Positively Skewed Distribution – Statistic Exam

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Positively Skewed Distribution, Data, Percentile Rank, Stem And Leaf, Final Exam

The key terms in these statistic chapters include Positively Skewed Distribution, Data, Variable, Percentile Rank, Stem And Leaf, Sample, Distribution, Population, Frequency, Normal Distribution, Qualitative Variable, Distribution of Data, Normal Distribution, Variance, Standard Deviation.


For the data in the following table, what is the percentile rank for 3?

X f(X)

4 1

3 3

2 4

1 2

90


For the data in the following table what proportion of people scored a 1?

X f(X)

4 1

3 3

2 4

1 2

0.2


What is a qualitative variable? Provide example of var and graphing.

Variable that describes a trait Example: var = family structure type, graph displays relative frequency of family structure


For the data in the following table, what is the percentile rank for 3?

X f(X)

4 1

3 3

2 4

1 2

90


What is a bar graph? Ex? Sig?

Graph for qualitative variable
Spaces left between categories
Examples: male and female average height
Helps compare groups


What is a qualitative variable? Provide example of var and graphing.

Variable that describes a trait Example: var = family structure type, graph displays relative frequency of family structure


What is a histogram? Example? Sig?

Picture version of frequency distribution for continuous data using bars
X axis is for values of the variable. Y axis for the frequency.
Axes must be labeled, no space between categories Example: grade data distribution
Helps understand distribution of data


Describe a frequency polygon. Sig?

Use dots at frequency rather than rectangles, join dots
Helps understand distribution of data


Describe a stem and leaf plot. Sig?

Where you have stems for categories (3-10 for grades 30-100)
Put numbers for each iteration in ones place on the right side, the leaves
Easy way to visualize distribution of data


You record the height (in inches) of each student in the class. If these data are presented in a graph, it would be acceptable to use a bar graph.

False

A professor recorded the academic major for each student in an introductory psychology class. If the data are presented in a graph, what type of graph should be used?

Bar graph


A professor recorded scores from a 5-point quiz for each student in an introductory psychology class. If the data are presentenced in a graph, what type of graph should be used?

Histogram or polygon


What are some common shapes of distributions? Describe normal distribution, bimodal distribution, positive skew, negative skew, and uniform distribution. Sig?

Normal distribution: bell shape distribution with most values in the middle
Bimodal distribution: two most frequently occurring peaks, two bell shapes
Positive skew: tail points towards positive direction
Negative skew: tail points towards negative direction
Uniform distribution: like rectangle, so each score has equal probability of occurring


If a set of scores forms a positively skewed distribution, it suggests that the majority of the students did not score well on the exam.

True


Another term for a positively skewed distribution is a left-skewed distribution.

False

Describe skew. Sig?

Skews the mean in some direction
Positive skew (right skew/skewed to the right): mean pulled to the right due to extreme values
Negative skew (left skew/skewed to the left): mean pulled to the left due to extreme values. Example: exam scores

Conflicts with normal distributions


What is a qualitative variable? Provide example of var and graphing.

Variable that describes a trait Example: var = family structure type, graph displays relative frequency of family structure


What is a histogram? Example? Sig?

Picture version of frequency distribution for continuous data using bars
X axis is for values of the variable. Y axis for the frequency.
Axes must be labeled, no space between categories Example: grade data distribution
Helps understand distribution of data


Describe a frequency polygon. Sig?

Use dots at frequency rather than rectangles, join dots
Helps understand distribution of data


Describe a stem and leaf plot. Sig?

Where you have stems for categories (3-10 for grades 30-100)
Put numbers for each iteration in ones place on the right side, the leaves
Easy way to visualize distribution of data


What is kurtosis? Compare leptokurtic and platykurtic. Sig?

Peaked/pointed: leptokurtic, like
Flattened: platykurtic, like platypus
Conflicts with normal distributions


If a set of scores forms a positively skewed distribution, it suggests that the majority of the students did not score well on the exam.

True


Another term for a positively skewed distribution is a left-skewed distribution.

False

The normal shaped distribution is an example of a symmetrical distribution.

True


In a positively skewed distribution, scores with the highest frequencies are _____.

On the left side of the distribution


What is the shape of the distribution for the following set of data? (Hint: Construct a histogram.) Scores: 1, 2, 2, 2, 2, 3, 3, 4, 5, 6

Positively skewed


Last week, Sarah had exams in her math and Spanish classes. On the math exam, the mean was µ = 30 with σ = 5, and Sarah had a score of X = 45. On the Spanish exam, the mean was µ = 60 with σ = 8, and Sarah had a score of X = 68. For which class should Sarah expect the better grade relative to her peers in each class?

Math


A population has µ = 50. Which value of σ would make X = 55 an extreme value out in the tail of the population distribution?

σ = 1


For a sample of n = 20 scores, X = 25 corresponds to z = -1.20 and X = 40 corresponds to z = +1.80. What are the values for the sample mean and standard deviation?

M = 31 and s = 5


A population has SS = 100 and σ 2 = 5. How many scores are in the population?

20


For a population with µ = 100 and σ = 20, what is the X value corresponding to z = -0.25?

X = 95

Under which circumstance is a score that is located 5 points above the mean a central value that is relatively close to the mean?

When the population standard deviation is much greater than 5


If sample variance were to be computed by dividing SS by n, then the average value of the sample variances from all the possible random samples would consistently _____ the population variance.

Underestimate


Which of the following is not a unique advantage of the interquartile range as measure of variability?

The interquartile range can be used for data measured with a ratio scale of measurement.


Which of the following characteristics tends to increase the likelihood that a clear difference between two sample means is detected statistically?

Small variances within each sample


A sample with M = 85 and s = 12 is transformed into z-scores. After the transformation, what are the values for the mean and standard deviation for the sample of z-scores?

M = 0 and s = 1


Using z-scores, a population with µ = 37 and σ = 6 is standardized so that the new mean is µ = 50 and σ = 10. After the standardization, one individual has a score of X = 55. What was this individual’s score in the original distribution?

X = 40

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