What are the basics of statistics and probability?

Probability And Statistics are the two important concepts in Maths. Probability is all about chance. Whereas statistics is more about how we handle various data using different techniques . It helps to represent complicated data in a very easy and understandable way.

What is an example of a statistic in math?

A statistic is a number that represents a property of the sample. For example, if we consider one math class to be a sample of the population of all math classes, then the average number of points earned by students in that one math class at the end of the term is an example of a statistic.

Is statistics harder than calculus?

Some students might find Calculus harder, while others might struggle more with Statistics . It's highly personal, so talk to your teachers and peers to help you make the best decision.

Is statistics math hard?

As previously discussed, the hardest part of statistics is figuring out how to approach each problem. Once the correct logic is understood and correct formulas are selected to answer a certain problem type, the actual math computation is relatively easy and involves basic algebra and calculator skills.

What are the 5 basic statistics?

5 basic statistics concepts Regression. Regression is a method for comparing two variables when one of them is independent and the other, or the others, depends on that first variable. ... Calculating the mean. ... Standard deviation. ... Sample size determination. ... Hypothesis testing. Feb 3, 2023

What are the 5 main statistics?

A summary consists of five values: the most extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median . These values are presented together and ordered from lowest to highest: minimum value, lower quartile (Q 1 ), median value (Q 2 ), upper quartile (Q 3 ), maximum value.

How to calculate p value?

For a lower-tailed test, the p-value is equal to this probability; p-value = cdf(ts). For an upper-tailed test, the p-value is equal to one minus this probability; p-value = 1 - cdf(ts). More items...

What are the 4 types of probability in statistics?

Classical Probability, Empirical Probability, Subjective Probability, Axiomatic Probability are the four types of probabilities.

What are the 8 basic statistics concepts?

Inferential statistics is a field that interprets or makes inferences about a set of observations. Common concepts include population, sample and parameter, measures of Central tendency, variance, covariance and standard deviation, regression, skewness, and ANOVA .

What is the best way to learn statistics and probability?

In general, the best way to learn statistics is through the use of real-world examples . Statistics and probability are used in many aspects of daily life, including sports, playing games that involve dice, and card games.

Basics of Statistics - Others Questions & Answers

Q: Happy often? The 1996 GSS asked, “How many days in the past seven days have you felt happy?” (This was the most recent year this question was posed.) a. Using the GSS variable HAPFEEL, verify that the sample had a mean of 5.27 and a... Posted 2 years ago

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Q: How often feel sad? Refer to the previous exercise. This question was asked of 10 students in a class at the University of Wisconsin recently. The responses were 0, 0, 1, 0, 7, 2, 1, 0, 0, 3. Find and interpret a 90% confidence interval for the... Posted 11 days ago

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Q: How often do women feel sad? A recent GSS asked, “How many days in the past seven days have you felt sad?” The 816 women who responded had a median of 1, mean of 1.81, and standard deviation of 1.98. The 633 men who responded had a median... Posted 2 years ago

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Q: How long lived in town? The General Social Survey has asked subjects, “How long have you lived in the city, town, or community where you live now?” The responses of 1415 subjects in one survey had a mode of less than 1 year, a median of... Posted 2 years ago

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Q: More time on emails per week Refer to the previous exercise. Interpret each item in the following printout for a sample of 7446 Americans. 95% confidence interval results: µ : Mean of variable Posted 11 days ago

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Q: Time spent on emails per week In a survey conducted in 2014, the General Social Survey (GSS) asked a sample of 7446 Americans how many minutes or hours they spent sending and answering emails. The results showed an average of 5.234 hours of email... Posted 11 days ago

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Q: Fuel efficiency The government website fueleconomy. gov has data on thousands of cars regarding their fuel efficiency. A random sample from this website of SUVs manufactured between 2012 and 2015 gives the following data on the combined (city and... Posted 2 years ago

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Q: t-scores a. Show how the t-score for a 95% confidence interval changes as the sample size increases from 10 to 20 to 30 to infinity. b. What does the answer in part a suggest about how the t distribution compares to the standard normal distribution? Posted 11 days ago

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Q: Travel to work As part of the 2000 census, the Bureau of the Census surveyed 700,000 households to study transportation to work. It reported that 76.3% drove alone to work, 11.2% carpooled, 5.1% took mass transit, 3.2% worked at home, 0.4% bicycled,... Posted 2 years ago

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Q: Grandpas using e-mail When the GSS asked in 2012, “About how many hours per week do you spend sending and answering e-mail?” the nine males in the sample of age at least 80 responded: 0, 0, 0, 1, 2, 3, 4, 4, 13 a. The TI-83+/84 screen... Posted 2 months ago

