Data Analysis Unit 1

What is the primary purpose of data visualizations?

To summarize data and communicate findings

When would you use a scatter plot in data analysis

To show relationships between two numeric variables

What does a pie chart primarily illustrate

Part of a whole

Which chart type is best used to show the distribution and outliers of a dataset?

Bow Plot

In which scenario would you best use a histogram?

To show frequency distribution of continuous data

Comparing Test Scores

Evaluates performance across different classes

Analyzing salary ranges

Summarizes income distribution in a job sector

Summarizing survey responses

Provides insights into public opinion or preferences

Identifying outliers

Highlights values that fall far outside typical ranges

IQR

Interquartile range, the difference between Q3 and Q1

Skewness

A measure of the asymmetry of the data distribution

Outliers

Values that are significantly higher or lower than most of the data

Box Plot

A graphical representation of the Five-Number Summary

Summarizes key aspects of data

Provides a quick overview of data distribution

Identifies center

Helps locate the median of the dataset

Useful for skewed distributions

Can describe data that isn’t symmetrically distributed

Visualizing with a Box Plot

Uses the Five-Number summary to illustrate data characteristics

Minimum

The smallest value in a dataset

First Quartile (Q1)

The median of the lower half of the dataset

Median (Q2)

The middle value separating the higher half from the lower half of the dataset

Maximum

The largest value in a dataset

Mean

Average of data

Median

Middle value of data

Skewness

Asymmetry of data distribution

Mode

Most frequently occurring value

Left Skew

Mean < Median

Right Skew

Mean > Median

Symmetric Distribution

Mean = Median

Extreme Left Skew

Mean «« Median (mean much lower than median)

Which of the following measures is NOT considered a measure of center?

Range

What is the primary purpose of descriptive statistics?

To summarize and describe data sets

What does a confidence interval represent

A range of values that likely contains the population parameter

In hypothesis testing, a one-tailed test is used for what purpose?

To test a claim in one specific direction

Which sampling method ensures that every individual in the population has an equal chance of being selected?

Simple Random Sampling

In which scale can all three measures of central tendency (mean, median, mode) be used effectively?

Raito Scale

Which scale of measurement is used when data can be categorized, ordered, but the intervals between categories are not equal?

Ordinal Scale

What type of data measurement is ‘gender’ classified as?

Nominal Scale

Which of the following is an example of a Ratio Scale measurement

Height of a person

Why is it important to understand scales of measurement in statistics?

To select appropriate statistical methods and ensure accuracy in research

Which measure of dispersion is most sensitive to outliers?

Range

Why is standard deviation often preferred over variance in data analysis?

It is expressed in the same units as the data, making it easier to interpret

What is the primary purpose of measure of data dispersion?

To describe how spread out data values are

What does the range of dataset indicate

The difference between the maximum and minimum values

What is a major advantage of using non-probability sampling methods?

It is convenient and cot-effective

Which of the following is a type of non-probability sampling?

Snowball sampling

Which situation is most appropriate for using convenience sampling?

Surveying students in a classroom setting

What is a key limitation of non-probability sampling

Results may not generalize to the entire population

What is non-probability sampling

Selecting participants without giving every member of the population an equal chance

What strategy is recommended to reduce measurement error in surveys

Increase the number of survey respondents

What is the primary cause of sampling error

Natural variability between a smaple and the population

Which of the following is NOT a type of non-sampling error

Sampling error

How can sampling error be minimzed?

By increasing the sample size

Which error occurs when respondents fail to participate in a survey

Nonresponse Error

When using a z-score, a higher z-value indicates that the sample proportion is further from the population proportion, which can impact the probability calculation

true

To reliability use a normal approximation for sample proportions, random sampling is not necessary as long as the sample size is large enough

False

The shape of the sampling distribution of sampling proportions will always be normal regardless of sample size or population proportion

False

In the context of estimating probabilities using sampling distributions for proportions, what is the primary purpose of calculating the z-score

To standardize the sample proportion for use with the standard normal distribution

Why is it important to ensure that the sampling distribution is approximately normal before finding probabilities

Because the properties of the normal distribution are use to calculate probabilities

What does the Central Limit Theorem (CLT) state about the sampling distribution of the sample mean for a large enough sample size?

It is approximately normal even if the population distribution is not

Hypothesis Testing

CLT allows us to use normal approximation to determine the significance of results

Confidence intervals

Provides a range around the sample estimate that reflects uncertainty due to sample variability

Approximation of probabilities

Helps in estimating probabilities for sample statistics using the normal distribution

Data visualization

Plays a critical role in creating visuals to represent raw data

CLT

States that the distribution of sample means approaches a normal distribution as sample size increases

Standard Error (SE)

Calculated as the standard deviation divided by the square root of the sample size

Sampling Distribution

The probability distribution of a statistic obtained through a large number of samples drawn from a specific population

Population proportion

The true proportion of a certain characteristic in the entire population

Which measure of central tendency can be used for categorical data?

Mode

In which scenario would you prefer to use the median over the mean?

When the data is skewed or contains outliers

Which measures of central tendency is calculated by summing all values and dividing by the number of values?

mean

What is a key benefit of using stratified sampling?

It ensures representation across key subgroups of the population

Which of the following is an example of systematic sampling

Selecting every 5th participant from a list of volunteers

In which scenario might cluster sampling be most advantageous

For research involving large, geographically dispersed populations

What is the primary characteristic of probability sampling

Every member of the population has a known, non-zero chance of being selected

Which method of probability sampling is most effective for subgroup

Stratified sampling