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Quantitative data is data that measures quantity, as opposed to qualitative data which describes quality. Some examples of quantitative data pertaining to weather would be: measurements of precipitation, records of number of days per month without precipitation, percentage of the chance of precipitation, records of daily high temperatures.
A qualitative datum is one that is expressed as some quality/property of a particular entity, rather than a numerical value. Conversely, a quantitative datum is one that is expressed as a quantity (or number), as opposed to a quality of a particular entity. Hence, qualitative and quantitative data are essentially opposite data types.
It is numerical information about some characteristic. By contrast, qualitative data might be something like the colour of your eyes, or the name of your maths teacher.
In statistics numerical data is quantitative rather than qualitative.
Some variables in the data set might be qualitative, others might not. For example, if one were to sample newly arrived immigrants to Toronto, Canada and create a data set of information about them one could include both qualitative and quantitative data. One might measure each person's height which would be quantitative, and observe each person's eye colour, which would be qualitative.