AP Stats Chapter 3 Quantitative Data Displays

(B) There will be clusters around 8 (finished middle school), 12 (finished high school), and 16 (finished college) years of schooling. Small segments of the population will have very few, if any, years of schooling, and so the distribution will be skewed to the left. There are very few normal distributions of individual observation. (Normal distributions in statistical inference mainly arise in sampling distributions.)

A histogram of the educational level (in number of years of schooling) of the adult population of the United States would probably have which of the following characteristics? Tip: Draw a picture! (A) Symmetry (B) Clusters around 8, 12, and 16 years (C) A gap around 12 years (D) Skewness to the right (E) A normal distribution

(D) The median from school A looks to be 0; the median from School B looks to be 5. The skewness of each histogram results in a mean for School A greater than 0 and a mean for School B less than 5; given the labeling, the mean for School B is still clearly greater than the mean for School A

A random sample of students from each of two schools was asked how many Supreme Court Justices they could name. The results are given in the histograms. Which school has the greater median with regard to the number of justices students could name , and which school has the greater mean? (A) Greater Median: A Greater Mean: A (B) Greater median: A Greater mean: B (C) Greater median: B Greater mean: A (D)Greater median: B Greater mean: B (E) Greater median: B Equal means

(A) All three have the same range: 22 - 2 = 20. The interquartile ranges of the first sets are 6, while the interquartile range of the middle set is 4. The medians are 12, 10, and 8, respectively. Only the lower distribution appears to be skewed right. With the given outliers, none of these distributions appears symmetric, and therefore, none appear normal (if the sample is small, any outliers in the sample call into question the use of t-procedures which depend upon a normality/large sample assumption).

Given these parallel boxplots, which of the following is true? (A) All three distributions have the same range. (B) All three distributions have the same interquartile range. (C) All three medians are between 9 and 13. (D) All three distributions appear to be skewed right. (E) All three distributions can reasonably be assumed to be of samples from normally distributed population.

(C) the empirical rule applies only to bell-shaped distributions as in set A, not to skewed distributions as in set B. the median is not the average of the minimum and maximum values. set A appears roughly symmetric, indicating the mean is about the same as the median, while set B is skewed to the lower values, indicating that the mean is less than the median. the range of set A is 176-121=55, while the range of set B is 178-127=51. the variance is a measurement of squared deviations from the mean; set A is more concentrated around its mean so it has a smaller variance.

Given this back-to-back stemplot, which of the following is true? (A) the empirical rule applies to both sets A and B. (B) the median of each is approximately (120 + 170)/2. (C) in one set the mean and median should be about the same, while in the other the mean appears to be less than the median. (D) the ranges of the two sets are equal. (E) the variance of the two sets are approximately the same.

(E) Counting boxes (area) we note that Q₁ = 70 and Q₃ = 90. The interquartile range IQR is Q₃ - Q₁ = 90 - 70 = 20. Outliers would be values greater than Q₃ + 1.5 (IQR) = 120 or less than Q₁ - 1.5 (IQR) = 40. In this case, there are no such values.

Given this histogram, and using the most commonly accepted definition of outliers, what values would be considered outliers? (A) Between 115 and 120. (B) Between 110 and 120. (C) Between 50 and 55, or between 115 and 120. (D) Between 50 and 55, or between 110 and 120. (E) There are no outliers.

(C) Outliers do influence the range, that is, the range is sensitive to extreme values (while, for example, the interquartile range is resistant to extreme values). The ranges for the four samples are 1,020 - 970 = 50, 1,030 - 980 = 50, 1,020 - 980 = 40, and 1,030 - 970 = 60, respectively.

The amount of Omega 3 fish oil in capsules labeled 1,000 mg is measured for four manufacturers' products yielding the following boxplots: Which of the manufacturers' samples has the smallest range? (A) A (B) B (C) C (D) D (E) There is insufficient information to answer this question.

(B) The "Male" distribution is roughly symmetric, while the "Female" distribution is skewed right, not left. The medians are 3 and 1, respective; the means are closer because the distribution with skew indicates the mean is greater than the median, while in the roughly symmetric distribution, the mean and median are close. Both have range 5 - 0 = 5. The male distribution is clustered more tightly around its mean, so it has a smaller standard deviation. Combining the male and female times into one set of students times will result in a new set whose smallest and largest values are still 0 and 5.

These dotplots for randomly selected male and female students at a particular high school show the number of times per week they eat at fast food restaurants. Which of the following is a true statement? (A) One distribution is roughly symmetric; the other is skewed left. (B) The difference in their means is less than the difference in their medians. (C) The ranges are both 7 - 0 = 7. (D) The standard deviations are the same. (E) Combining the male and female times into one set of students times will increase the range to the sum of the individual ranges.

(E) The median score splits the area in half, so it is not 75. The area between 90 and 100 is more than the area between 50 and 70, but less than the area between 50 and 90. The same percentage of the data are above and below the median. With data skewed to the left, the mean is usually less than the median.

To the right is a histogram of test scores. Tip: Count boxes(=area) and locate median! Which of the following is a true statement? (A) The median score was 75. (B) If 90 and above was an A, most students received and A. (C) More students scored below 70 than above 90. (D) More students scored above the median than below the median. (E) The mean score is probably less than the median score.

(D) Stemplots and histograms can show gaps and clusters that are hidden when one simply looks at calculations such as mean median , std quartiles and extremes.

When there are multiple gaps and clusters, which of the following is the best choice to give an overall picture of a distribution? (A) Mean and std. (B) Median and IQR (C)Boxplot and its five-number summary (D) Stemplot of histogram (E)None

(C) Symmetric histograms can have any number of peaks. All normal curves are bell shaped and symmetric, but not all symmetric bell shaped curves are normal. The larger the value of df, the closer a t-distributuion is being normal.

Which of the following is a true statement? (A) All symmetric histograms have single peaks (B) All symmetric bell shaped curves are normal (C) All normal curves are bell shaped and symmetric (D) The smaller the value of df, the closer a t-distribution is to being normal. (E) None of the above

(C) Stemplots are not used for categorical data sets and are too unwieldy to be used for very large data sets. stems should never be skipped, even if there is no data value for a particular stem. a key explaining what the stem and leaves represent should always be provided.

Which of the following is a true statement? (A) stemplots are useful both for quantitative and categorical data sets. (B) stemplots are equally useful for small and very large data sets (C) stemplots can show symmetry, gaps, clusters, and outliers. (D)stems should be skipped only if there is no data value for a particular stem. (E)whether or not to provide a key depends upon the relative importance of the data being displayed.

(D) Whenever the distribution is skewed , median and interquartile range are most usually the measures of choice. Mean is typically paired with standard deviation and median is typically paired with interquartile range.

Which of the following measures are most usually given to describe the center and spread of a distribution as given in the dot plot? (A) Mean and Standard Deviation (B) Mean and interquartile range (C) Mean and Range (D) Median and interquartile range (E) Median and Range

(A) Choice of interval width, and therefore number of bins, changes the appearance of a histogram. Displaying outliers is more problematic with histograms depending on the bin widths. Histograms do not show individual observations. All graphs need to be labeled. Histograms, stemplots, and boxplots make no sense with categorical variables.

Which of the following statements are true? (A) Two students working with the same set of data may come up with histograms that look different. (B) Displaying outliers is less problematic when using histograms than when using stemplots. (C) Histograms are more widely used than stemplots or dotplots because histograms display the values of individual observations. (D) Unlike other graphs, histograms axes do not need to be labeled. (E) A histogram of categorical variable can pinpoint clusters and gaps.