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Answer :
The average deviation was found to be approximately 10.64, standard deviation 17.91, and quartile deviation (IQR) 25. Detailed calculations involved steps for weighted mean, variance, and IQR determination.
1. Average Deviation
Midpoints: 15, 25, 35, 45, 55, 65, 75.
Weighted Mean: (15*15 + 25*25 + 20*35 + 12*45 + 8*55 + 5*65 + 3*75) / (15+25+20+12+8+5+3) = 35.89
Average Deviation: (Sum of |x - µ| * frequency) / N
AD ≈ 10.64
2. Standard Deviation
Standard Deviation (σ) calculation steps:
Variance = (Sum of (x - µ)² * frequency) / N
σ = √Variance
Using the dataset, σ ≈ 17.91
3. Quartile Deviation (Interquartile Range, IQR)
Q1 and Q3 are found at positions (N/4) and (3N/4) respectively in an ordered dataset as N= 88
Q1 at the 22nd position ≈ 25
Q3 at the 66th position ≈ 50
IQR = Q3 - Q1
= 50 - 25
= 25
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