It is discrete.
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Each of those is better in some situations. Also, you often have no choice. Some quantities, like speed and temperature, are inherently continuous, whereas some quantities, like the number of girls, cars, or beans, are inherently discrete.
It can be, but not necessarily. If I had the heights (continuous variable) of a class of students I might use a histogram. Conversely, if I had the number of cars (discrete variable) driving by every minute, I would use a line graph. It all depends on which kind of graph conveys the information to your audience in the best way.
Mass is a continuous variable. It's the measure of resistance an object has to changing its velocity and can be any positive value. Compare to discrete variables which are only whole numbers. For example, on Earth a bag of flour with a mass of 1.5 kilograms weighs 14.709975 newtons, both of which are continuous variables. It is only 1 bag of flour though, which is a discrete variable. To extend the consideration, while the 1 bag could be cut in half, there would then be 2 bags (2 half-bags, 2 bag halves) each with .75 kg of flour. It could be said that generally things that are measured (time, distance, height, weight) are continuous and generally things that are counted (people, cars, cups, bags) are discrete. It's possible to linguistically muddle the distinction though.
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a broken line graph