Free Printable Worksheets for learning Statistics at the College level

Here's some sample Statistics info sheets Sign in to generate your own info sheet worksheet.

Statistics

Statistics is the study of collecting, analyzing, interpreting and presenting data.

Key Concepts

Data: Facts, figures, or information collected for analysis
Population: The entire group of individuals or instances about whom information is needed
Sample: A subset of the population
Variables: Characteristics of interest for each individual in the population
Descriptive Statistics: Methods to summarize and describe characteristics of a set of data
Inferential Statistics: Methods to estimate characteristics of a population based on a sample of data
Probability: The chance of an event occurring
Hypothesis Testing: A method of making decisions using data
Confidence Intervals: A range of values that is likely to contain an unknown parameter

Statistical Data Types

Nominal: Categories without order or ranking
Ordinal: Categories with order or ranking
Interval: Differences between values are consistent, but there is no true zero point
Ratio: Differences between values are consistent, and there is a true zero point

Measures of Central Tendency

Mean: Average of a set of numbers
Median: Middle value of a set of numbers
Mode: The value that appears most frequently in a set of numbers

Measures of Variability

Range: The difference between the maximum and minimum values in a set of numbers
Variance: The average of the squared differences from the mean
Standard Deviation: The square root of the variance

Sampling Techniques

Random Sampling: Each member of the population has an equal chance of being selected for the sample
Stratified Sampling: Divide the population into groups, or strata, and randomly select individuals from each group
Cluster Sampling: Divide the population into clusters and randomly select entire clusters for inclusion in the sample
Systematic Sampling: Choose a random starting point and select every nth member of the population

Conclusion

Statistics is an important tool for analyzing and making decisions based on data. By understanding the key concepts and measures, as well as different sampling techniques, you will be able to effectively collect, analyze, and interpret data in your research and decision-making processes.

Here's some sample Statistics vocabulary lists Sign in to generate your own vocabulary list worksheet.

Word	Definition
Mean	The average of a set of numbers. It is calculated by adding all the numbers together and then dividing by the total number of values.
Median	The middle value in a set of numbers when they are arranged in order. If there is an even number of values, it is the average of the two middle values.
Mode	The value(s) that appear most frequently in a set of numbers.
Range	The difference between the highest and lowest values in a set of numbers.
Variance	A measure of how spread out a set of numbers is. It is calculated by taking the average of the squared differences from the mean.
Standard deviation	Another way to measure how spread out a set of numbers is. It is the square root of the variance.
Probability	The likelihood of an event occurring. It ranges from 0 (impossible) to 1 (certain).
Normal distribution	A bell-shaped curve that represents a set of data whose values fall close to the mean. It is characterized by its mean and standard deviation.
Quartile	Values that divide a set of numbers into quarters, or segments of 25%. The first quartile is the value at the 25th percentile, the second quartile is the median, and the third quartile is the value at the 75th percentile.
Skewness	A measure of the asymmetry of a distribution, or how lopsided it is. Positive skewness means the tail is longer on the right side, negative skewness means the tail is longer on the left.
Outlier	An observation that lies an abnormal distance from other values in a random sample from a population.
Sample size	The number of observations in a sample. A larger sample size reduces the sampling error and makes the sample more representative of the population.
Confidence interval	An estimate of the range of values that is likely to contain the true value of a population parameter, with a specified level of confidence.
Hypothesis	An idea or theory that is proposed and tested through experimentation or observation.
Null hypothesis	A hypothesis that there is no significant difference between specified populations or samples, or that a proposed theory is false.
Alternative hypothesis	A hypothesis that there is a significant difference between specified populations or samples, or that a proposed theory is true.
Correlation	A measure of the association between two variables. A positive correlation means both variables move in the same direction, a negative correlation means they move in opposite directions.
Regression	A statistical analysis that measures the relationship between two or more quantitative variables.
Coefficient of determination	A measure of how well a set of observations can be predicted by a linear function. It ranges from 0 to 1, with higher values indicating a stronger correlation.
Chi-squared test	A statistical test used to compare observed and expected values in different categories, and to determine whether they are significantly different.

Here's some sample Statistics study guides Sign in to generate your own study guide worksheet.

Statistics Study Guide

Introduction

Statistics is a branch of mathematics that deals with collecting, analyzing, interpreting, presenting, and organizing data. It is essential in modern society because it enables us to make informed decisions based on data and evidence.

Descriptive Statistics

Descriptive statistics involves describing and summarizing data using numbers, graphs, and charts. It includes measures of central tendency (mean, median, mode) and measures of variability (range, standard deviation).

