In an office, the distribution of work hours is as shown in the following table.Consider the following inferences drawn from the table : I. > The average number of hours worked by a staff member is about 30. II. > The percentage of those who worked 35 or

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Q: 146 (IAS/1999)
In an office, the distribution of work hours is as shown in the following table.Consider the following inferences drawn from the table :
I. The average number of hours worked by a staff member is about 30.
II. The percentage of those who worked 35 or more hours is less than 25.
III. At least 5 staff members worked more than 44 hours.
Which of these inferences is/are valid ?
No. of Staff MembersNo. of hours worked
50 - 19
120 - 24
2525 - 29
4030 - 34
1535 - 39
840 - 45

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,0,2,0,1,0,1

keywords: 

{'following inferences': [0, 1, 0, 0], 'inferences': [0, 1, 0, 0], 'work hours': [0, 1, 1, 0], 'distribution': [0, 0, 1, 0], 'percentage': [1, 2, 2, 3], 'more hours': [0, 1, 1, 0], 'following table': [0, 2, 1, 1], 'average number': [0, 0, 0, 1], 'table': [0, 0, 1, 0], 'hours': [7, 2, 16, 9], 'staff members': [0, 1, 0, 0], 'office': [5, 1, 2, 4]}

The correct answer is option 3, which means that both inference I and II are valid.

Inference I states that the average number of hours worked by a staff member is about 30. As it is not possible to calculate the exact average from the given data, we could assume that most of the staff members fall into the 30-34 hour work week and thus the average might be around 30 hours.

Inference II states that the percentage of people who worked 35 or more hours is less than 25%. Given that 15 staff members worked 35-39 hours and 8 worked 40-45 hours, the total working 35 or more hours is 23 out of a total of 94 (all staff). Hence, about 24.4% of staff worked 35 hours or more, which is slightly less than 25%, making this statement valid.

Inference III suggests that at least 5 staff members worked more than 44 hours. But from the table, we understand that there are only 8 employees who worked within the range 40-45 hours. We do not have data that specifies how many of them exceeded 44 hours. Therefore, we cannot confirm this inference, and it`s not included in the correct answer

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