# How to determine whether a data set is symmetric or approximately symmetric

According to the textbook my lecturer is following, a set of data is "said to be symmetric about the value x0 if the frequencies of the values x0 − c and x0 + c are the same for all c. That is, for every constant c, there are just as many data points that are c less than x0 as there are that are c greater than x0"

So, according to the book, when we have

 values = [0,2,3,4,6,0]


and

 frequencies = [1,2,3,2,1,0]


the data set is symmetric around 3. (Put aside how the value '0' can have a frequency of 1 and 0 at the same time. I'm lost there).

My lecturer has now issued a quiz asking whether the following data sets are symmetric, approximately symmetric or not at all symmetric:

 Data set A: 5, 9, 5, 4, 0, 4, 5

Data set B: 5, 2, 5, 4, 2, 3, 1, 5, 0, 2, 1, 4

Data set C: 2, 8, 3, 5, 6, 0

Data set D: 1, 0, 1, 3, 1, 3, 4, 2


But here, there is just one data set each time and never a set of values with an associated set of frequencies, so surely the definitions don't apply? I am being stupid, clearly, but quite confused about what is being asked of me. Can anyone help?

• Perhaps each observation was seen once, so in data set A you had $5$ appearing three times, $4$ appearing two times and $0$ and $9$ once each Oct 17, 2022 at 22:21