Measures of Central Tendency and Standard Deviation Quiz

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Questions and Answers

What happens to the median if the smallest value in a data set is increased?

The median decreases

Cannot be determined

The median remains the same (correct)

The median increases

What does the standard deviation measure in a set of data?

The most frequent value

The spread of the values (correct)

The average value

The middle value

How does an increase in standard deviation affect the spread of data?

Decreases the spread

Inverts the spread

Does not affect the spread

Increases the spread (correct)

What is the square of the standard deviation called?

Variance Signup and view all the answers

Which statement is TRUE of the score distribution with different standard deviations (SDs) but equal means?

The scores of Set B have less variability than the scores in Set A Signup and view all the answers

If the variance of a data set is correctly computed with the formula using n-1 in the denominator, which of the following is true?

The variance is underestimated Signup and view all the answers

What characterizes a response variable in an experiment?

It is monitored to characterize system performance/behavior Signup and view all the answers

Why is it important to address extraneous variables in experiment planning?

To avoid loss of information in interpreting effects of primary factors Signup and view all the answers

Which probability sampling technique involves selecting every kth individual from a list after a random starting point?

Systematic Sampling Signup and view all the answers

What does it mean when half of the observations in a data set are greater than the mean?

The data set is skewed to the right Signup and view all the answers

In a normal distribution, which measure of central tendency is equal to the mode and the median?

Mean Signup and view all the answers

What does a high standard deviation indicate about a data set?

There are extreme variations in the data set Signup and view all the answers

What is the correct formula to calculate the standard deviation?

Square root of the variance Signup and view all the answers

If a survey uses simple random sampling, what can be inferred about the selected sample?

It represents the entire population accurately Signup and view all the answers

When calculating the mean salary of a group, which value is most susceptible to being affected by extreme outliers?

Mean Signup and view all the answers

What is the primary reason behind using probability sampling techniques in research studies?

To ensure every individual has an equal chance of being selected Signup and view all the answers

Which situation represents a type I error in hypothesis testing?

Rejecting a true null hypothesis Signup and view all the answers

When planning an experiment, what term describes factors that could influence the response variable but are not the primary focus of study?

Extraneous variables Signup and view all the answers

Study Notes

Median and Data Changes

Increasing the smallest value in a data set can maintain or shift the median if it affects the overall arrangement of values.
Median is the middle value when data is ordered; if the number of values is even, it's the average of the two middle values.

Standard Deviation Insights

Standard deviation measures the amount of variability or dispersion of data points around the mean.
An increase in standard deviation indicates a greater spread or variability in the data set.
The square of the standard deviation is called variance.

Distribution and Characteristics

In distributions with the same mean but different standard deviations, the distribution with the higher standard deviation shows a wider spread of scores.
If variance is calculated using n-1, it indicates a sample rather than a population, providing an unbiased estimate of the population variance.

Response Variables and Experimental Design

A response variable in an experiment is the outcome or effect that is measured and analyzed in response to changes in independent variables.
Addressing extraneous variables is crucial to minimize their influence on the response variable, ensuring valid results.

Probability Sampling Techniques

Systematic sampling involves selecting every kth individual from a list after starting from a random point.
Simple random sampling ensures each individual in the population has an equal chance of being selected, allowing for generalized conclusions about the population.

Data Set Implications

When half of the observations in a data set are greater than the mean, it implies a left-skewed distribution.
In a normal distribution, the mode, median, and mean are all equal, representing the most common, middle, and average values respectively.

Data Analysis and Outliers

A high standard deviation signals that data points are spread out over a wider range, indicating more variability.
The mean salary of a group is particularly sensitive to extreme outliers, which can skew average values significantly.

Importance of Probability Sampling

Probability sampling techniques are utilized primarily to ensure that the sample is representative of the population, which improves the reliability of statistical inferences.

Error Types in Hypothesis Testing

A type I error occurs when a true null hypothesis is incorrectly rejected, indicating a false positive in hypothesis testing.

Experimental Factors

Factors influencing the response variable but not the main focus of study are termed extraneous variables, which need to be controlled for accurate experimentation.

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Description

Test your knowledge on measures of central tendency like mean, median, and mode, as well as understanding standard deviation. Learn how to determine reliable measures of central tendency and how changing data values can affect the median.