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The description you gave of symmetric and continuous is also akin to a normal distribution curve. A normal distribution curve looks like an inverted bell therefore often called a bell curve. Using the normal distribution, one can view whether or not the data has a skew which may mean using the median or mode could be preferable.
Also, a normal distribution helps us visually see frequencies and central tendencies. From there, we can calculate the standard deviation to measure the width of the distribution. YOU NEED TO COMMENT FROM THIS POST, NO MORE THAN 150 WORDS NEEDED AND A REFERENCE PLEASE
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