if you have 70 calls that come in during one minute and 3 seconds..and then you have 10 calls come in at a total of 15 seconds. what is the weighted average of calls and time?
I assume you want the weighted average of the frequency of receiving calls. The easiest way to get this is to divided the total number of calls by the total time interval,
Avg. call rate = 80 calls/78 s
1.026 calls/sec
You would get the same average by first computing the call rate in each interval (1.270 and 0.667 calls/s) and then computing a weighted average using the length of the interval as a weighting factor.
To find the weighted average of calls and time, follow these steps:
1. Calculate the call rate in each interval. In the first interval (70 calls in 1 minute and 3 seconds), convert the time to seconds: 1 minute = 60 seconds.
Call rate in the first interval = (70 calls) / (1 minute + 3 seconds) = 70 / (60 + 3) = 70 / 63 ≈ 1.111 calls/second.
In the second interval (10 calls in 15 seconds), the call rate is simply the number of calls divided by the time interval: 10 calls / 15 seconds = 0.667 calls/second.
2. Compute the weighted average. To do this, multiply each call rate by its respective time interval, and then divide the sum of these products by the total time interval.
Weighted Average = (Call Rate in First Interval × Length of First Interval + Call Rate in Second Interval × Length of Second Interval) / Total Time Interval
Total Time Interval = 1 minute + 3 seconds + 15 seconds = 63 seconds.
Weighted Average = (1.111 calls/second × 63 seconds + 0.667 calls/second × 15 seconds) / 63 seconds
Weighted Average = (69.993 + 10.005) / 63 seconds ≈ 1.825 calls/second.
Therefore, the weighted average call rate is approximately 1.825 calls per second.