Question

the box plots shown represent two data sets. use the box plots to compare the data sets.
drag each value to show if it is the same for both data sets, different for each data set, or if there is not enough information to tell.
mean, iqr, mode
same in both data sets, different in each data set, cannot tell if the value is the same or different
median, minimum value, 3rd quartile

Explanation:

Step1: Analyze Mean

Box plots show median, quartiles, min, max, but not mean (depends on data distribution, not visible in box plot). So can't tell.

Step2: Analyze IQR

IQR is \( Q_3 - Q_1 \). From box plots, we can see quartiles. If boxes (IQR range) look different, IQR is different. The lower box plot has a wider box, so IQR is different.

Step3: Analyze Mode

Box plots don't show mode (most frequent value), so can't tell from box plots.

Step4: Analyze Median

Median is the line inside the box. In the two box plots, the median line (inside the box) seems aligned (same position), so median is same.

Step5: Analyze Minimum Value

Whiskers start at different points (lower whisker of top box plot vs bottom), so min values are different.

Step6: Analyze 3rd Quartile (\( Q_3 \))

\( Q_3 \) is the end of the box. The boxes end at different positions, so \( Q_3 \) is different.

Now, drag:

• Mean: Cannot Tell (since box plots don't show mean)
• IQR: Different (wider box in one, so \( Q_3 - Q_1 \) different)
• Mode: Cannot Tell (box plots don't show mode)
• Median: Same (median line same position)
• Minimum value: Different (whiskers start differently)
• 3rd Quartile: Different (box ends at different positions)

Answer:

• Mean: Drag to "Cannot Tell If the Value Is the Same or Different"
• IQR: Drag to "Different in Each Data Set"
• Mode: Drag to "Cannot Tell If the Value Is the Same or Different"
• Median: Drag to "Same in Both Data Sets"
• Minimum value: Drag to "Different in Each Data Set"
• 3rd Quartile: Drag to "Different in Each Data Set"