Question

Angie has the following data:

88 98 86 82 h
If the median is 88, which number could h be?
92 or 29

Answer 1

To determine which value \( h \) could be such that the median of the numbers \( 88, 98, 86, 82, h \) is 88, we first need to order the numbers.

1. The current list of numbers without \( h \) ordered is:
- 82
- 86
- 88
- 98

We need to consider how \( h \) will fit into this ordered list. The median will be the middle value of the ordered list when there are an odd number of values (in this case, 5 values).

**If \( h \) is higher than 98:**
- Ordered list: \( 82, 86, 88, 98, h \)
- Median = 88 (3rd value, which is fine)

**If \( h \) is between 88 and 98:**
- The ordered list will change based on its value:
- Example, if \( h = 92 \): \( 82, 86, 88, 92, 98 \) - Median = 88 (still valid)

**If \( h \) is 88:**
- It will count in the middle, resulting in \( 82, 86, 88, 88, 98 \). Median = 88 (still valid)

**If \( h \) is lower than 82:**
- Ordered list: \( h, 82, 86, 88, 98 \) - Median = 86 (not valid)

**If \( h \) is 86:**
- Ordered list: \( 82, 86, 86, 88, 98 \) - Median = 86 (not valid)

**If \( h \) is between 82 and 86:**
- Ordered: \( h, 82, 86, 88, 98 \) - Median = 86 (not valid)

**If \( h \) is 29:**
- Ordered: \( 29, 82, 86, 88, 98 \) - Median = 86 (not valid)

So, to maximize the possibility of 88 being the median from the two choices presented:

- **92 would work**, because it maintains 88 as the median.
- **29 would not work**, because it would lower the median to 86.

Thus, the correct option for \( h \) that could maintain the median as \( 88 \) is **92**.