Data Set A [Dot plot showing: At position 22: 4 dots vertically stacked At position 23: 4 dots vertically stacked...

1. TRANSLATE the dot plot information

Given information:

• Data Set A has 15 values total
• From the dot plot (carefully counting the dots):
  • 22 appears 5 times
  • 23 appears 4 times
  • 24 appears 3 times
  • 25 appears 2 times
  • 26 appears 1 time
• Data Set B is created by adding 46 to each value in Data Set A

What this tells us:
We need to find and compare the median and range for both data sets.

2. VISUALIZE Data Set A in order

Listing all 15 values in order:
22, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 26

Position numbers help track the middle value:

• Positions 1-5: value 22
• Positions 6-9: value 23
• Positions 10-12: value 24
• Positions 13-14: value 25
• Position 15: value 26

3. Find the median of Data Set A

INFER which position is the middle: With 15 values (odd number), the median is the middle value at position 8.

Counting to position 8: We pass through all five 22s (positions 1-5) and reach the 23s at positions 6-9.

The 8th value is 23

Median of Data Set A = 23

4. Find the range of Data Set A

APPLY the range formula:

• Maximum value = 26
• Minimum value = 22
• Range = \(\mathrm{26 - 22 = 4}\)

Range of Data Set A = 4

5. INFER the effect of adding 46 to every value

When we add 46 to each value in Data Set A:

• The smallest value: \(\mathrm{22 + 46 = 68}\)
• The largest value: \(\mathrm{26 + 46 = 72}\)
• The 8th value (median): \(\mathrm{23 + 46 = 69}\)

Key insight: Adding the same number to all values shifts every data point but doesn't change the spread (distance) between them.

Data Set B in order:
68, 68, 68, 68, 68, 69, 69, 69, 69, 70, 70, 70, 71, 71, 72

6. Find the median of Data Set B

The median is still at position 8.

The 8th value is 69

Median of Data Set B = 69

7. Find the range of Data Set B

APPLY the range formula:

• Maximum value = 72
• Minimum value = 68
• Range = \(\mathrm{72 - 68 = 4}\)

Range of Data Set B = 4

8. TRANSLATE the comparison back to answer choices

Comparing medians:

• Median of B \(\mathrm{(69) \gt}\) Median of A \(\mathrm{(23)}\) ✓
• So "median of data set B is greater than the median of data set A"

Comparing ranges:

• Range of B \(\mathrm{(4) =}\) Range of A \(\mathrm{(4)}\) ✓
• So "range of data set B is equal to the range of data set A"

Answer: A

---

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skill: Not recognizing that adding a constant to all values doesn't change the range.

Students might think: "Since we're adding 46 to everything, the range must get bigger too." They might incorrectly calculate the range of B as \(\mathrm{4 + 46 = 50}\), or think that since all values increased, the range must also increase.

This may lead them to select Choice B (median of B > median of A, range of B > range of A).

Second Most Common Error:

Poor VISUALIZE execution: Miscounting the dots in the original plot or incorrectly identifying the 8th position as the median.

For example, if a student misreads the plot and thinks value 22 appears only 4 times instead of 5, they might list Data Set A as having 14 values. This shifts which value is in the "middle" position, leading to median = 23.5 or another incorrect value. Alternatively, they might think the median of 15 values is at position 7 or position 9 instead of position 8.

This leads to confusion and incorrect median values, potentially causing them to select Choice C or D depending on what other errors they make.

The Bottom Line:

This problem tests whether you understand how data transformations affect measures of center (median) versus measures of spread (range). The key insight is that adding the same constant to all values shifts the entire data set but preserves the distances between values—so the range stays the same while the median increases. Careful counting and systematic organization are also critical to avoid simple but costly position-tracking errors.