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Zorluk: OrtaMeasures of Central Tendency

A maintenance technician is tracking the number of work orders completed each day. Over a 55-day work week, the technician wants to achieve a mean of 1414 completed work orders per day. If the technician completed 1212, 1616, 1111, and 1313 work orders on the first four days, how many work orders must be completed on the fifth day to exactly meet the target mean?

Cevap: 18 work orders

Cevap

The technician must complete 18 work orders on the fifth day.
To find a missing value when the mean is known, first determine the total sum required by multiplying the target mean (14) by the total number of data points (5), which equals 70. Next, add the known values from the first four days (12 + 16 + 11 + 13 = 52). Finally, subtract the sum of the known values from the total required sum (70 - 52 = 18). Therefore, 18 work orders must be completed on the fifth day.

Adım Adım Çözüm

1
Determine the total sum required for all 5 days.
14×5=7014 \times 5 = 70
The mean is the total sum divided by the number of values. To find the required total sum, multiply the target mean by the total number of days.
2
Calculate the sum of the work orders completed so far.
12 + 16 + 11 + 13 = 52
This gives the total number of work orders already completed in the first four days.
3
Find the difference between the required total and the completed total.
70 - 52 = 18
Subtracting the sum of the first four days from the required 5-day total yields the exact value needed for the fifth day.

Anahtar Kavram

Calculating a missing value from a given mean requires multiplying the mean by the total number of items to find the required sum, then subtracting the known values.
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