Student Study Guide to Accompany Statistics Alive!. Wendy J. Steinberg
Читать онлайн книгу.
this mean about the responses in your sample?
5 What is kurtosis, and what are its two forms?
6 What do the slices on a pie graph represent?
Answers
1 From a boxplot, we can obtain the median of the distribution, where the middle 50% of scores fall, and the maximum and minimum values.
2 This indicates that the values could fall anywhere between the intervals.
3 A positively skewed distribution has a large amount of cases at the lower end of the scale and a few at the upper end. A negatively skewed distribution has a large amount of cases at the upper end of the scale and few toward the lower end.
4 Each score (interval) on your survey received an equal amount of responses.
5 Kurtosis refers to having either more or fewer scores in the center of a distribution, relative to a normal distribution. A distribution with more scores at the center is referred to as leptokurtic, and one with fewer is referred to as platykurtic.
6 The proportion of cases falling in each category. Pie charts are used for nominal data.
Multiple-Choice Questions
1 A pizza restaurant finds that a lot of customers appeared to eat a less number of pizza slices, and a large portion also appeared to eat more number of slices. How should the restaurant expect the distribution to look?Positively skewedNegatively skewedBimodalSymmetrical
2 The X-axis is sometimes referred to as the ______.abscissaordinateplatykurticleptokurtic
3 In a study examining the rate at which a person can mentally rotate an object, the results indicate that the majority of people take 15 seconds, with an equal amount of participants falling above and below this time. You could expect the relative frequency curve of these scores to appearsymmetric.positively skewed.negatively skewed.bimodal.
4 What would be the best method to graph data obtained for the question of “What is your favorite type of ice cream?”HistogramRelative frequency curveBar graphBoxplot
5 Bar and pie charts are best used for which type of variables?ContinuousOrdinalNominalRatio
6 You administer an anxiety measure to a group of 30 participants with different severity of anxiety symptoms. Two participants obtain each possible score. How will this distribution appear?UniformSymmetricalPositively skewedNegatively skewed
7 A common symptom of depression is a lack of desire to do things that are entertaining. If you were to ask a sample of 100 individuals with depression how many fun activities they have done in the past week, how would you expect the distribution to appear?UniformSymmetricalPositively skewedNegatively skewed
8 You are interested in determining how moviegoers rated a new film on opening day, on a scale of 1 to 8. After collecting data, you discover that most people in the sample provided ratings of either 4 or 5. How would you expect this distribution to appear?Positively skewedNegatively skewedLeptokurticPlatykurtic
Multiple-Choice Answers
1 C
2 A
3 A
4 C
5 C
6 A
7 C
8 C
Module Quiz
1 Create a histogram for the following data:1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 8, 9.What shape best describes this distribution?
2 You are working at an advertising firm and want to determine the interest of a focus group in a new product. If the scale ranges from 0 (no interest) to 10 (great interest), what type of distribution would be most preferable?
3 After giving his class a quiz worth 10 points (1–10 scale), your professor notices that the distribution was negatively skewed. What conclusion should the professor draw from this information?
4 What types of variables are histograms best used for?
5 What does the height of a bar in a histogram represent?
Quiz Answers
1 Positively skewed.
2 Negatively skewed.
3 The test was potentially too easy, he may need to add more challenging questions next time he gives a quiz.
4 Continuous variables.
5 The frequency of scores in that particular grouping or category.
Module 5 Mode, Median, and Mean
Learning Objectives
Define central tendency as it applies to a set of data
Calculate the mode
Calculate the median
Calculate the mean
Determine how measures of central tendency are affected by skew
Module Summary
An entire data set can be described in a single number with a measure of central tendency. Central tendency provides a single value that best describes, or is most representative of, the entire set of scores. It enables you to quickly determine the center, which is usually the location of the majority of scores, of a large group of data.
The mode is the most commonly occurring score in the data set. Although the mode is referred to as a measure of central tendency, it does not necessarily occur at the center of the data set (there may not be equal amounts of scores above and below the mode). The mode is the least stable measure of central tendency, meaning that it may change drastically from sample to sample of a population. This aspect of the mode reduces how often it is used.
The median is the center score; half of the scores in the distribution are above the median, and half of the scores in the distribution are below it. In other words, the median is the score that occurs at the 50th percentile. The median does not have to be an actual score. For example, the mean of the distribution 3, 4, 6, 7 is 5. If you do not know all of the specific scores in a data set, you can use the following formula for a precise measure of the median:
The mean is the average score for a data set and is symbolized as M for samples and as μ for populations. The mean is the most commonly used and most stable measure of central tendency. The formula for a mean is as follows:
There are three important aspects to the mean. First, the numerical weight of the scores above the mean is equal to the numerical weight of the scores below the mean. This indicates that if you were to find the distance of all the scores from the mean (i.e., X − M), the sum of the distances for the scores below the mean would be equal to the sum of the distances for the scores above the mean. Second, the mean includes all values of the data in its calculation, which indicates that each score in the distribution matters. Finally, the mean is also a sensitive measure of central tendency, in that a change in any score in the data set will change the mean.
An extreme score in a data set, one that is drastically different from the others, is called an outlier. Outliers can influence which measure of central tendency is most appropriate to use. Because the mean is so sensitive to score values, the median may be a more appropriate measure if there are many outliers in a data set.
The skew of a distribution will affect the location of the measures of central tendency. In a symmetrical distribution, the mean, median, and mode are all equal. In a skewed distribution,