One-Variable Data: 11-20

24) Given that the median is 270 and the IQR is 20, which of the following statements is true?

• Equal percents of the data are greater than and less than 270.

• Fifty percent of the data are between 260 and 280.

• Seventy-five percent of the data are less than or equal to 280.

• The mean is between 250 and 290.

• The standard deviation is approximately 13.5

Tags

CCSS.7.SP.B.4

26) Suppose the average score on a national exam is 500 with a standard deviation of 100. If each score is increased by 20 and then the result is increased by 10 percent, what are the new mean and standard deviation?

28) A teacher is teaching two AP Statistics classes. On the final exam, the 25 students in the first class averaged 87, while the 30 students in the second class averaged 98. If the teacher combined the classes, what will the average final exam score be?

• 92

• 92.5

• 93

• 94.5

• 95

29) Which of the following statements is incorrect?

• Both dotplots and stemplots can show symmetry, gaps, clusters, and outliers.

• Sets with different distribution shapes can have identical boxplots.

• Dotplots, stemplots, and histograms can all show skewness.

• In histograms, relative areas correspond to relative frequencies.

• In histograms, frequencies can be determined from relative heights.

Answer explanation

In general, histograms give information about relative frequencies, not actual frequencies. Histograms may have vertical axes labeled with frequencies, but then the height, not relative height, gives frequency.

Tags

CCSS.6.SP.B.4

CCSS.HSS.ID.A.1

30) If the standard deviation of a set of observations is 0, you can conclude

• that there is not relationship between the observations.

• that the average value is 0.

• that all observations are the same value.

• that mistake in arithmetic has been made.

• non of the above.

Answer explanation

Because of the squaring operation in the definition, the standard deviation (and also the variance) can be zero only if all the values in the set are equal.

• 0

• 1

• 2

• At least 1

• At least 2

34) Which of the following statements is true?

• Two students working with the same set of data may come up with histograms that look different.

• Displaying outliers is always less problematic when using histograms than when using stemplots.

• Histograms are more widely used than stemplots or dotplots because histograms display the values of individual observations.

• Unlike other graphs, histogram axes do not need to be labeled.

• A histogram of a categorical variable can pinpoint clusters and gaps.

Answer explanation

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

Tags

CCSS.6.SP.B.4

CCSS.HSS.ID.A.1

36) Suppose that by using the most commonly accepted definition of outliers, a set has five outliers. If every value of the set is increased by 20 percent, how many outliers will there now be?

• Fewer than five

• Five

• Six

• More than six

• It is impossible to determine without further information.

38) When a set of data has suspect outliers, which of the following are preferred measures of central tendency and variability?

• Mean and standard deviation

• Mean and variance

• Mean and range

• Median and range

• Median and interquartile range

Answer explanation

The mean, standard deviation, variance, and range are all affected by outliers; the median and interquartile range are not.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Which of the following statements is incorrect?

• The range of the sample data set can never be greater than the range of the population.

• Although the range is affected by outliers, the interquartile range is not.

• Changing the order from ascending to descending changes the sign of the range.

• The range is a single number, not an interval of values.

• The interquartile range is the range of the middle half of the data.

Tags

CCSS.6.SP.B.5C