1. **Problem statement:** We are given population data by age category along with births, immigrants, emigrants, marriages, and deaths. We need to calculate various fertility, migration, and marriage rates. 2. **Given data:** - Population 0-14: 100000 - Population 15-25: 98345 - Population 25-30: 96963 - Population 30-35: 94948 - Population 35-40: 92252 - Population 45-49: 87080 - Population 50-55: 54584 - Population 56-60: 41587 - Population 0-4: 11000 (i) **General Fertility Rate (GFR):** GFR is the number of births per 1000 women of reproductive age (usually 15-49). Sum births in reproductive ages (15-49): $$1655 + 818 + 686 + 1254 + 2183 + 4702 = 11298$$ Sum female population 15-49: $$98345 + 96963 + 94948 + 92252 + 87080 = 469588$$ Calculate GFR: $$GFR = \frac{\text{Total births}}{\text{Female population 15-49}} \times 1000 = \frac{11298}{469588} \times 1000 \approx 24.06$$ (ii) **Age Specific Net Migration:** Net migration = Immigrants - Emigrants for each age group. Calculate for each age group: - 0-14: $1650 - 1400 = 250$ - 15-25: $880 - 600 = 280$ - 25-30: $700 - 300 = 400$ - 30-35: $1300 - 1000 = 300$ - 35-40: $2200 - 1200 = 1000$ - 45-49: $4600 - 33000 = -28400$ - 50-55: $12800 - 0 = 12800$ - 56-60: $11000 - 8000 = 3000$ (iii) **Total Fertility Rate (TFR) for age categories 15-25, 35-40, 45-49:** TFR is the sum of age-specific fertility rates multiplied by the width of age intervals (usually 5 years). Age-specific fertility rate (ASFR) = births / female population in age group Calculate ASFR: - 15-25: $\frac{818}{98345} \approx 0.00832$ - 35-40: $\frac{2183}{92252} \approx 0.02366$ - 45-49: $\frac{4702}{87080} \approx 0.054} TFR = $5 \times (0.00832 + 0.02366 + 0.054) = 5 \times 0.086 = 0.43$ (iv) **Age Standardized Fertility Rate (ASFRate) for 15-25, 35-40, 45-49:** Use a standard population to weight the ASFRs. Assume standard population weights $w_i$ for these age groups (not given, so assume equal weights for simplicity: $w_i = \frac{1}{3}$). Calculate: $$ASFRate = \sum w_i \times ASFR_i = \frac{1}{3}(0.00832 + 0.02366 + 0.054) = 0.02866$$ (v) **Age Standardized Marriage Rate for 15-25, 35-40, 45-49:** Marriage rate = marriages / population in age group Calculate marriage rates: - 15-25: $\frac{13000}{98345} \approx 0.1321$ - 35-40: $\frac{12000}{92252} \approx 0.1300$ - 45-49: $\frac{12500}{87080} \approx 0.1435$ Age standardized marriage rate (equal weights): $$\frac{1}{3}(0.1321 + 0.1300 + 0.1435) = 0.1352$$ (vi) **Age Standardized Migration Rate for 15-25, 35-40, 45-49:** Net migration rate = net migration / population Calculate net migration: - 15-25: $880 - 600 = 280$ - 35-40: $2200 - 1200 = 1000$ - 45-49: $4600 - 33000 = -28400$ Migration rates: - 15-25: $\frac{280}{98345} \approx 0.00285$ - 35-40: $\frac{1000}{92252} \approx 0.01084$ - 45-49: $\frac{-28400}{87080} \approx -0.3261$ Age standardized migration rate: $$\frac{1}{3}(0.00285 + 0.01084 - 0.3261) = -0.1048$$ (vii) **Sex/Age Standardized Marriage Rate:** Data for sex-specific population or marriages is not provided, so cannot calculate precisely. **Final answers:** - (i) General Fertility Rate $\approx 24.06$ births per 1000 women - (ii) Age Specific Net Migration: see values above - (iii) Total Fertility Rate $\approx 0.43$ - (iv) Age Standardized Fertility Rate $\approx 0.0287$ - (v) Age Standardized Marriage Rate $\approx 0.1352$ - (vi) Age Standardized Migration Rate $\approx -0.1048$ - (vii) Sex/Age Standardized Marriage Rate: insufficient data