What values of k make the proportion of observations with |di| ≥ k meaningful?

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In summary, the conversation discusses the proportion of observations for which the absolute difference between di and k cannot exceed 1/(k^2). It is shown that this proportion cannot exceed 1/(k^2) when r≥(n-1)/(k^2). It is determined that k is not meaningful when it equals 0, but for other values, the variables need to be defined to determine its meaningfulness.
  • #1
Mark53
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Homework Statement



Given that r≥(n-1)/(k^2)

a) Show that the proportion of observations for which |di | ≥ k cannot exceed 1/(k^2)

b) For what values of k is this meaningful.

The Attempt at a Solution


[/B]
a)

(r/n)≥(n-1)/(n*k^2)

(r/n)≥(n-1)/(n*k^2)

(r/n)≥(n)/(n*k^2) -1/(n*k^2)

1/(n*k^2)+(r/n) ≥ 1/(k^2)

Is this the correct way to solve it?

b)

would k only be meaningful if it does not =0
 
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  • #2
What are r,n,k,di?

It is clearly not meaningful for k=0, yes. For other values, it would help to have the variables defined.
 

1. What is the purpose of stats observations in research?

Stats observations help researchers to collect and analyze data in order to make informed conclusions and predictions about a particular phenomenon or population.

2. How are stats observations different from other types of data collection methods?

Stats observations involve systematically collecting and recording data from a sample or population, using statistical methods to analyze the data, and drawing conclusions based on the results. This differs from other methods such as surveys or experiments, which may use different techniques for collecting and analyzing data.

3. What are some common statistical tools used in observations?

Some common statistical tools used in observations include measures of central tendency (such as mean, median, and mode), measures of variability (such as standard deviation and range), and correlation coefficients. Other tools may include t-tests, ANOVA, and regression analysis.

4. How do stats observations help in making decisions or predictions?

By analyzing data collected through observations, researchers can identify patterns and relationships, make comparisons between groups, and draw conclusions about the larger population. This information can then be used to make decisions or predictions about future outcomes.

5. What are some potential limitations of stats observations?

Some potential limitations of stats observations include biases or errors in data collection, small sample sizes, and confounding variables that may affect the results. It's important for researchers to carefully design their observations and use appropriate statistical methods to mitigate these limitations.

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