Multiple choice

Study the given table and answer the question that follows. The daily wages of 50 employees of a company is shown in the table. Daily Wages Interval Frequency (No. of Employees) 80-90 9 90-100 3 100-110 31 110-120 5 120-130 2 Select the correct statement from the following options.

  1. The average wage of the employees lie between 80-90.

  2. The average wage of the employees lie between 110-120.

  3. The average wage of the employees lie between 100-110.

  4. The average wage of the employees lie between 90-100.
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C Correct answer
Explanation

Calculate the weighted mean: (85*9 + 95*3 + 105*31 + 115*5 + 125*2) / 50 = (765 + 285 + 3255 + 575 + 250) / 50 = 5130 / 50 = 102.6. This value falls in the 100-110 interval.

AI explanation

To find the average wage, we first calculate the midpoints of each interval, which are 85, 95, 105, 115 and 125. The total wage is calculated by multiplying each midpoint by its corresponding frequency and adding the products, giving (9 times 85) plus (3 times 95) plus (31 times 105) plus (5 times 115) plus (2 times 125), which equals 5240. Using the direct mean formula, the average wage is 5240 divided by the 50 total employees, resulting in 104.8. Since 104.8 falls within the 100 to 110 range, the average wage of the employees lies between 100 and 110.

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