Question

Please could u help me with this Thank u sooo much:)

Answer 1

Ok so the spread can be given by the range, interquartile range and standard deviation in this case.
Gretchen's data: Range = 22 - 3 = 19, IQR = 5, Sx = 4.69
Manuel's data: Range = 14 - 3 = 11, IQR = 4, Sx = 3.14

1. Gretchen's data is more spread out than Manuel's, which is primarily displayed by the much larger range and standard deviation for Gretchen's data (range = 19, standard deviation = 4.69) compared to Manuel's data (range = 11, standard deviation = 3.14). The interquartile range of both data sets are almost equal however, with the IQR of Gretchen's data equal to 5 and that of Manuel's data equal to 4, which may show that the greater spread of Gretchen's data is affected by the larger values in his data, namely the outlier at 22.

2. Gretchen's data set with outlier removed:
Mean = 8.71
Median = 8.5
Standard deviation = 3.31
Interquartile range = 3

3. Removing the outlier moved the centre closer, with the mean now at 8.71 and median at 8.5, compared to Manuel's data's mean of 8 and median of 8. The spread was also closer to Manuel's, with the standard deviation now equal to 3.31 (Manuel's data's standard deviation = 3.14) and the range now equal to 12 (compared to Manuel's data's range of 11). The IQR range did change from 5 to 3 after removing the outlier but there is still a difference of 1 between the IQR of Gretchen's data and that of Manuel's data. Overall however, both the centre and spread moved closer to that of Manuel's data after removing the outlier.