Part A) Jasper should use the median because there is an outlier that affects the mean is the correct answer.
Part B) Option (D) no, because there is a lot of variability in the art book data is the correct answer.
In this question,
Part A)
The median is the middle number in a sorted, ascending or descending list of numbers and can be more descriptive of that data set than the average. The numbers are ordered in ascending order. Once the numbers are ordered, the middle number is called the median of the given data set.
The median is important because it gives us an idea of where the center value is located in a dataset. The median is the most informative measure of central tendency for skewed distributions or distributions with outliers.
The house values in Jasper's neighborhood,
a) $150,000, b) $175,000, c) $200,000 ,d) $167,000, e) $2,500,000
The value of house E is very high from other houses in Jasper's neighborhood. The value of house E will make the mean house value above the center of the data as House E is an outlier for our given data.
Thus the median of a data set with an outlier is not affected by the value of outlier. Therefore, Jasper should use the median because there is an outlier that affects the mean is the correct answer.
Part B)
The mean absolute deviation of a dataset is the average distance between each data point and the mean. It gives us an idea about the variability in a dataset. The mean absolute deviation is specially important in data analysis where the average value can be deceptive.
A small mean absolute deviation tells us that most of the data values are very close to the mean. A high mean absolute deviation tells us that many of the data values are spread out further from the mean.
Magdeline selects 25 pages from each book, then Calculates Mean, Median, Mean Absolute Deviation of number of words on each page.
Book Mean Median Mean Absolute Deviation
Art 68.7 50 15.4
Science 54.2 55 7.9
Magdeline claims that the mean number of words on each page in the art book is greater than the mean number of words on each page in the science book, the art book has more words per page is not a valid inference.
Because variability from mean in art book is more than variability from mean in science book and the mean absolute deviation measures variability from mean. Thus option (D) no, because there is a lot of variability in the art book data is the correct answer.
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