Question

What does it mean for a sample to have a standard deviation of zero? Describe the scores in such a sample?

Data distributions
ANSWERED
asked 2020-11-30
What does it mean for a sample to have a standard deviation of zero? Describe the scores in such a sample?

Answers (1)

2020-12-01
Given that sample standard deviation is Zero. this indicates that the variance of Sample is also Zero as square of sample standard deviation is Sample Variance.
Variance is average of the squared deviations from mean. As shown in below formula
Since Variance = 0 , we substitute in formula and we get the sum of squares of deviations of all data points from mean should be zero. This is only possible if and only if all the data points in the data distribution are same as mean of the data distribution. In this case the variance and standard deviaiton will be zero.
Variance \(\displaystyle={\sum_{{{i}={1}}}^{{n}}}\frac{{{\left({X}_{{I}}-\overline{{X}}\right)}^{{2}}}}{{{n}-{1}}}\)
\(\displaystyle{0}={\sum_{{{i}={1}}}^{{n}}}\frac{{{\left({X}_{{I}}-\overline{{X}}\right)}^{{2}}}}{{{n}-{1}}}\)
\(\displaystyle{\sum_{{{i}={1}}}^{{n}}}{\left({X}_{{I}}-\overline{{X}}\right)}^{{2}}={0}\)
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-07-02
Do piano lessons improve the spatial-temporal reasoning of preschool children? A study designed to investigate this question measured the spatial-temporal reasoning of a random sample of 34 preschool children before and after 6 months of piano lessons. The differences (After - Before) in the reasoning scores have mean 3.618 and standard deviation 3.055.
asked 2021-08-22
At Western University the historical mean of scholarship examination scores for freshman applications is 900. Ahistorical population standard deviation \(\displaystyleσσ={180}\) is assumed known.
Each year, the assistant dean uses a sample of applications to determine whether the mean examination score for the new freshman applications has changed.
a. State the hypotheses.
b. What is the 95% confidence interval estimate of the population mean examination score if a sample of 200 applications provided a sample mean \(\displaystyle{x}‾{x}\)= 935?
c. Use the confidence interval to conduct a hypothesis test. Using \(\displaystyleαα={.05}\), what is your conclusion?
d. What is the p-value?
asked 2021-05-14
Consider the accompanying data on flexural strength (MPa) for concrete beams of a certain type.
\(\begin{array}{|c|c|}\hline 11.8 & 7.7 & 6.5 & 6 .8& 9.7 & 6.8 & 7.3 \\ \hline 7.9 & 9.7 & 8.7 & 8.1 & 8.5 & 6.3 & 7.0 \\ \hline 7.3 & 7.4 & 5.3 & 9.0 & 8.1 & 11.3 & 6.3 \\ \hline 7.2 & 7.7 & 7.8 & 11.6 & 10.7 & 7.0 \\ \hline \end{array}\)
a) Calculate a point estimate of the mean value of strength for the conceptual population of all beams manufactured in this fashion. \([Hint.\ ?x_{j}=219.5.]\) (Round your answer to three decimal places.)
MPa
State which estimator you used.
\(x\)
\(p?\)
\(\frac{s}{x}\)
\(s\)
\(\tilde{\chi}\)
b) Calculate a point estimate of the strength value that separates the weakest \(50\%\) of all such beams from the strongest \(50\%\).
MPa
State which estimator you used.
\(s\)
\(x\)
\(p?\)
\(\tilde{\chi}\)
\(\frac{s}{x}\)
c) Calculate a point estimate of the population standard deviation ?. \([Hint:\ ?x_{i}2 = 1859.53.]\) (Round your answer to three decimal places.)
MPa
Interpret this point estimate.
This estimate describes the linearity of the data.
This estimate describes the bias of the data.
This estimate describes the spread of the data.
This estimate describes the center of the data.
Which estimator did you use?
\(\tilde{\chi}\)
\(x\)
\(s\)
\(\frac{s}{x}\)
\(p?\)
d) Calculate a point estimate of the proportion of all such beams whose flexural strength exceeds 10 MPa. [Hint: Think of an observation as a "success" if it exceeds 10.] (Round your answer to three decimal places.)
e) Calculate a point estimate of the population coefficient of variation \(\frac{?}{?}\). (Round your answer to four decimal places.)
State which estimator you used.
\(p?\)
\(\tilde{\chi}\)
\(s\)
\(\frac{s}{x}\)
\(x\)
asked 2021-08-10
The high price of medicines is a source of major expense for those seniors in the United States who have to pay for these medicines themselves. A random sample of 2000 seniors who pay for their medicines showed that they spent an average of \(\displaystyle\${4600}\) last year on medicines with a standard deviation of \(\displaystyle\${800}\). a) Make a \(\displaystyle{98}\%\) confidence interval for the corresponding population mean. b) Suppose the confidence interval obtained in part a is too wide. How can the width of this interval be reduced? Discuss allpossible alternatives. Which alternative is the best?
...