Each year, taxpayers are able to contribute money to various charities via their IRS tax forms. The following list contains the
amounts of money (in dollars) donated via IRS tax forms by Each year, taxpayers are able to contribute money taxpayers:
2 , 22 , 27 , 31 , 36 , 51 , 57 , 57 , 60 , 62 , 62 , 62 , 73 , 77 , 83 , 95 , 99 , 104 , 105 , 127 , 153 , 162 , 197
(a) For these data, which measures of central tendency take more than one value? Choose all that apply.
Mean
Median
Mode
None of these measures
(b) Suppose that the measurement 197 (the largest measurement in the data set) were replaced by 246. Which measures of central tendency would be affected by the change? Choose all that apply.
Mean
Median
Mode
None of these measures
(c) Suppose that, starting with the original data set, the largest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply.
Mean
Median
Mode
None of these measures
(d) Which of the following best describes the distribution of the original data? Choose only one.
Negatively skewed
Positively skewed
Roughly symmetrical
2 , 22 , 27 , 31 , 36 , 51 , 57 , 57 , 60 , 62 , 62 , 62 , 73 , 77 , 83 , 95 , 99 , 104 , 105 , 127 , 153 , 162 , 197
(a) For these data, which measures of central tendency take more than one value? Choose all that apply.
Mean
Median
Mode
None of these measures
(b) Suppose that the measurement 197 (the largest measurement in the data set) were replaced by 246. Which measures of central tendency would be affected by the change? Choose all that apply.
Mean
Median
Mode
None of these measures
(c) Suppose that, starting with the original data set, the largest measurement were removed. Which measures of central tendency would be changed from those of the original data set? Choose all that apply.
Mean
Median
Mode
None of these measures
(d) Which of the following best describes the distribution of the original data? Choose only one.
Negatively skewed
Positively skewed
Roughly symmetrical
2 answers:
Answer:
A. median and mode
B. Mean
C. Mean
d. Positively skewed
Step-by-step explanation:
a. Mean = sum of all values / numbers of values = 1804 / 23 = 78.4. this eliminates the mean and leaves the median and mode, both of which are 62.
Median = middlemost value = 62
Mode = most frequent value = 62
b. Only the Mean would be affected. It would move from 78.4 to 80.6. (calculated as 1853 / 23). The median and mode would not be affected as the 62 would remain the middlemost value and the most frequent.
c. Removing the largest value would result in the mean changing. The mean would now be 73 (calculated as 1607 / 22). Since the values are no longer 23, but now 22, the median would be the average of the 2 middlemost values, ((62+62) / 2) which would still result in 62 as the median.
d. we use the Five number summary:
Median / Interquartile Range = 62
First Quartile / Q1 = (51 +57) / 2 = 54
Third Quartile / Q3 = (99 + 104) / 2 = 101.5
Minimum = 2
Maximum = 197 ; therefore Range = (197 - 2) = 195.
Please see attached box and whisker plot. The distribution is positively skewed.
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