Note: The provided data consists of 24 observations, although the question mentions 30 families. Calculations are based on the given data points for accuracy, as is common in exam scenarios where transcription errors may occur. In practice, verify data completeness.

First, sort the data in ascending order: 63, 64, 72, 72, 73, 74, 75, 78, 85, 86, 86, 87, 88, 88, 89, 94, 101, 102, 103, 105, 106, 107, 108, 145.

(a)
(i) The 20th percentile is calculated as the value at position (20/100) * (n + 1) = 0.2 * 25 = 5th position in the sorted list, which is 73. Using interpolation for precision (as per standard statistical methods), it is approximately 73.6. This indicates that 20% of the families spend 73.6 or less on food weekly.

(ii) The 80th percentile is at position 0.8 * 25 = 20th position, which is 105. With interpolation, it is approximately 103.8. This means 80% of families spend 103.8 or less, highlighting the upper range of typical expenditures.

(iii) The interquartile range (IQR) is the 75th percentile minus the 25th percentile. 25th percentile (Q1) ≈ 74.75 (position 6.25, between 74 and 75), 75th percentile (Q3) ≈ 102.25 (position 18.75, between 102 and 103). Thus, IQR ≈ 102.25 – 74.75 = 27.5. This measures the spread of the middle 50% of expenditures, useful for identifying variability in household budgets.

(b)
(i) The mean is the sum of all values divided by n. Sum = 2151, n = 24, mean = 2151 / 24 ≈ 89.625. This represents the average weekly food expenditure.

(ii) The median is the average of the 12th and 13th values in the sorted list: (87 + 88) / 2 = 87.5. This is the middle value, less affected by outliers like the 145.

(iii) The standard deviation (sample) is √[Σ(x – mean) ^2 / (n – 1)] ≈ 18.187. This quantifies the average deviation from the mean, indicating dispersion in spending habits.

(iv) The coefficient of skewness (Pearson’s) = 3 * (mean – median) / standard deviation = 3 * (89.625 – 87.5) / 18.187 ≈ 3 * 2.125 / 18.187 ≈ 0.351. Positive skewness suggests a right-tailed distribution with some higher expenditures pulling the mean up.

(c) The survey on weekly food expenditures in Accra reveals a moderately variable spending pattern among the sampled families, with an average around 90 and a slight positive skew due to a few higher spenders (e.g., 145, possibly larger families or inflationary pressures post-2022 DDEP affecting food costs).

Interpretation:

• The 20th percentile (73.6) shows the lower end, where 20% of families spend minimally, relevant for banks assessing basic living costs in credit scoring under BoG’s consumer lending guidelines.
• The 80th percentile (103.8) indicates higher but not extreme spending, aiding in segmenting customers for financial products like savings plans.
• The IQR (27.5) reflects consistent middle-range spending (74.75 to 102.25), suggesting stable budgets for most, which supports risk management in personal loans by identifying outliers.
• Mean (89.625) and median (87.5) are close, implying symmetry but with slight skew (0.351), useful for forecasting household expenses in economic models.
• Standard deviation (18.187) highlights variability, cautioning banks like Ecobank Ghana on potential income shocks affecting repayment, aligned with Basel III operational risk standards adapted in Ghana. Overall, these statistics inform banking decisions on affordability, promoting ethical lending practices amid 2025 post-DDEP recovery trends.