Descriptive Statistics

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Primary data is collected directly from the field or individuals through surveys, observations, or case studies. Example: A teacher measuring students' heights directly. Secondary data is taken from

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(a) Univariate data - involves only one variable (height) (b) Bivariate data - involves two variables (age and height) (c) Multivariate data - involves more than two variables (cost, labor, marketing,

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The four scales of measurement in order from least to most informative: 1. Nominal - Categories with no order (e.g., gender, religion) 2. Ordinal - Categories with order but no equal intervals (e.g.,

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Histogram: - Used for continuous data (class intervals) - No gaps between bars - Area of bars represents frequency - Shows distribution of quantitative data Bar Graph: - Used for categorical/discrete

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Using direct method: x̄ = Σfᵢxᵢ/Σfᵢ Calculation: Σfᵢxᵢ = (10×2) + (15×4) + (20×6) + (25×3) + (30×5) = 20 + 60 + 120 + 75 + 150 = 425 Σfᵢ = 2 + 4 + 6 + 3 + 5 = 20 Mean = 425/20 = 21.25 The a

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Median = l + [(n/2 - cf)/f] × h Where: l = lower limit of median class n = total number of observations cf = cumulative frequency of class preceding median class f = frequency of median class h = cla

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Mode = 5 (appears 3 times, most frequent) This is a unimodal distribution because it has only one mode. Types of modal distributions: - Unimodal: one mode (like this example) - Bimodal: two modes -

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For unimodal frequency distributions: Mean - Mode = 3(Mean - Median) This relationship helps in: - Estimating one measure when others are known - Checking calculations for consistency - Understandin