Inferential Statistics

Inferential statistics involves using sample data to make inferences or predictions about a larger population. It includes hypothesis testing and confidence intervals.

Probability

Probability is the study of uncertainty and randomness. It allows us to predict the likelihood of an event occurring. It includes probability rules, conditional probability, and Bayes' theorem.

Sampling

Sampling is the practice of selecting a subset of individuals from a population to estimate characteristics of the entire population. It includes simple random sampling, stratified random sampling, and cluster sampling.

Linear Regression

Linear regression is a statistical method that allows us to model the relationship between two variables. It helps us to predict the value of one variable based on the value of another variable. It includes simple linear regression and multiple linear regression.

Experimental Design

Experimental design is the process of planning and conducting experiments to measure the effect of one or more variables on an outcome. It includes the design of experiments, control groups, and randomization.

Conclusion

Statistics is an important branch of mathematics that has many applications in various fields. By understanding the concepts of descriptive statistics, inferential statistics, probability, sampling, linear regression, and experimental design, you will be able to analyze and interpret data and make informed decisions based on evidence.

Here's some sample Statistics practice sheets Sign in to generate your own practice sheet worksheet.

Practice Sheet for Statistics

Section 1: Descriptive Statistics

Calculate the mean, median, and mode for the following data set:

5, 8, 3, 9, 2, 7, 5, 4
Find the range, variance, and standard deviation for the following data set:

12, 15, 17, 21, 24
Calculate the percentile rank of the following score for the given data set:

Score: 83 Data set: 65, 72, 78, 83, 89, 94
Construct a box plot for the following data set:

12, 16, 18, 21, 23, 24, 29

Section 2: Probability

What is the probability of getting a sum of 8 when rolling two dice?
A bag contains 5 red balls and 3 green balls. If two balls are drawn at random without replacement, what is the probability that both balls are red?
A coin is flipped 3 times. What is the probability of getting exactly 2 heads?

Section 3: Inferential Statistics

A sample of 50 people is taken from a population of 1000. The mean age of the sample is 25 with a standard deviation of 5. Calculate the 95% confidence interval for the population mean age.
A study was conducted to determine whether a new medication is effective in reducing blood pressure. The sample consisted of 1000 individuals, with 500 individuals receiving the medication and 500 individuals receiving a placebo. After 8 weeks, the individuals who received the medication had an average reduction in blood pressure of 10 mmHg, with a standard deviation of 3.5 mmHg. The individuals who received the placebo had an average reduction in blood pressure of 6 mmHg, with a standard deviation of 4 mmHg. Test the hypothesis that the medication is effective in reducing blood pressure at a significance level of 0.05.
A survey is conducted to determine the proportion of American adults who support a particular policy. A sample of 500 people is taken and 300 of them support the policy. Calculate the 99% confidence interval for the population proportion who support the policy.

Section 4: Correlation and Regression

Calculate the correlation coefficient for the following data set:

X: 2, 3, 5, 6, 8 Y: 4, 6, 9, 12, 15
Find the regression equation for the following data set:

X: 1, 3, 4, 6, 8 Y: 2, 5, 6, 8, 11
Interpret the slope of the regression equation from question 12.

Section 5: Hypothesis Testing

A company claims that the average time it takes to assemble a product is less than 20 minutes. A random sample of 25 products is taken and the average assembly time is 18 minutes with a standard deviation of 2 minutes. Test the hypothesis at a significance level of 0.01.
A study is conducted to determine if there is a significant difference in the mean weight of participants before and after a weight loss program. A sample of 20 participants is taken and the mean weight before the program is 180 lbs with a standard deviation of 20 lbs. After the program, the mean weight is 170 lbs with a standard deviation of 15 lbs. Test the hypothesis at a significance level of 0.05.

Practice Sheet for Statistics

Problem 1

Calculate the mean, median, and mode of the following set of numbers:

2, 4, 7, 8, 9, 10

Problem 2

Calculate the variance and standard deviation of the following set of numbers:

2, 4, 7, 8, 9, 10

Problem 3

Calculate the probability of the following event:

A coin is flipped twice and both flips result in heads.

Problem 4

Calculate the z-score of the following data point:

A data point with a value of 8 from a data set with a mean of 5 and a standard deviation of 2.

