Answer:
Explanation:
To find the quartile deviation, we first need to calculate the first quartile (Q1) and the third quartile (Q3) of the data. The quartile deviation is then given by the formula:
Quartile Deviation = (Q3 - Q1) / 2
To find Q1 and Q3, we first need to calculate the cumulative frequency for each class interval. The cumulative frequency is the sum of the frequencies up to that point. Then, we can find Q1 and Q3 using the formula:
Q1 = L + (N/4 - F) * C
Q3 = L + (3N/4 - F) * C
Where:
L = Lower boundary of the class interval containing Q1 or Q3
N = Total number of data points (sum of frequencies)
F = Cumulative frequency of the class interval before Q1 or Q3
C = Width of the class interval
Now, let's calculate Q1 and Q3 step by step:
Calculate the cumulative frequencies:
Cumulative frequency for the first interval (30-40) = 50
Cumulative frequency for the second interval (40-50) = 50 + 54 = 104
Cumulative frequency for the third interval (50-60) = 104 + 85 = 189
Cumulative frequency for the fourth interval (60-70) = 189 + 45 = 234
Cumulative frequency for the fifth interval (70-80) = 234 + 30 = 264
Find Q1:
N = 264 (total number of workers)
Q1 falls in the second interval (40-50).
L = 40 (lower boundary of the second interval)
F = 50 (cumulative frequency before Q1)
C = 10 (width of the class interval)
Q1 = 40 + (264/4 - 50) * 10
Q1 = 40 + (66 - 50) * 10
Q1 = 40 + 160
Q1 = 200
Find Q3:
N = 264 (total number of workers)
Q3 falls in the fourth interval (60-70).
L = 60 (lower boundary of the fourth interval)
F = 189 (cumulative frequency before Q3)
C = 10 (width of the class interval)
Q3 = 60 + (3 * 264/4 - 189) * 10
Q3 = 60 + (198 - 189) * 10
Q3 = 60 + 90
Q3 = 150
Calculate the quartile deviation:
Quartile Deviation = (Q3 - Q1) / 2
Quartile Deviation = (150 - 200) / 2
Quartile Deviation = -50 / 2
Quartile Deviation = -25
The quartile deviation is -25. However, quartile deviation is a measure of spread, and it cannot be negative. It seems there might be an error in the data or calculations. Please double-check the data or calculations to ensure accuracy