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Answer :
A. The median of Miguel's data set is greater than Shona's median data set and the range of Miguel's data is less than the range of Shona's data.
B. Approximately 75% of Miguel's data values are greater than the median of Shona's data.
C. The statement that can be made from the box plot is Option C. There was at least one day on which Shona sent 40 text messages.
D. The outliers for Shona would be A. 5 and E. 75.
How the conclusions from the box plot are made:
A. Miguel's median = 40
Shona's median = 35
Therefore, Miguels median is greater than Shona's by = 5 (40 - 35)
Miguels range = 30 (55 - 25 )
Shona's range = 35 (60 - 25)
Therefore, Shona's range is greater than Miguel's range by = 5 (35 - 30)
B. 50% + 25% = 75% of Miguel's data values are greater than the median of Shona's data.
D. Interquartile Range (IQR) for Shona's data and determine the upper and lower limits for identifying outliers:
The IQR is calculated as Q3 - Q1.
For Shona:
IQR = 15 (45 - 30)
Now, we can calculate the upper limit and lower limit for outliers:
Lower limit = Q1 - 1.5 × IQR
= 30 - 1.5 × 15
= 7.5
Upper limit = Q3 + 1.5 × IQR
= 45 + 1.5 × 15
= 67.5
Therefore, any value less than 7.5 (5) or greater than 67.5 (75) would be considered an outlier in Shona's data.
Outliers are 5 and 75.
Boxplots are attached in the image.
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