# 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?

- All values in this dataset are greater than zero.
- All values in this dataset are less than zero
- Since mean is 0, all the data points are equal to 0
- Values in the dataset could be greater than zero, less than zero and equal to zero.
- 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