Shape of Distribution Example

Complete the following steps to describe the distribution shape of the data set:
{44, 50, 58, 96, 42, 47, 40, 39, 46, 50}.

  1. Find the mean and the median. Sample mean: x̄ = (Σx) / n = 510 / 10 = 51. To find the median, rank the data.
    {44, 50, 58, 96, 42, 47, 40, 39, 44, 50}
    becomes
    {39, 40, 42, 44, 44, 47, 50, 50, 58, 96}
    `d(x̄) = (n+1)/2 = (10+1)/2 = 11/2 = 5.5`
    Counting from either direction, the median is halfway between 44 and 47.
    `(44+47)/2 = 91/2 = 45.5`
    So, the median is 45.5.
  2. Describe the distribution shape. Because the mean is greater than the median, the distribution will be skewed to the right.