Weighted Average
1. The problem is to calculate the weighted average and percentage score for each feedback parameter, then find the overall average and overall percentage.
2. The formula for weighted average for each parameter is:
$$\text{Weighted Average} = \frac{(4 \times \text{count of 4}) + (3 \times \text{count of 3}) + (2 \times \text{count of 2}) + (1 \times \text{count of 1})}{\text{total responses}}$$
3. The percentage score is calculated by:
$$\text{Percentage} = \frac{\text{Weighted Average}}{4} \times 100$$
4. Calculate for each parameter:
- Parameter 1: Total responses = 16+3+3+0=22
Weighted Average = $\frac{(4\times16)+(3\times3)+(2\times3)+(1\times0)}{22} = \frac{64+9+6+0}{22} = \frac{79}{22} \approx 3.59$
Percentage = $\frac{3.59}{4} \times 100 = 89.55\%$
- Parameter 2: Total = 14+7+1+0=22
Weighted Average = $\frac{(4\times14)+(3\times7)+(2\times1)+(1\times0)}{22} = \frac{56+21+2+0}{22} = \frac{79}{22} \approx 3.59$
Percentage = $89.55\%$
- Parameter 3: Total = 15+4+3+0=22
Weighted Average = $\frac{(4\times15)+(3\times4)+(2\times3)+(1\times0)}{22} = \frac{60+12+6+0}{22} = \frac{78}{22} \approx 3.55$
Percentage = $88.64\%$
- Parameter 4: Total = 12+6+4+0=22
Weighted Average = $\frac{(4\times12)+(3\times6)+(2\times4)+(1\times0)}{22} = \frac{48+18+8+0}{22} = \frac{74}{22} \approx 3.36$
Percentage = $84.09\%$
- Parameter 5: Total = 14+5+3+0=22
Weighted Average = $\frac{(4\times14)+(3\times5)+(2\times3)+(1\times0)}{22} = \frac{56+15+6+0}{22} = \frac{77}{22} \approx 3.50$
Percentage = $87.73\%$
- Parameter 6: Total = 14+6+2+0=22
Weighted Average = $\frac{(4\times14)+(3\times6)+(2\times2)+(1\times0)}{22} = \frac{56+18+4+0}{22} = \frac{78}{22} \approx 3.55$
Percentage = $88.64\%$
- Parameter 7: Total = 12+6+3+1=22
Weighted Average = $\frac{(4\times12)+(3\times6)+(2\times3)+(1\times1)}{22} = \frac{48+18+6+1}{22} = \frac{73}{22} \approx 3.32$
Percentage = $83.18\%$
- Parameter 8: Total = 13+7+2+0=22
Weighted Average = $\frac{(4\times13)+(3\times7)+(2\times2)+(1\times0)}{22} = \frac{52+21+4+0}{22} = \frac{77}{22} \approx 3.50$
Percentage = $87.73\%$
- Parameter 9: Total = 17+4+1+0=22
Weighted Average = $\frac{(4\times17)+(3\times4)+(2\times1)+(1\times0)}{22} = \frac{68+12+2+0}{22} = \frac{82}{22} \approx 3.73$
Percentage = $93.18\%$
- Parameter 10: Total = 13+7+2+0=22
Weighted Average = $\frac{(4\times13)+(3\times7)+(2\times2)+(1\times0)}{22} = \frac{52+21+4+0}{22} = \frac{77}{22} \approx 3.50$
Percentage = $87.73\%$
- Parameter 11: Total = 16+3+3+0=22
Weighted Average = $\frac{(4\times16)+(3\times3)+(2\times3)+(1\times0)}{22} = \frac{64+9+6+0}{22} = \frac{79}{22} \approx 3.59$
Percentage = $89.55\%$
- Parameter 12: Total = 15+5+2+0=22
Weighted Average = $\frac{(4\times15)+(3\times5)+(2\times2)+(1\times0)}{22} = \frac{60+15+4+0}{22} = \frac{79}{22} \approx 3.59$
Percentage = $89.55\%$
- Parameter 13: Total = 16+4+2+0=22
Weighted Average = $\frac{(4\times16)+(3\times4)+(2\times2)+(1\times0)}{22} = \frac{64+12+4+0}{22} = \frac{80}{22} \approx 3.64$
Percentage = $90.91\%$
- Parameter 14: Total = 12+5+4+1=22
Weighted Average = $\frac{(4\times12)+(3\times5)+(2\times4)+(1\times1)}{22} = \frac{48+15+8+1}{22} = \frac{72}{22} \approx 3.27$
Percentage = $81.82\%$
- Parameter 15: Total = 17+4+1+0=22
Weighted Average = $\frac{(4\times17)+(3\times4)+(2\times1)+(1\times0)}{22} = \frac{68+12+2+0}{22} = \frac{82}{22} \approx 3.73$
Percentage = $93.18\%$
5. Calculate overall average weighted average:
$$\text{Overall Average} = \frac{\sum \text{Weighted Averages}}{15} = \frac{3.59+3.59+3.55+3.36+3.50+3.55+3.32+3.50+3.73+3.50+3.59+3.59+3.64+3.27+3.73}{15} \approx \frac{53.42}{15} = 3.56$$
6. Calculate overall percentage:
$$\text{Overall Percentage} = \frac{3.56}{4} \times 100 = 89.11\%$$
Final answers:
- Weighted averages and percentages for each parameter as above.
- Overall average weighted average = 3.56
- Overall percentage = 89.11\%