An intelligence test that has a maximum time for completion of 45 minutes was recently administered to a group of 21 people. Their respective times for completion (in minutes) were as follows.22, 26, 32, 33, 33, 34, 36, 37, 37, 37, 38, 39, 39, 41, 42, 42, 42, 43, 43, 43, 43Send data to calculator86420Frequency11478202530354045Time for completion (in minutes)(a) For these data, which measures of central tendency take more than one value? Choose all that apply.MeanMedianModeNone of these measures(b) Suppose that the measurement 22 (the smallest measurement in the data set) were replaced by 10. Which measures of central tendency would be affected by the change? Choose all that apply.MeanMedianModeNone of these measures(c) Suppose that, starting with the original data set, the smallest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply.MeanMedianModeNone of these measures(d) Which of the following best describes the distribution of the original data? Choose only one.
Question
An intelligence test that has a maximum time for completion of 45 minutes was recently administered to a group of 21 people. Their respective times for completion (in minutes) were as follows.22, 26, 32, 33, 33, 34, 36, 37, 37, 37, 38, 39, 39, 41, 42, 42, 42, 43, 43, 43, 43Send data to calculator86420Frequency11478202530354045Time for completion (in minutes)(a) For these data, which measures of central tendency take more than one value? Choose all that apply.MeanMedianModeNone of these measures(b) Suppose that the measurement 22 (the smallest measurement in the data set) were replaced by 10. Which measures of central tendency would be affected by the change? Choose all that apply.MeanMedianModeNone of these measures(c) Suppose that, starting with the original data set, the smallest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply.MeanMedianModeNone of these measures(d) Which of the following best describes the distribution of the original data? Choose only one.
Solution
(a) For these data, the measures of central tendency that take more than one value are the Mode. There are multiple numbers that appear more than once in the data set.
(b) If the smallest measurement in the data set (22) were replaced by 10, the measures of central tendency that would be affected are the Mean. The mean is calculated by adding all the numbers in the data set and dividing by the total number of data points. Changing a number in the data set would change the total sum, thus changing the mean.
(c) If the smallest measurement were removed from the original data set, the measures of central tendency that would be changed are the Mean. Removing a number from the data set would change the total sum and the total number of data points, thus changing the mean.
(d) The distribution of the original data is positively skewed. Most of the data points are on the lower end of the scale, with fewer data points on the higher end.
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