lainaschapell
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A school sells boxes of cookies each year for a charity fund. The data set shows the number of boxes the 10 families living on Willow Avenue buy, on average, every year.


{2, 3, 2, 2, 0, 5, 2, 1, 1, 3}


Does this data have negative, positive, or zero skew?

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roxannejosey800


0, 1, 1, 2, 2, 2, 2, 3, 3, 5

minimum: 0
maximum: 5
mean: 2.1
median: 2
mode: 2

I think the data have zero skew. Its mean, median, and mode are based on 2. It shows symmetry.

Answer:

This data set has zero skew as it is symmetric.

Step-by-step explanation:

We know that the symmetry exist in a data when the mean, median and mode of the data is same.

i.e. we are given a set of data as:

              {2, 3, 2, 2, 0, 5, 2, 1, 1, 3}

  • On arranging the data in increasing order we get :

    0  1   1   2   2   2   2   3   3   5

Hence, the value that occur in the middle is: 2

Hence, we have Median=2

  • Also, the mean is calculated as follows:

\(Mean=\dfrac{2+3+2+2+0+5+2+1+1+3}{10}\\\\\\Mean=\dfrac{21}{10}\\\\\\i.e.\\\\\\Mean=2.1\)

              Hence, Mean=2.1

  • Also, the mode of the data is the most frequently occurring data point in the set.

Here 2 occurs most number of times i.e. 4 times and hence we have:

                   Mode=2

Now, as the Mean, Median and Mode of the data are approximately same.

      Hence, we get the data is symmetric and hence has a zero skew.

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