np.std() and np.var() for spread in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does np.std() calculate in a dataset?

np.std() calculates the standard deviation, which measures how spread out the numbers are from the average (mean). A small value means data points are close to the mean, and a large value means they are more spread out.

beginner

What is the difference between np.var() and np.std()?

np.var() calculates variance, which is the average of squared differences from the mean. np.std() is the square root of variance. So, standard deviation is in the same units as the data, while variance is in squared units.

intermediate

How does changing the ddof parameter affect np.std() and np.var()?

The ddof parameter stands for 'Delta Degrees of Freedom'. Setting ddof=1 calculates the sample standard deviation or variance (dividing by N-1), which is used when data is a sample. The default ddof=0 calculates population values (dividing by N).

beginner

Why is standard deviation often preferred over variance to describe spread?

Standard deviation is preferred because it is in the same units as the original data, making it easier to understand and compare. Variance is in squared units, which can be harder to interpret.

beginner

If a dataset has values [2, 4, 4, 4, 5, 5, 7, 9], what is the approximate standard deviation using np.std() with default settings?

The mean is 5. The squared differences average to 4, so variance is 4. The standard deviation is the square root of 4, which is 2.

What does np.var() measure in a dataset?

A Average squared distance from the mean

B Square root of the average distance from the mean

C Median of the dataset

D Sum of all data points

np.var() calculates the variance, which is the average of squared differences from the mean.

Which function returns a value in the same units as the original data?

A np.std()

B np.var()

C np.mean()

D np.sum()

np.std() returns the standard deviation, which is in the same units as the data.

What does setting ddof=1 do in np.std()?

A Calculates population standard deviation

B Ignores the first data point

C Calculates median instead

D Calculates sample standard deviation

Setting ddof=1 calculates the sample standard deviation by dividing by N-1.

If variance is 9, what is the standard deviation?

A 9

B 3

C 81

D 1

Standard deviation is the square root of variance, so sqrt(9) = 3.

Why might variance be harder to interpret than standard deviation?

A It is always smaller than standard deviation

B It is not related to the mean

C It is in squared units, not original units

D It ignores outliers

Variance is in squared units, which can make it less intuitive than standard deviation.

Explain in your own words what np.std() and np.var() tell us about a dataset.

Think about how spread out the data points are and how these functions measure that.

Describe how changing the ddof parameter affects the calculation of spread using np.std() or np.var().

Consider why we sometimes divide by N-1 instead of N.