3.3 Averages (mean of workplace data sets)

Averages in the Workplace

The average, or mean, summarizes a set of numbers with a single typical value. Managers average daily sales, quality inspectors average defect counts, and drivers average fuel economy. The WorkKeys test asks you to compute a mean, work with a weighted average, and - a favorite of the harder levels - find a missing value when the average is already known.

Computing a simple mean

The mean equals the sum of all values divided by how many values there are:

mean = (sum of values) / (number of values)

Example - daily sales. A store records sales for one week, Monday through Friday: $420, $380, $510, $465, and $475. Find the average daily sales.

• Sum: 420 + 380 + 510 + 465 + 475 = 2,250
• Count: 5 days
• Mean: 2,250 / 5 = $450 per day

Example - production counts. A line produces 118, 122, 130, and 126 units over four shifts. Sum = 496; count = 4; mean = 496 / 4 = 124 units per shift.

Two habits keep this accurate: count the values carefully (an off-by-one in the divisor throws everything off), and add in a way you can double-check, such as pairing numbers.

Weighted averages

A plain mean assumes every value counts equally. When some values represent more items - more units purchased, more hours worked, a heavier category weight - you need a weighted average. Multiply each value by its weight, add those products, then divide by the total weight.

Example - mixed purchase prices. A buyer purchases 10 units at $4.00 each and 30 units at $6.00 each. What is the average cost per unit?

• Weighted total = (10 x 4.00) + (30 x 6.00) = 40 + 180 = 220
• Total units = 10 + 30 = 40
• Average = 220 / 40 = $5.50 per unit

Notice the answer ($5.50) sits closer to $6.00 than to $4.00, because more units were bought at $6.00. A simple unweighted average of $4 and $6 would have given $5.00 - the wrong figure for this situation.

Example - weighted score. An employee review weights quality 50%, speed 30%, and teamwork 20%. Scores are 90, 80, and 70. Weighted score = (0.50 x 90) + (0.30 x 80) + (0.20 x 70) = 45 + 24 + 14 = 83.

Example - averaging two crews. A morning crew of 4 workers averages 30 units each and an afternoon crew of 6 workers averages 25 units each. The overall average per worker is not (30 + 25) / 2 = 27.5, because the crews are different sizes. Use a weighted average: (4 x 30) + (6 x 25) = 120 + 150 = 270 units total, divided by 4 + 6 = 10 workers, which gives 27 units per worker.

Finding a missing value

If you know the target average and all but one of the values, work backward. The total of all values must equal the average times the count; subtract the values you already have to find the missing one.

Example - fuel economy. A driver wants to average 45 miles per gallon over 4 fill-ups. The first three tanks give 43, 46, and 44 mpg. What must the fourth tank average to hit the goal?

• Required total = 45 x 4 = 180
• Sum of first three = 43 + 46 + 44 = 133
• Fourth tank = 180 - 133 = 47 mpg

Example - training scores. A trainee needs an 80 average across 5 module quizzes. So far the scores are 76, 85, 78, and 82. What score is needed on the fifth?

• Required total = 80 x 5 = 400
• Sum of four = 76 + 85 + 78 + 82 = 321
• Fifth quiz = 400 - 321 = 79

Reading data from a table

Workplace problems often bury the numbers in a small table or chart. Read the labels first, then pull out only the values the question actually asks about before you average them.

Example. A time sheet shows hours worked: Mon 8, Tue 7.5, Wed 9, Thu 8.5, Fri 6. Average daily hours = (8 + 7.5 + 9 + 8.5 + 6) / 5 = 39 / 5 = 7.8 hours.

Common pitfalls

• Miscounting the divisor. Always divide by how many numbers you actually added, including any zeros - a day with $0 in sales still counts as a day.
• Averaging the averages. You cannot average two group averages unless the groups are the same size; use a weighted average instead.
• Forgetting the goal is a total. Missing-value problems are really what total do I need questions in disguise.

Test-day strategy

Add carefully, count the values, divide, and sanity-check: the mean must land between the smallest and largest values in the set. If your average of $420 to $510 sales came out to $600, you know an arithmetic error crept in. That single check - is my average inside the range - catches most mistakes on this topic.