Question

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?

Answer 1

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 2

This data set has zero skew as it is symmetric.

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=(2+3+2+2+0+5+2+1+1+3)/(10)\\\\\\Mean=(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.