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Q: More NSA spying Refer to the previous exercise. a. Of the 1001 adults surveyed in Turkey, 49% said yes to the question from the Pew Research Center, resulting in a 95% confidence interval of (0.46, 0.52). True or false: We can be 95% confident that... Posted 11 days ago

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Q: Legalize marijuana? The General Social Survey has asked respondents, “Do you think the use of marijuana should be made legal or not?” Go to the GSS website, sda.berkeley. edu/GSS. For the 2008 survey with variable GRASS: a. Of the... Posted 2 years ago

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Q: Wife supporting husband Consider the statement that it is better for the man to work and the woman to tend the home, from the GSS (variable denoted FEFAM). a. Go to the sda.berkeley.edu/GSS website. Find the number who agreed or strongly agreed with... Posted 2 years ago

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Q: Alternative therapies The Department of Public Health at the University of Western Australia conducted a survey in which they randomly sampled general practitioners (GP) in Australia. One question asked whether the GP had ever studied... Posted 2 months ago

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Q: Work agreement for nannies According to a 2016 poll of families in New York City who employ a nanny, 75% did not enter into a written work agreement with them. a. What has to be assumed about this sample to construct a confidence interval for the... Posted 2 years ago

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Q: Female belief in life after death Refer to the previous exercise. The following printout shows results for the females in the sample, where X = the number answering yes. Explain how to interpret each item, in context. Posted 11 days ago

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Q: Life after death The variable POSTLIFE in the 2012 General Social Survey asked, “Do you believe in life after death?” A report based on these data stated that “81% of Americans believe in life after death. The margin of error for... Posted 2 years ago

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Q: Technology and productivity In 2014, a survey was conducted among a sample of adults who use the Internet. It included 535 respondents employed in full-time or parttime jobs. 46% of online workers felt their productivity increased because of... Posted 11 days ago

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Q: British monarchy After the British monarchy celebrated its diamond jubilee in 2012, a July poll conducted by YouGov.com and the Sunday Times of 1,667 British residents showed that 86% think the Queen personally has done a good job during her time on... Posted 11 days ago

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Q: Approval rating for president In July 2014, midway through his second term as president, Gallup estimated Obama’s approval rate at 42%. According to gallup.com, “. . . [R]esults are based on telephone interviews with approximately 1,500... Posted 11 days ago

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Q: Unemployed college grads The U.S Bureau of the Census reports that based on data from the American Community Survey in 2012, 3.6 percent of all college graduates between the ages of 25 and 64 were unemployed. A larger percentage of men than women... Posted 11 days ago

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Q: Before conducting a study, we can determine the sample size n having a certain margin of error. Table 8.6 shows the sample size formulas. To use them, we must (1) select the margin of error m, (2) select the confidence level, which determines the... Posted 11 days ago

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Q: For estimating a mean, the t distribution accounts for the extra variability due to using the sample standard deviation s to estimate the population standard deviation in finding a standard error. The t method assumes that the population distribution... Posted 11 days ago

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Q: For estimating a proportion, the formulas rely on the central limit theorem. For large random samples, this guarantees that the sample proportion has a normal sampling distribution. For estimating a proportion with small samples (fewer than 15... Posted 11 days ago

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Q: The z- or t-score depends on the confidence level, the probability that the method produces a confidence interval that contains the population parameter value. For instance, the probability that the sample proportion pn falls within 1.96 standard... Posted 11 days ago

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Q: j For the proportion, the score is a z-score from the normal distribution. For the mean, the score is a t-score from the t distribution with degrees of freedom df ∙ n ∙ 1. The t-score is similar to a z-score when df >= 30. Table 8.6... Posted 11 days ago

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Q: A confidence interval contains the most plausible values for a parameter. Confidence intervals for most parameters have the form Estimate ± margin of error, which is estimate±(z- or t- score) * (se) where se is the standard error of the... Posted 11 days ago

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Q: We’ve now learned how to estimate the population proportion p for categorical variables and the population mean m for quantitative variables. An estimate of the population mean m is the sample mean x. An estimate of the population proportion p... Posted 11 days ago

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Q: Sample versus sampling Each student should bring 10 coins to class. For each coin, observe its age, the difference between the current year and the year on thecoin. a. Using all the students’ observations, the class should construct a... Posted 11 days ago

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Q: Coin-tossing distributions For a single toss of a balanced coin, let x = 1 for a head and x = 0 for a tail. a. Construct the probability distribution for x and calculate its mean. (You can think of this as the population distribution corresponding to... Posted 8 months ago

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Q: Simulate a sampling distribution The table (data are available on the book’s website) provides prices per night for all 51 available hotel rooms (as of December 2014) in Panama City Beach, Florida, for a week in March 2015 (spring break). The... Posted 11 days ago

