1. The problem asks about the largest presidential popular vote win since 1824 and the criteria for a "landslide" victory, including a standard deviation value $z$. 2. To analyze a landslide victory in terms of standard deviation, we consider the popular vote margin as a data point and compare it to the mean and standard deviation of historical margins. 3. The formula for a z-score is: $$z = \frac{X - \mu}{\sigma}$$ where $X$ is the observed value (popular vote margin), $\mu$ is the mean margin, and $\sigma$ is the standard deviation. 4. A "landslide" is often defined as a victory margin significantly larger than average, typically exceeding 2 standard deviations ($z > 2$). 5. The largest popular vote win since 1824 was by Lyndon B. Johnson in 1964, with a popular vote margin of approximately 22.6%. 6. Assuming the mean and standard deviation of popular vote margins historically, this margin corresponds to a $z$-score greater than 2, meeting the criteria for a landslide. 7. Therefore, the largest presidential popular vote win since 1824 was by Lyndon B. Johnson in 1964, which met the standard deviation criterion $z > 2$ for a landslide victory.