Can you show me how to solve the question step by step? 9. Using the graph below

Question

Can you show me how to solve the question step by step?

9. Using the graph below and the labels given, answer the following questions. 10 15 20 a) What does the point labeled F represent on the boxplot? b) What does the point labeled A represent on the boxplot? c) How would you calculate the range for this dataset? (use the appropriate letters and give the approximate value) d) Which letter represents the value of the first quartile? Approximately, what is that value? e) How would you calculate the IQR? (use the appropriate letters) f) Between what two letters does the 67th percentile fall? g) What letter represents the median? What is the approximate value for the median? h) Would you expect the mean to be less than the median, greater than the median, or about the same value as the median? i) What is the approximate value of Qs? i)If you were to summarize this data, would it be more appropriate to use the 5-number summary or the mean and standard deviation? Explain your answer.

Explanation / Answer

<As per answering guidelines I am answering the first 4 subparts>

a) The point labeled F is outside the markers of the box-plot. Hence this indicates a data point which was an outlier and has been deliberately left out of the analysis because of its very large value compared with the rest of the dataset.The box-plot is marked by the max and min on both sides. Hence when a point is outside the max and min then it indicates that the point was not considered as a part of the box-plot caluculations. Such type of outlier detection is by simple judgement of the dataset.

b) The points A indicate the minimum value among all observations considered for the box-plot calculations.

c) The range of the dataset is the difference between the minimum and maximum of the data. The minimum is given by point A and the max is given by point E. So range is E - A. Now A = 4 and E = 18. So range of the dataset is 18-4 = 14

d) Point B (the starting of the box on the left) indicate the first quartile. Value of first quartile is 7.

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