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3 years ago

Which statements are true about the interquartile range? Select all that apply.

Mathematics

2 answers:

Dima020 [189]3 years ago

8 0

Answer:

* Lower and upper quartiles are needed to find the interquartile range.

*The data values should be listed in order before trying to find the interquartile range

PilotLPTM [1.2K]3 years ago

4 0

Answer:

The true statements are:

B. Interquartile ranges are not significantly impacted by outliers

C. Lower and upper quartiles are needed to find the interquartile range

E. The data values should be listed in order before trying to find the interquartile range

Step-by-step explanation:

The interquartile range is the difference between the first and third quartiles

Steps to find the interquartile range:

Put the numbers in order
Find the median Place parentheses around the numbers before and after the median
Find Q1 and Q3 which are the medians of the data before and after the median of all data
Subtract Q1 from Q3 to find the interquartile range

The interquartile range is not sensitive to outliers

Now let us find the true statements

A. Subtract the lowest and highest values to find the interquartile range ⇒ NOT true (because the interquartial range is the difference between the lower and upper quartiles)

B. Interquartile ranges are not significantly impacted by outliers ⇒ True (because it does not depends on the smallest and largest data)

C. Lower and upper quartiles are needed to find the interquartile range ⇒ True (because IQR = Q3 - Q2)

D. A small interquartile range means the data is spread far away from the median ⇒ NOT true (because a small interquartile means data is not spread far away from the median)

E. The data values should be listed in order before trying to find the interquartile range ⇒ True (because we can find the interquartial range by finding the values of the upper and lower quartiles)

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Answer:

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Answer:

a) $X \sim Binom(n=16, p=0.2)$

The probability mass function for the Binomial distribution is given as:

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Where (nCx) means combinatory and it's given by this formula:

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The expected value is given by this formula:

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Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Part a

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=16, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The expected value is given by this formula:

$E(X) = np=16*0.2=3.2$

Part b

For this case we want this probability:

$P(X=0)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And using this function we got:

$P(X=0)=(16C0)(0.2)^{0} (1-0.2)^{16-0}=0.02815$

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