### 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?