartile and maximum.

  59. What does the box in a box plot cover?

    The middle half of the data, from the lower to the upper quartile.

  60. What does a smaller interquartile range mean?

    The data is more consistent.

  61. How should you compare two distributions?

    Compare a median and a measure of spread, with numbers and in context.

  62. What is the 90th percentile of 100 values?

    The value at cumulative frequency 90.

  63. Why draw construction lines on a graph?

    They show the method and earn the marks.

  64. What should the last point on a cumulative frequency graph equal?

    The total number of values.

  65. What is the formula for frequency density?

    Frequency divided by class width.

  66. What does the area of a bar in a histogram represent?

    The frequency.

  67. How do you find a frequency from a histogram bar?

    Frequency density multiplied by class width.

  68. What label goes on the vertical axis of a histogram?

    Frequency density.

  69. Why are there no gaps between the bars of a histogram?

    The data is continuous.

  70. How do you estimate the frequency in part of a class?

    Take that fraction of the class's frequency.

  71. What is a population?

    Everyone or everything you want to know about.

  72. What is a sample?

    The part of the population that you actually measure.

  73. What is a biased sample?

    One where some members of the population are more likely to be chosen than others.

  74. What is a random sample?

    One where every member has an equal chance of being chosen.

  75. What is a stratified sample?

    A sample with each group represented in proportion to its size.

  76. How do you find the number from a group in a stratified sample?

    Group size divided by population size, times the sample size.

  77. What is the capture-recapture formula?

    \(N = \dfrac{M \times n}{m}\).

  78. 50 fish are marked, and a sample of 40 has 8 marked. What is the population estimate?

    \(\dfrac{50 \times 40}{8} = 250\).

  79. What assumption does capture-recapture make?

    The marked animals mix evenly and the population does not change.

  80. Why does a larger sample usually give a better estimate?

    It is more likely to represent the whole population.