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Calculating Mean and Standard Deviation of Random Variables

Calculating Mean and Standard Deviation of Random Variables

Assessment

Interactive Video

•

Mathematics

•

6th - 10th Grade

•

Practice Problem

•

Hard

•
CCSS
7.SP.C.6, 6.SP.A.3, HSS.MD.A.2

Standards-aligned

Created by

Amelia Wright

FREE Resource

Standards-aligned

CCSS.7.SP.C.6
,
CCSS.6.SP.A.3
,
CCSS.HSS.MD.A.2
This video tutorial covers the concepts of probability, random variables, and probability distributions, focusing on the mean and standard deviation of random variables. It explains the law of large numbers, illustrating how true probabilities and means are only observed after many trials. The video uses examples, such as LeBron James' scoring, to differentiate between sample statistics and population parameters. It also provides a step-by-step guide on calculating mean and standard deviation, both manually and using a calculator, emphasizing the importance of interpreting these values in context.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the Law of Large Numbers tell us about probability?

It is always 50%.

It is only seen in the long run after many trials.

It is the same for all events.

It can be determined after a few trials.

Tags

CCSS.7.SP.C.6

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the context of the Law of Large Numbers, what is the probability of getting heads in 10 coin tosses?

50%

It varies and is not necessarily 50%

0%

100%

Tags

CCSS.7.SP.C.6

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the difference between a sample mean (x-bar) and a population mean (mu)?

There is no difference.

Sample mean is always larger than population mean.

Population mean is always 50%.

Sample mean is from a small sample, population mean is from a large number of trials.

Tags

CCSS.6.SP.A.3

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What symbol is used to represent the population mean?

sigma

mu

p

x-bar

Tags

CCSS.6.SP.A.3

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is another term for the mean of a random variable?

Probability

Variance

Expected value

Standard deviation

Tags

CCSS.HSS.MD.A.2

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the mean of a random variable calculated?

Sum of probabilities

Sum of all outcomes

Sum of each outcome multiplied by its probability

Sum of outcomes divided by the number of trials

Tags

CCSS.HSS.MD.A.2

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the standard deviation of a random variable represent?

The probability of outcomes

How far outcomes vary from the mean

The expected value

The mean value

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