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Here is the whole paragraph. I am very confused that what does the "bother" here mean. Does that mean "we" are very unhappy to treat

The second quality of big data is its embrace of messiness. Looking at vastly more data permits us to loosen up our desire for exactitude. Remember, when we only quantified a little, we had to treat what we did bother to measure as precisely as possible. In contrast, big data is often messy and of varying quality

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To "bother" to do something is to make the effort, even if the effort may not have significant benefit. I don't always bother to make my bed in the morning, it seems to be a rather futile activity. The word is generally used in situations where the activity one "bothers" to undertake isn't particularly enjoyable or rewarding, but not a great hardship.

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The writer is contrasting two approaches to data, the old way and the new way (‘big data’). With the old way, they didn’t need to bother, or make the effort, to gather very much data. However, this small amount of data needed to be precise.

You could rephrase that section without using ‘bother’ and keep the general sense quite easily:

‘When we only quantified a little, we had to make very precise measurements, unlike today with big data.’

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