Calculate discrete value from a series of averages

[Sandy771]

I have a device that records a sample hourly but reports the average of the last 24 hours. I.e. the reported value is a sliding 24 hour window at hourly intervals.

i would like to determine the actual value that was recorded every hour! I feel that with enough data this should be possible but implementing a solution is beyond my skill set

if it helps I don’t need historic values to be reported accurately and in fact I don’t need to determine the actual value to a high degree of precision

A selection of real world values is:

285 282 282 293 280 279 264 264 262 264 231 233 230 234 225 231 234 234 253 271 253 254 259 258 259 263 240 238 234 217 217 213 217 223 229 229 234 248 256 266 274 283 286 277 267 267 256 259 259 255 249 240 237 227 209 207 206 206

If you need any more info then please just ask!

I hope this is the right place to post this?

thanks in advance

 

[Dr.Peterson]

Suppose you have 24 hours of averages. That would let you write 24 equations; but there will be 47 variables to solve for (these 24 hours, and the previous 23 hours, which also affected the averages). That's not enough equations to solve for all the variables.

Now, if you could start the whole process in a known state (say, with 0 for the previous 24 hours' data, before a process started), then you could us that fact to determine all subsequent values. The change from one average to the next is equal to 1/24 of the difference between the latest value and the 24-hour-old value that it is replacing.

But I am concerned about the data you show, because it varies more than I expect averages to vary. A change of 23 in the average (e.g. from 263 to 240) means that the number is 24*23 = 552 less than 24 hours before. Is that what you expect of the data?