Descriptive statistics problems for practice and concept clarity

Descriptive statistics problem 1

Question (Descriptive statistics problems): Consider a dataset that has mean 0 and standard deviation of 3. What could be inferred about the values in this dataset?

  1. All values in this dataset are greater than zero.
  2. All values in this dataset are less than zero
  3. Since mean is 0, all the data points are equal to 0
  4. Values in the dataset could be greater than zero, less than zero and equal to zero.
  5. Since mean is 0, 50% of values are above 0 and 50% are below zero.

Solution

Answer is option 4

Values in the dataset could be greater than zero, less than zero and equal to zero.

Explanation:

Mean is 0. So, average value of all data points in the dataset is 0.

This leaves two possibilities – either all datapoints in the dataset must be equal to zero

or

datapoints are spread around 0.

Given that the standard deviation is 3 (This rules out the possibility of option 3). It means that the average deviation of each point in the dataset from the mean value is 3 in both directions (above mean as well as below mean)

Option 5 could be true if the median of the dataset is 0. However, we have information only about the mean.

Refer to Measures of central tendency and dispersion