# How can I prove something rarely happens using statistics and mathematics?

I want to prove that something rarely happens. I have a dataset generated by air-conditioners and I need to prove that it is not worth providing statistics including mean, max, median, min, and max mode to other departments because the target temperature of the air conditioner, which is adjusted by people for the air conditioner to reach it to cool down the air around us, hardly ever changes.

The number of air conditioner dataset is 500,452. The maximum number of changes in the target temperature of air conditioners is 27 a day and the average number of target temperature changes is 0.0032. The averages tells the target temperature hardly ever changes so I don't think I need to calculate the five statistics but I am not sure if I don't really need to provide the statistics because the average is extremely low.

Therefore, I think it is almost meaningless to provide the above five numbers of statistics because most of target temperatures of air conditioners do not change a day. I want to prove that the five statistics hardly change using statistics or mathematics.

How can I prove the target temperature hardly ever changes so that I can only provide the dataset but I don't have to provide the five statistics above as I am so sure that the target temperature hardly ever changes?

The goal of proving my thought using statistics or mathematics is that I want to justify myself that providing the five statistics for the dataset with almost no changes in them is meaningless.

• what is 0.0032? the number makes no sense. also, I understand your idea, the fact that something is rare doesn't make it not worth tracking. Apr 22 '21 at 14:04
• I am not so sure that I agree with your assessment that the numbers are worthless. However, the best way to show that they're worthless is to provide them and explain their lack of value. When your company has to spend resources (your compensation) to do something they see to be worthless, they might reconsider having you do that worthless task. (I think the downside to this is obvious, but I suspect you provide value for other reasons.)
– Dave
Apr 22 '21 at 14:23
• @Akasaka, 0.0032 is the average target teperature frequency that comes from [total_number_of_target_temperature_change_frequency / the number of air conditioners]. The average looks a bit odd. It shouldn't be like that. I think I did something wrong when calculating it because air conditioners in the total number of target temperature change frequency at least have one temperature change so it shouldn't be like that. Apr 22 '21 at 15:38
• @StoryMay, this avg should be calculated conditionally to make sense, i.e. divide the temperature change by the number of ACs that actually changed the temp, not by 500k total. your answer would be then the avg temp change given that the temp was changed Apr 22 '21 at 19:34

## 2 Answers

The fact that an event happens rarely doesn't automatically mean that statistics shouldn't be tracked. You need to understand the business reason for the request. Also, tracking can be done on conditional and unconditional base. That's why I'm afraid you will not get any help from statisticians here.

The statistics that you mention could help you to prove your point that the temperature rarely changes - things like the inter-quartile range would provide evidence of how stable it is.

Instead of providing evidence that you don't need these statistics, you should see these statistics as tools for understanding whether your hypothesis is correct.

• Things like variance and IQR test how much a dataset changes. So, if the IQR is very small, then it means that there is not much change over time. Apr 22 '21 at 15:44
• Can I do a hypothesis testing on the target temperature by stating that the average target temperature is a certain average target temperature for null hypothesis and the alternative hypthesis is the average target temperature is different from a certain average target temperature? Do I need to have a previous or past average target temperature to do the hypothesis testing? Apr 26 '21 at 13:27