CLJ 262 exam 2

A research team is trying to determine if their distribution approximates a normal curve. More specifically, they want to know if the distribution has too much kurtosis. Which of the following values of a kurtosis statistic would suggest the research team has a problem?

+1.972

The mean score among students who completed an exam in statistics was 72 with a standard deviation of 4. Your score on the exam was 80. How many standard deviations above the mean is your score?

+2σ above the mean

To the right is an image from the Invisible Institute's Citizens Police Data Project. It captures the misconduct record of Jason Van Dyke of the CPD. Assume all measures on this infographic follow a normal curve, and use what you know about descriptive statistics to answer the following prompts. Identify which of the following benchmarks best approximates where Jason Van Dyke stands relative to other officers in regards to officer allegations of misconduct?

+2σ above the mean

To the right is an image from the Invisible Institute's Citizens Police Data Project. It captures the misconduct record of Jason Van Dyke of the CPD. Assume all measures on this infographic follow a normal curve, and use what you know about descriptive statistics to answer the following prompts. Identify which of the following benchmarks best approximates where Jason Van Dyke stands relative to other officers in regards to use of force reports?

+2σ above the mean

To the right is an image from the Invisible Institute's Citizens Police Data Project. It captures the misconduct record of Jason Van Dyke of the CPI. Assume all measures on this infographic follow a normal curve, and use what you know about descriptive statistics to answer the following prompts. Identity which of the following benchmarks best approximates where Jason Van Dyke stands relative to other officers in regards to civilian allegations of misconduct?

+2σ above the mean

The mean score among students who completed an exam in statistics was 72 with a standard deviation of 4. Your score on the exam was 80. If you scored a 70 on the exam, how many standard deviations below the mean is your score?

-0.5σ below the mean

What is the value of the typical case in our sample?

2.000

Assume that the incidents of police conduct in the United States follow a normal distribution. If we defined a "bad apple" [i.e., a high-disparity officer] as any police officer with incidents of misconduct that exceed two standard deviations above the mean, approximately what percentage of our sample would qualify as bad apples?

2.5%

What is the average for all the cases in our sample?

2.588

What is the value of the range of our distribution?

29.000

What is the value for the 75th percentile of our distribution?

3.000

An investigator at Chicago's Office of Inspector General is evaluating absenteeism among officers of the Chicago Police Department. This investigator collects data from a sample of 45 people. The number of days absent during the past year for each officer is recorded and the variance is determined to be 9. What is the standard deviation?

3σ

When two distributions are linearly related [where the values for "x" approximate the values for "y"], the points in a Q-Q plot will align at what angle?

45 Degree angle

In normal distribution, approximately what percentage of the areas under the curve is found between one standard deviation and the mean?

68%

In normal distribution, approximately what percentage of the area under the curve is found between two standard deviations above and below the mean?

95%

A Q-Q plot compares a "goodness of fit" assessment that evaluates which two types of distributions?

Actual vs. Theoretical

Which of the following are the features of a normal curve?

All of the above

What is the name for a distribution that has two modes?

Bimodal

When researchers are standardizing a continuous variable, the act of ______ refers to subtracting the mean score from each data point.

Centering

Which of the following procedures is not used by social scientists to inspect whether a continuous variable follows a normal distribution?

Counting the number of cases with missing data

Whereas central tendency refers to where most the values cluster, _______ refers to how much data points within a variable deviate from the mean.

Dispersion

In terms of variance, a[n] _________ refers to the difference between the mean and a data point.

Error or standard error

Which of the following diagnostic tools quantifies how "heavy" the tails are within the distribution of a numerical variable?

Kurtosis

The __________________ identifies the observation that sits at the midpoint between all the observations in a numerical or ordinal variable.

Median

The ______ identifies the most frequently observed value in a dataset.

Mode

Based on the skew statistic provided above, is the distribution symmetrical?

No

The distribution of wealth in the United States deviates from a normal distribution. If the net worth of every U.S. citizen was plotted on a histogram, most cases would cluster near the lower end of x-axis with outliers at the tail pointing to high values (e.g., Elon Musk, Jeff Bezos, Bill Gates). What is the most accurate way of describing this distribution?

Positively Skewed

Which of the following option best describes this distribution?

Postitively skewed (All to the left and going down)

Which of the following statistics does not govern the mathematical formula for where cases fall under the curve in a normal distribution?

Range

When researchers are standardizing a continuous variable, the act of ______ refers to changing the unit of measure to z-scores

Scaling

_______ refer to a procedure that evaluates how the results of an analysis are impacted by changes in the underlying methodological decisions. What this kind of analysis does is allow researchers to understand the reliability (and robustness) of their findings. It allows researchers to determine if they are identifying true data patterns and not just patterns that result from methodological decisions.

Sensitivity analysis

A logarithmic transformation is a procedure that social scientists often use to "normalize" continuous variables that follow which of the following distributions?

Skewed

Because of the sum of deviations from the mean always equal zero, the variance statistic gets around the problem by _________ the deviations before they are summed.

Squaring

While very simplistic, the mean can be thought of a[n] ___________ because it represents a summary of the data.

Statistical model

The ________ of a skewed distribution refers to the elongated portion of distribution.

Tail or tail of the distribution

A z-score of zero carries the same value as the mean of the distribution.

True

What descriptive statistic does not offer a straightforward interpretation because it is expressed in squared units?

Variance

Based on the kurtosis statistic provided above, is the distribution too peaked or flat to be considered normal?

Yes

Identify the Q-Q plot that resembles a normally distributed curve.

a ( straight and together)