Sample paper
Word Count: approximately 700 words
Question 1: Population, Sample, Variable Classification, and Class Width
The population is all primary school students in Hong Kong; the sample is students from three randomly selected primary schools who completed the reading-habits questionnaire. Four survey variables are classified: main purpose of reading (qualitative, nominal), time spent reading per week (quantitative, continuous, ratio), reading frequency per week (quantitative, discrete, ordinal), and preferred reading location (qualitative, nominal). Using a personalised dataset with minimum 0.2 and maximum (5 + 0.1T), the range is (5 + 0.1T) - 0.2, and dividing by 4 classes yields a final class width of 1.2 + 0.025T.
Question 2: Descriptive Statistics and Frequency Distribution Analysis
Part (a): From histogram data, the median is 75.5 and the mode is 80; summing four class-interval frequencies (71-75: 3, 75-79: 10, 79-83: 7, 83-87: 5) gives 25 students spending more than HK$70.
Part (b) -- MTra descriptive statistics: Range = 86 - 57 = 29. Pearson's first coefficient of skewness = 3 x (Mean - Median) / SD = 3 x (73.58 - 75.5) / 8.04 = -0.72, indicating a negative (left-skewed) distribution. Coefficient of variation = (SD / Mean) x 100 = (8.04 / 73.58) x 100 = 10.9%.
Part (c) -- MLun descriptive statistics: Quartiles from Python output are Q1 = 35.125, Q2 (median) = 39.1, and Q3 = 43.725, with no outliers detected via boxplot. A 10% trimmed mean calculation removes the 4 smallest (26.3, 27.1, 28.5, 30.7) and 4 largest (45.5, 46.2, 46.5, 47.2) of 40 total values, computing the trimmed sum from the original 36-value mean (38.71) minus the trimmed values' sum (298), yielding a trimmed mean of 1203.56 / 32 = 37.61.
Part (d) -- Cumulative frequency table analysis: Solving for an unknown class frequency parameter (W) using the constraint that all class frequencies sum to 36 yields W = 0, confirming the table's original frequencies (4, 4, 2, 14, 12 across five class intervals). Using these frequencies and midpoints, the sample mean is computed as Σ(f×x)/n = 1434/36 = 39.83, and the sample variance as Σf(x-mean)²/(n-1) = 1115.66/35 = 31.88.
Conclusion
The assignment demonstrates a complete grouped-data descriptive statistics workflow -- from population/sample definition and variable classification through skewness, variation, quartile, trimmed mean, and cumulative-frequency-based mean and variance estimation -- applied to a primary school reading habits survey dataset.
References
No formal reference list was required for this problem set.