MAT251

Data is defined as __________.

individual facts

Information is processed, organized, and __________ data that provides useful knowledge.

structured

Qualitative data can be categorized, while __________ data takes numerical values.

Quantitative

______________ data can take values in categories such as country, gender, favorite color.

Qualitative

The difference between the largest and smallest values in a dataset is known as the __________.

Range

A dataset can be divided into __________, which split it into four equal parts.

quartiles

In statistics, the __________ is the value that occurs most frequently in a dataset.

Mode

The __________ is the average value calculated by summing all data points and dividing by the count.

Mean

The measure of __________ helps to describe the variability of data points around the mean.

dispersion

A __________ distribution exhibits a longer tail on one side, indicating skewness.

skewed

Confidence intervals provide an estimate of the __________ characteristics using samples.

population

Pearson’s median skewness is calculated using the formula __________.

3 * (Mean - Median) / Standard Deviation

Inferential statistics help make predictions about a __________ based on sample data.

population

The interquartile range (IQR) is used to measure the __________ of a dataset, focusing on the middle 50%.

dispersion

The _____ value represents the central point in a dataset identified after sorting.

Median

A standard score, also known as a z-score, indicates how many __________ a certain score is from the mean.

standard deviations

__________ statistics summarize and describe characteristics of a dataset.

Descriptive

What is dispersion in statistics?

Dispersion refers to the extent to which data points differ from the mean.

Name a common measure of dispersion.

Range, variance, and standard deviation are common measures of dispersion.

What does a small standard deviation indicate?

A small standard deviation indicates that data points are close to the mean.

What does a large standard deviation signify?

A large standard deviation shows that data points are spread out over a wider range of values.

How is variance different from standard deviation?

Variance is the average of the squared differences from the mean; standard deviation is the square root of variance.

When is the mode a useful measure?

The mode is useful for categorical data where we want to know the most common category.

Can there be more than one mode in a dataset?

Yes, a dataset can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes).

What is the formula for calculating the mean?

Mean = (Sum of all data points) / (Number of data points).

What is the primary measure of central tendency?

The mean is often referred to as the primary measure of central tendency.

What is the median and how is it calculated?

The median is the middle value in a sorted dataset. If the dataset has an even number of points, it is the average of the two middle points.

What does it mean if the mode is higher than the mean?

It may indicate a left-skewed distribution.

What is a skewed distribution?

A skewed distribution is one in which data points are not symmetrically distributed around the mean.

What can affect the mode of a dataset?

The mode can change with the frequency of certain values in the dataset.

What is the relationship between mean and median in a symmetric distribution?

In a symmetric distribution, the mean and median are equal.

How do you find the mode in a frequency distribution?

Identify the value with the highest frequency in the distribution.

Which measure of central tendency is most affected by outliers?

The mean is most affected by outliers.

What is the interquartile range (IQR)?

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

How does the IQR help in data analysis?

The IQR is used to measure the spread of the central 50% of the data, reducing the effect of outliers.

What does a higher IQR indicate?

A higher IQR indicates greater variability and dispersion among the middle values.

In what situations is the median preferred over the mean?

The median is preferred when dealing with skewed distributions or when there are outliers.

Can the mean be a non-existent value in some datasets?

Yes, if all values are undefined or if all numbers are 0, the mean may also be undefined.

What indicates a zero standard deviation?

A zero standard deviation indicates that all values in the dataset are identical.

What is a cumulative frequency?

Cumulative frequency is the sum of the frequencies of all data points up to a certain value.

How can data be visually displayed to represent dispersion?

Box plots and histograms can visually display the dispersion of data.

What is a uniform distribution?

A uniform distribution is one where all outcomes are equally likely.

What role does mode play in a bimodal distribution?

Both modes in a bimodal distribution represent the two most frequently occurring values.

What is the purpose of calculating the range?

Calculating the range provides a measure of the spread of values in a dataset.

How does one calculate the interquartile range?

IQR = Q3 - Q1.

What does it mean if the mode is equal to the mean and median?

It indicates a symmetric distribution.

When analyzing data, why is it important to consider dispersion?

Considering dispersion helps understand data variability and consistency.

What is the difference between absolute and relative dispersion?

Absolute dispersion deals with measures like standard deviation, while relative dispersion is represented as a fraction or percentage of the mean.

How do outliers affect the mean?

Outliers can significantly distort the mean, making it less representative of the dataset.

What is a probability distribution?

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes.

What does a box plot display?

A box plot displays the distribution of data based on a five-number summary: minimum, first quartile, median, third quartile, and maximum.

What is normalized data?

Normalized data adjusts values measured on different scales to a common scale.

What statistical methods help deal with outliers?

Winsorizing, trimming, and using median-based methods help deal with outliers.

What is the purpose of confidence intervals?

Confidence intervals estimate the uncertainty around a sample statistic.

When describing a dataset, why use the mode?

The mode identifies the most common value, which can highlight trends in the data.

How can measures of central tendency mislead?

If examined in isolation without measures of dispersion, they may not provide a complete picture of the data.

What is a histogram?

A histogram is a graphical representation of the distribution of numerical data.

How does the mean change when a constant is added to all values in a dataset?

The mean increases by that constant.

What does it indicate if the mean is less than the median?

It may indicate a right-skewed distribution.

What is the role of standard scores (z-scores)?

Z-scores indicate how many standard deviations a data point is from the mean.

What type of datasets are best represented by the mean?

Datasets that are normally distributed are best represented by the mean.

How does one identify an outlier?

An outlier can be identified if it lies beyond 1.5 times the IQR above Q3 or below Q1.

What is the mean of a dataset with equal values?

The mean will be the same as any value in the dataset.

Why is the mode not appropriate for numerical average calculations?

The mode reflects frequency, not the average value of a dataset.

What concepts should be compared with measures of central tendency?

Dispersion and variability should be compared with measures of central tendency.

What are the characteristics of a normal distribution?

It is symmetric, bell-shaped, and has mean = median = mode.

How can understanding mean, median, and mode help in real-world applications?

It aids in summarizing data, making decisions, and performing statistical analyses.

In analyzing healthcare data, which measure is often preferred?

In healthcare data, the median is often preferred to minimize the influence of outliers.

What are dummy variables?

Dummy variables are used in regression analysis to represent categories with binary values.

What is a scatter plot?

A scatter plot is a graph that shows the relationship between two quantitative variables.

What does a diagonal line on a scatter plot indicate?

A diagonal line indicates a positive or negative correlation between the variables.

How can one interpret high positive correlation?

A high positive correlation means that as one variable increases, so does the other.

What does a negative correlation in a scatter plot imply?

A negative correlation implies that as one variable increases, the other decreases.

What are the essential components of statistical inference?

Statistical inference includes point estimation, confidence intervals, and hypothesis testing.

When is the mean less informative than the median?

The mean may be less informative when dealing with skewed data or outliers.

Why is it critical to understand the shape of distribution?

Understanding the shape helps in choosing the appropriate statistical methods for analysis.