Problem 5

Calculate the correlation coefficient between the following two sets of data:

Set 1: 2, 4, 6, 8 Set 2: 3, 6, 9, 12

Practice Sheet for Learning Statistics

What is the definition of probability?
What is the difference between a population and a sample?
What is the difference between a discrete and a continuous random variable?
What is the formula for calculating the mean of a set of numbers?
What is the formula for calculating the variance of a set of numbers?
What is the Central Limit Theorem?
What is the difference between a normal and a binomial distribution?
What is the formula for calculating the standard deviation of a set of numbers?
What is a confidence interval?
What is the formula for the coefficient of determination?

Here's some sample Statistics quizzes Sign in to generate your own quiz worksheet.

Problem	Answer
What is the difference between descriptive statistics and inferential statistics?	Descriptive statistics summarizes and describes data, while inferential statistics makes inferences about a larger population based on a sample.
What is the standard deviation?	The standard deviation is a measure of the amount of variation or dispersion of a set of values.
What is a z-score and what is its significance?	A z-score measures the distance of a value from the mean of a distribution in terms of the number of standard deviations. It is significant because it allows comparison of values from different distributions.
What is the difference between correlation and causation?	Correlation is a relationship between two variables, while causation is the relationship where one variable causes the other to change. Correlation does not imply causation.
Describe the central limit theorem.	The central limit theorem states that as the sample size increases, the distribution of the sample means approaches a normal distribution, even if the original population is not normally distributed.
Explain what is meant by hypothesis testing.	Hypothesis testing is a statistical method that is used to test a hypothesis or claim about a population parameter, based on sample data.
What is the difference between a Type I error and a Type II error?	A Type I error occurs when a null hypothesis is rejected when it is actually true, and a Type II error occurs when a null hypothesis is not rejected when it is actually false.
What is the formula for calculating the coefficient of determination (R-squared)?	R-squared = (Explained variation / Total variation), where Explained variation is the sum of squares of the regression (SSR) and Total variation is the total sum of squares (SST).
What is ANOVA used for?	ANOVA (Analysis of Variance) is used to test for differences in means among more than two groups.
What is a p-value?	A p-value is the probability of observing a test statistic as extreme as the one computed from sample data, assuming the null hypothesis is true. A small p-value (less than the significance level) indicates strong evidence against the null hypothesis.

Question	Answer
What is the definition of a population in Statistics?	A population is a set of all elements or objects of interest in a statistical study.
What is the definition of a sample in Statistics?	A sample is a subset of the population that is used to represent the population in a statistical study.
What is the definition of a parameter in Statistics?	A parameter is a numerical characteristic of a population, such as the mean or the standard deviation.
What is the definition of a statistic in Statistics?	A statistic is a numerical characteristic of a sample, such as the mean or the standard deviation.
What is the difference between a population and a sample?	A population is the entire set of elements or objects of interest in a statistical study, while a sample is a subset of the population used to represent the population in a statistical study.
What is the difference between a parameter and a statistic?	A parameter is a numerical characteristic of a population, while a statistic is a numerical characteristic of a sample.
What is the definition of a probability distribution?	A probability distribution is a mathematical function that describes the probability of obtaining a given value of a random variable.
What is the definition of a random variable?	A random variable is a variable whose value is determined by a random process or by chance.
What is the definition of a hypothesis test?	A hypothesis test is a statistical test used to determine whether a hypothesis about a population parameter is true or false.
What is the definition of a confidence interval?	A confidence interval is an interval of values that is likely to contain the true value of a population parameter with a certain level of confidence.

Quiz: Statistics

Question	Answer
What is the most common measure of central tendency?	Mean
What is the formula for the standard deviation?	σ = √[ Σ (x - μ)2 / N ]
What is the formula for the coefficient of variation?	Coefficient of variation = (Standard Deviation / Mean) x 100
What is the difference between a population and a sample?	A population is the entire set of observations from which samples are taken, while a sample is a subset of the population.
What is a confidence interval?	A confidence interval is a range of values that is likely to contain the true value of a population parameter.
What is a correlation coefficient?	A correlation coefficient is a numerical measure of the strength of the relationship between two variables.
What is the difference between parametric and non-parametric tests?	Parametric tests make assumptions about the data, while non-parametric tests do not.
What is the difference between a descriptive and an inferential statistic?	Descriptive statistics are used to describe the characteristics of a population, while inferential statistics are used to make inferences about a population based on a sample.
What is the difference between a normal distribution and a binomial distribution?	A normal distribution is a continuous distribution, while a binomial distribution is a discrete distribution.
What is the difference between a Type I and a Type II error?	A Type I error is a false positive, while a Type II error is a false negative.