Measures of central tendency — A/L Combined Mathematics

Measures of central tendency summarize a data distribution by identifying a single representative central location: (1) Mean (Arithmetic Average): x̄ = (∑ f_i x_i) / N, or using an assumed mean A with deviation d_i = x_i - A: x̄ = A + (∑ f_i d_i) / N (or with step-deviation u_i = d_i / c: x̄ = A + c (∑ f_i u_i) / N); (2) Median: The middle observation dividing sorted data into two equal halves. For grouped data: Median = L + [(N/2 - F) / f_m] × c (where L is lower class boundary, F is cumulative frequency of preceding class, f_m is median class frequency, c is class width); (3) Mode: The most frequently occurring value. For grouped data: Mode = L + [Δ₁ / (Δ₁ + Δ₂)] × c.

Check before you answer (A/L Applied Maths Paper 2)

1. Assumed Mean Method Application: Correctly setting up columns for midpoints x_i, deviations d_i (or u_i), and products f_i d_i.
2. Grouped Median Formula Execution: Identifying the median class containing N/2 observation and using lower class boundary L (not limit).
3. Skewness Comparison: Comparing Mean, Median, and Mode to assess distribution skewness: Mean = Median = Mode (Symmetric); Mean > Median > Mode (Positive Skew); Mean < Median < Mode (Negative Skew).