No, your Wave Mini is always on and always measuring your indoor air quality. 

The data collected by the Wave Mini is saved logged locally on the device, and becomes visible in the Airthings App/ Dashboard as soon as you sync your device again. Measurements are stored locally on the device itself for 80 days.
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Once you sync to the App, it allows you to visualize your air quality data on your phone or tablet, and see how temperature, humidity, VOCs, and mold risk has behaved over the past 48 hours, 1 week, 1 month, and 1 year.

In order to get the latest readings from your Wave Mini you must be in proximity of the device, have Bluetooth turned on, and open the Airthings App. Once the the Wave has synced with your phone, all of the measurements that are saved on the Wave will upload to the cloud and be available for you to see in the app or from your online dashboard at https://dashboard.airthings.com/