skottyrottenmf
2022-05-24
Answered

Why are measures of central tendency essential to descriptive statistics?

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thoumToofwj

Answered 2022-05-25
Author has **16** answers

Explanation:

In descriptive statistics, we are explaining the characteristics of a set of data in hand - we are not making conclusions on the larger population from where the data come (That's inferential statistics).

In doing so, our main question is usually 'where is the center of the distribution'. To answer that question, we normally employ either the mean, the median or the mode, depending on the type of data. These three central tendency measures indicate the central point around which all the data gather. That is why it is one of the two essential parts of descriptive statistics. The other part is the measure of dispersion, which explains how far data is distributed around the central tendency.

So with central tendency, we know the center of the distribution of data. With dispersion, we know how spread the data are.

In descriptive statistics, we are explaining the characteristics of a set of data in hand - we are not making conclusions on the larger population from where the data come (That's inferential statistics).

In doing so, our main question is usually 'where is the center of the distribution'. To answer that question, we normally employ either the mean, the median or the mode, depending on the type of data. These three central tendency measures indicate the central point around which all the data gather. That is why it is one of the two essential parts of descriptive statistics. The other part is the measure of dispersion, which explains how far data is distributed around the central tendency.

So with central tendency, we know the center of the distribution of data. With dispersion, we know how spread the data are.

asked 2021-06-13

1. Who seems to have more variability in their shoe sizes, men or women?

a) Men

b) Women

c) Neither group show variability

d) Flag this Question

2. In general, why use the estimate of$n-1$ rather than n in the computation of the standard deviation and variance?

a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation

b) The estimate n-1 is never used to calculate the sample variance and standard deviation

c)$n-1$ provides an unbiased estimate of the population and allows more variability when using a sample and gives a better mathematical estimate of the population

d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.

$\begin{array}{|cc|}\hline \text{Shoe Size (in cm)}& \text{Gender (M of F)}\\ 25.7& M\\ 25.4& F\\ 23.8& F\\ 25.4& F\\ 26.7& M\\ 23.8& F\\ 25.4& F\\ 25.4& F\\ 25.7& M\\ 25.7& F\\ 23.5& F\\ 23.1& F\\ 26& M\\ 23.5& F\\ 26.7& F\\ 26& M\\ 23.1& F\\ 25.1& F\\ 27& M\\ 25.4& F\\ 23.5& F\\ 23.8& F\\ 27& M\\ 25.7& F\\ \hline\end{array}$

$\begin{array}{|cc|}\hline \text{Shoe Size (in cm)}& \text{Gender (M of F)}\\ 27.6& M\\ 26.9& F\\ 26& F\\ 28.4& M\\ 23.5& F\\ 27& F\\ 25.1& F\\ 28.4& M\\ 23.1& F\\ 23.8& F\\ 26& F\\ 25.4& M\\ 23.8& F\\ 24.8& M\\ 25.1& F\\ 24.8& F\\ 26& M\\ 25.4& F\\ 26& M\\ 27& M\\ 25.7& F\\ 27& M\\ 23.5& F\\ 29& F\\ \hline\end{array}$

a) Men

b) Women

c) Neither group show variability

d) Flag this Question

2. In general, why use the estimate of

a) The estimate n-1 is better because it is used for calculating the population variance and standard deviation

b) The estimate n-1 is never used to calculate the sample variance and standard deviation

c)

d) The estimate n-1 is better because it is use for calculation of both the population and sample variance as well as standard deviation.

asked 2021-11-14

Each night different meteorologists give us the probability that it will rain the next day. To judge how well these people predict, we will score each of them as follows: If a meteorologist says that it will rain with probability p, then he or she will receive a score of

$1-{(1-p)}^{2}$ if it does rain

$1-{p}^{2}$ if it does not rain

We will then keep track of scores over a certain time span and conclude that the meteorologist with the highest average score is the best predictor of weather. Suppose now that a given meteorologist is aware of our scoring mechanism and wants to maximize his or her expected score. If this person truly believes that it will rain tomorrow with probability$p\cdot$ , what value of p should he or she assert so as to maximize the expected score?

We will then keep track of scores over a certain time span and conclude that the meteorologist with the highest average score is the best predictor of weather. Suppose now that a given meteorologist is aware of our scoring mechanism and wants to maximize his or her expected score. If this person truly believes that it will rain tomorrow with probability

asked 2022-03-31

The bad debt ratio for a financial institution is defined to be the dollar value of loans defaulted divided by the total dollar value of all loans made. A random sample of 6 Ontario banks is selected and that the bad debt ratios (in percentages) for these banks are:

$7,\text{}4,\text{}6,\text{}7,\text{}5,\text{}8$

Compute and interpret a$95\mathrm{\%}$ confidence interval for the mean bad debt ratio. What needs to be true in order for this interval and interpretation to be valid?

Compute and interpret a

asked 2020-12-29

CNBC recently reported that the mean annual cost of auto insurance is $998. Assume the standard deviation is $298.

Find the probability that a single randomly selected value is less than $985.

Write your answers as numbers accurate to 4 decimal places.

asked 2022-04-15

Least squares regression analysis is a common method for modelling trip generation. What are the main assumptions of the least squares regression analysis in that context? Discuss with examples the consequences of violating two of these assumptions.

asked 2021-02-25

Find the type and the number of variables for which the Chi-square goodness-of-fir tests are used.

asked 2020-12-02

Gastroenterology

We present data relating protein concentration to pancreatic function as measured by trypsin secretion among patients with cystic fibrosis.

If we do not want to assume normality for these distributions, then what statistical procedure can be used to compare the three groups?

Perform the test mentioned in Problem 12.42 and report a p-value. How do your results compare with a parametric analysis of the data?

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