Random sampling distributions in NumPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a random sampling distribution?

A random sampling distribution shows how a statistic (like the mean) varies when we take many samples from the same population. It helps us understand the spread and behavior of that statistic.

beginner

How do you generate random samples using numpy?

You can use numpy's functions like numpy.random.choice() to pick random samples from data, or numpy.random.normal() to generate samples from a normal distribution.

beginner

Why do we use many samples to create a sampling distribution?

Using many samples helps us see the range and pattern of the statistic's values. This shows how much the statistic can change just by chance.

intermediate

What does the Central Limit Theorem say about sampling distributions?

It says that if you take many samples of a large enough size, the distribution of the sample means will look like a normal (bell-shaped) curve, no matter the original data shape.

beginner

How can you visualize a sampling distribution in Python?

You can collect many sample statistics (like means) in a list or array, then use a histogram plot (e.g., with matplotlib) to see the shape and spread of the sampling distribution.

Which numpy function can generate random samples from a normal distribution?

A numpy.random.shuffle()

B numpy.random.choice()

C numpy.random.normal()

D numpy.random.randint()

numpy.random.normal() generates samples from a normal distribution. The others serve different purposes.

What does a sampling distribution represent?

A The distribution of a statistic from many samples

B The distribution of the original data

C The distribution of a single sample

D The distribution of random numbers

A sampling distribution shows how a statistic (like the mean) varies across many samples.

According to the Central Limit Theorem, the sampling distribution of the mean will be approximately normal if:

A Population is normal

B Sample size is large

C Sample size is small

D Population is uniform

The Central Limit Theorem states that with a large sample size, the sampling distribution of the mean is approximately normal regardless of population shape.

Which of these is NOT a reason to use random sampling?

A To estimate population parameters

B To get a representative sample

C To reduce bias

D To guarantee the sample mean equals population mean

Random sampling helps reduce bias and estimate parameters but does not guarantee the sample mean equals the population mean.

What Python library is commonly used to visualize sampling distributions?

A matplotlib

B numpy

C pandas

D scipy

matplotlib is commonly used to create histograms and plots to visualize sampling distributions.

Explain what a random sampling distribution is and why it is important in statistics.

Think about how sample means change when you take many samples.

Describe how you would use numpy to create a sampling distribution of the mean from a dataset.

Imagine picking many small groups from your data and finding their averages.