ENR 2000 Exam #1 Review Problems

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Questions and Answers

What is the mean, median, and mode for the given values?

Mean: 7.5, Median: 7.5, Mode: 6

Compute the range and interquartile range for the given values.

Range: 14, Interquartile Range: 7

Are there any outliers in the data set?

Yes

For each of the following data types (a-e), indicate if they are nominal, ordinal, interval, or ratio data: a. Types of birds, b. Marathon winners, c. Temperature readings, d. Height of trees, e. Highways.

a. Nominal, b. Ordinal, c. Interval, d. Ratio, e. Nominal Signup and view all the answers

For which of the above data types is it appropriate to compute a mean?

c. Temperature readings and d. Height of trees Signup and view all the answers

What does it mean if the distribution of data is skewed?

It means that the data tails off more on one side than the other. Signup and view all the answers

Which of the following is an open-ended class interval?

Less than 5 Signup and view all the answers

Compute the mean for the provided Semester GPA and Credit Hours.

Mean: 3.33 Signup and view all the answers

If your essay for a college scholarship was ranked in the 10th percentile, should you be excited about this news?

False Signup and view all the answers

What is the difference between σ and S?

σ is the population standard deviation, while S is the sample standard deviation. Signup and view all the answers

What is the difference between µ and 𝑋?

µ is the population mean, while 𝑋 is the sample mean. Signup and view all the answers

What is a deviation score?

A deviation score measures how far a data point is from the mean. Signup and view all the answers

Compute the standard deviation for the following values: (4, 2, 10, 6, 0, 2).

Standard Deviation: 3.16 Signup and view all the answers

Convert each value to standard deviation units (z scores).

Z-scores: (0.63, -0.32, 2.02, 0.32, -1.58, -0.32) Signup and view all the answers

What is the mean and standard deviation of the z scores?

Mean: 0, Standard Deviation: 1 Signup and view all the answers

If you obtain a z score of 3.5, how would you describe this value?

Far away from the mean Signup and view all the answers

Is the data positively or negatively skewed if the mean is 48 and the median is 60?

Negatively skewed Signup and view all the answers

Given the means of two groups, how would you classify the effect size between Group 1 (mean = 25) and Group 2 (mean = 35) with σ = 8?

Medium Signup and view all the answers

What does effect size mean?

Effect size quantifies the strength of a phenomenon or the magnitude of an effect. Signup and view all the answers

How would you describe a correlation of -0.85 between time to complete a hike and hours of sleep?

Strong negative correlation Signup and view all the answers

How would you interpret the correlation between time to complete a hike and sleep for a -0.85 value?

The more sleep you obtained, the less time it takes to complete the hike. Signup and view all the answers

How would you describe the correlation of 0.45 between time to complete a hike and age?

Moderate positive correlation Signup and view all the answers

What are the 3 formulas for computing r, the correlation coefficient?

Pearson's r, Spearman's rank correlation, and Kendall's tau. Signup and view all the answers

In the equation 𝑌 = a + bX, if a is the y-intercept and b is the slope, how much will the value of Y change for each unit change in X?

Y will change by b units. Signup and view all the answers

Given a correlation of 0.42 between automobiles and cyclists, what is the predicted value of cyclists when X = 80, Sx = 12, and Sy = 3?

Predicted value of cyclists: 14.5 Signup and view all the answers

What does Σ mean?

Summation, or the total sum of a set of values. Signup and view all the answers

Compute the correlation between mood score (X) and hours of sunshine (Y).

Need additional data to compute. Signup and view all the answers

Study Notes

Frequency Distribution and Descriptive Statistics

Formal grouped frequency distribution requires categorizing data into intervals.
Parameters for distribution: interval size (i=3) and midpoint calculation is essential.

Measures of Central Tendency

Mean, median, and mode are critical for summarizing data.
Mean reflects the average of the values, median indicates the middle value, and mode identifies the most frequently occurring value.

Range and Interquartile Range

Range is computed as the difference between the maximum and minimum values.
Interquartile range (IQR) shows the spread of the middle 50% of data, calculated as Q3 - Q1.

Identifying Outliers

Analyze data to check for any values significantly distant from others, which may be considered outliers.

Visualization Techniques

Box and whisker plots represent the distribution, highlighting median, quartiles, and outliers.
Stem-and-leaf diagrams display data while preserving the original values.

Data Types

Nominal: Categorical data without order (e.g., types of birds).
Ordinal: Categorical data with order (e.g., race placements).
Interval: Numerical data without a true zero (e.g., temperature).
Ratio: Numerical data with a true zero (e.g., tree height, credit hours).

Mean Calculation Appropriateness

Only interval and ratio data allow mean computation (e.g., temperatures, heights).

Skewness in Data

A skewed distribution indicates asymmetry; skewness can be positive (tail to the right) or negative (tail to the left).

Open-ended Class Intervals

Open-ended class intervals do not have fixed upper or lower limits (e.g., "less than 5").

Mean Calculation Example

Semester GPA weighted mean requires multiplying GPAs with credit hours, summing the products, then dividing by total credit hours.

Percentile Ranking

Being in the 10th percentile signifies ranking lower than 90% of peers, generally not an encouraging outcome.

Statistical Notation Differences

σ represents population standard deviation, while S denotes sample standard deviation.
µ denotes population mean, whereas X̄ indicates sample mean.

Deviation Scores

A deviation score quantifies how far a data point is from the mean, used in calculating standard deviation.

Standard Deviation Calculation

Standard deviation quantifies data variability, calculated through deviation scores or raw data formulas.

Z-scores Conversion

Each value converted into z-scores reflects how many standard deviations away the value is from the mean.

Description of Z-scores

A z-score of 3.5 indicates an extreme value well beyond the mean, suggesting it is far from the average.

Analysis of Skewed Data

Mean and median comparison helps assess skewness; if mean < median, data is negatively skewed, vice versa.

Effect Size Interpretation

Effect size provides insight into the significance and magnitude of study findings, categorized as small, medium, or large based on mean differences and standard deviations.

Correlation Insights

A strong negative correlation (like -0.85) indicates an inverse relationship, where one variable increases as the other decreases.

Correlation Interpretation

An increase in sleep correlates with less time for completing a hike, based on the negative correlation.

Additional Correlation Assessment

A moderate positive correlation (0.45) implies some direct relationship between age and hiking time.

Formulas for Correlation Coefficient

Three formulas exist for computing Pearson's r; each requires pairs of correlated data points and deviations from their means.

Predictive Equation Understanding

In the equation Y = a + bX, a is the constant (y-intercept), while b indicates the change in Y for a one-unit increase in X.

Correlation Prediction Example

Using given values, predicted cyclist count can be calculated based on the correlation between vehicles and cyclists.

Summation Notation

Σ symbolizes the summation of a series of values, fundamental in statistical calculations.

Mood and Weather Correlation

Calculating correlation between mood scores and sunshine hours will quantify the relationship between these two variables.

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Description

Prepare for ENR 2000 with these review problems focusing on developing a formal grouped frequency distribution. This quiz involves data analysis techniques applied to visits at a state park over a two-month period. Practice calculating midpoints and working with frequency distributions to sharpen your skills.