Statistics
Term 3
Descriptive measures · Boxplots · Cumulative frequency
Objectifs d'apprentissage
ImprimerDescriptive Measures
- 1. Calculate the mean, median and mode of an ungrouped data set.
- 2. Estimate the mean of a grouped frequency distribution using midpoints.
- 3. Identify the modal class and median class of a grouped distribution.
- 4. Calculate measures of variability: range, interquartile range (IQR) and standard deviation (using technology).
- 5. Discuss the effect of outliers on the mean, median and standard deviation.
Representations: Histograms and Cumulative Frequency
- 6. Construct a frequency histogram and a relative-frequency histogram for grouped data.
- 7. Construct a cumulative frequency table from a grouped frequency distribution.
- 8. Draw a cumulative frequency curve (ogive) and use it to estimate the median, quartiles and percentiles.
- 9. Construct a box-and-whisker plot from a five-number summary.
- 10. Use the $1.5 \times \text{IQR}$ rule to identify potential outliers from a boxplot.
Shape, Skew and Comparison
- 11. Describe the shape of a distribution as symmetric, positively skewed or negatively skewed.
- 12. Predict the effect of skew on the relative positions of the mean and median.
- 13. Compare two distributions using measures of centre, spread and shape.
- 14. Use boxplots side by side to compare two data sets.
- 15. Justify which measure of centre and which measure of spread are most appropriate for a given data set.
Évaluations
Univariate statistics end-of-unit test
Critère A
50 min
Written test on calculating descriptive measures (mean, median, mode, quartiles, standard deviation), drawing and interpreting boxplots, and using cumulative frequency curves.
Statistical data report
Critère C
60 min
Students are given a small dataset, choose appropriate summary statistics and a chart to display it, and write a short report that communicates the main features of the data using correct statistical vocabulary.
Pack de révision
Ouvrir le hub de révision
Fluency Pack A — 40 questions
Fluency Pack B — 40 questions
Problem-solving — 12 unfamiliar tasks
Worked solutions (Pack A + B + problems)