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For a school project, two students, Shona and Miguel, recorded the number of text messages each of them sent each day for a 60-day period. The box plots summarize the recorded data.

**Part A**

Select from the drop-down menus to correctly complete the sentence:

The median of Miguel's data is greater than the median of Shona's data, and the range of Miguel's data is greater than the range of Shona's data.

**Part B**

Select from the drop-down menu to correctly complete the sentence:

Approximately 50% of Miguel's data values are greater than the median of Shona's data.

**Part C**

Which of the statements can be concluded from the box plots? Select all that apply.

A. For approximately 15 days, Miguel sent 50 or more text messages per day.
B. For at least 5 days, Shona sent 55 or more text messages per day.
C. There was at least one day on which Shona sent 40 text messages.
D. The number of days on which Shona sent more text messages than Miguel is greater than 30.
E. Shona and Miguel each sent 25 text messages on the same day.

**Part D**

There are different methods of identifying outliers in a set of data values. One method is described:

1. Multiply the interquartile range by 1.5.
2. Add the result to the third quartile to determine the upper limit, and subtract the result from the first quartile to determine the lower limit.
3. Any value greater than the upper limit or less than the lower limit is considered an outlier.

On the st day, Shona sent text messages, which will be considered an outlier based on the described method. Which number could be the value of the outlier? Select all that apply.

A. 555
B. 101010
C. 151515
D. 656565
E. 757575

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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Rewritten by : Barada