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Q: Finite populations The formula / n for the standard deviation of x actually is an approximation that treats the population size as infinitely large relative to the sample size n. The exact formula for a finite population size N is The term is... Posted 11 days ago

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Q: Standard deviation of a proportion Suppose x = 1 with probability p, and x = 0 with probability (1 – p). Then, x is the special case of a binomial random variable with n = 1, so that = n p (1 – p) = p( 1 – p). With n trials, using... Posted 11 days ago

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Q: Sample = population Let X = GPA for students in your school. a. What would the sampling distribution of the sample mean look like if you sampled every student in the school, so the sample size equals the population size? (Hint: The sample mean... Posted 11 days ago

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Q: Multiple choice: Sampling distribution The sampling distribution of a sample mean for a random sample size of 100 describes a. How sample means tend to vary from random sample to random sample of size 100. b. How observations tend to vary from person... Posted 2 years ago

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Q: Multiple choice: CLT The central limit theorem implies a. All variables have approximately bell-shaped data distributions if a random sample contains at least about 30 observations. b. Population distributions are normal whenever the population size... Posted 2 years ago

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Q: True or false As the sample size increases, the standard deviation of the sampling distribution of x increases. Explain your answer. Multiple choice: Standard deviation Which of the following is not correct? The standard deviation of a statistic... Posted 2 years ago

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Q: Winning at roulette Part b of Example 7 used the central limit theorem to approximate the probability of coming out ahead if you bet $10 on red on each of 40 roulette wheel spins. For each spin, the winnings are $10with probability 18/38 and -... Posted 11 days ago

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Q: Simulating pizza preference with p = 0.6 Access the Sampling Distribution of the Sample Proportion web app. When p = 0.6 and the sample size n = 3, the mean and standard deviation of the sampling distribution (given in the table in part a of Exercise... Posted 11 days ago

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Q: Simulating pizza preference with p = 0.5 Access theSampling Distribution of the Sample Proportion webapp. a. For p = 0.5 and a sample of size n = 3, the graph of the sampling distribution is given below. (This is the graph corresponding... Posted 11 days ago

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Q: Pizza preference with p = 0.6 Refer to the previous two exercises but now suppose the population proportion in Boston preferring pizza A is p = 0.6 instead of p = 0.5. (Then, the eight possible outcomes (AAA, AAD, . . . , DDA, DDD) of a sample of... Posted one month ago

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Q: Sampling distribution via the binomial Refer to the previous exercise, in which the proportion of people preferring pizza A is p = 0.5 and a sample of size n = 3 is taken. The sampling distribution of the sample proportion of people preferring pizza... Posted 11 days ago

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Q: Purpose of sampling distribution You’d like to estimate the proportion of all students in your school who are fluent in more than one language. You poll a random sample of 50 students and get a sample proportion of 0.12. Explain why the... Posted 11 days ago

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Q: What is a sampling distribution? How would you explain to someone who has never studied statistics what a sampling distribution is? Explain by using the example of polls of 1000 Canadians for estimating the proportion who think the prime minister is... Posted 11 days ago

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Q: CLT for custom population Access the Sampling Distribution for a Sample Mean web app and select Build Own as the shape for the population distribution. By typing numbers into the text field, you can create your own population distribution. Repeating... Posted 11 days ago

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Q: Too little or too much cola? Refer to the previous exercise. When a machine for dispensing a cola drink intobottles is in statistical control, the amount dispensed has a mean of 500 ml (milliliters) and a standard deviation of 4 ml. a. In... Posted 11 days ago

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Q: Using control charts to assess quality In many industrial production processes, measurements are made periodically on critical characteristics to ensure that the process is operating properly. Observations vary from item to item being produced,... Posted 11 days ago

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Q: Number of pets According to data on StatCrunch.com, the mean number of X = pets owned per household in a certain area in the United States was 1.88 pets, and the standard deviation was 1.67. a. Does X have a normal distribution? Explain. b. For a... Posted one month ago

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Q: PDI The scores on the Psychom*otor Development Index (PDI), a scale of infant development, have a normal population distribution with mean 100 and standard deviation 15. An infant is selected at random. a. Find the z-score for a PDI value of 90. b. A... Posted 2 years ago

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Q: Bank machine withdrawals An executive in an Australian savings bank decides to estimate the mean amount of money withdrawn in bank machine transactions. From past experience, she believes that $50 (Australian) is a reasonable guess for the standard... Posted 11 days ago

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Q: Home runs Based on data from the 2010 Major League Baseball season, X = number of home runs the San Francisco Giants hit in a game has a mean of 1.0 and a standard deviation of 1.0. a. Do you think X has a normal distribution? Why or why not? b.... Posted one year ago

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Basics of Statistics - Others Questions & Answers

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