Question

E. Choose the numbers that make the statement true.

The median is $

, the lower quartile is$

, and the upper quartile is$

.

Answer 1

I don’t have the full problem or the target values — can you paste the list or tell me what median, lower quartile and upper quartile you need?

If you meant “how to choose numbers so the median is M, Q1 is Q1, and Q3 is Q3,” here’s a short recipe and an example.

Recipe (using 7 numbers — easiest because quartiles are single data points):
- Pick an ordered list of 7 numbers: a1 ≤ a2 ≤ a3 ≤ a4 ≤ a5 ≤ a6 ≤ a7.
- The median will be a4, so set a4 = M.
- The lower quartile Q1 is the median of the lower half (a1, a2, a3), so set a2 = Q1 (choose a1 ≤ Q1 ≤ a3).
- The upper quartile Q3 is the median of the upper half (a5, a6, a7), so set a6 = Q3 (choose a5 ≤ Q3 ≤ a7).

Example:
- Want median = 10, Q1 = 7, Q3 = 14.
- Choose a1 = 5, a2 = 7, a3 = 8, a4 = 10, a5 = 12, a6 = 14, a7 = 16.
- Ordered list: 5, 7, 8, 10, 12, 14, 16.
- Median = 10, lower quartile = 7, upper quartile = 14.

If you prefer an even number of data points (e.g., 8), quartiles may be averages of two middle values; let me know if you need that and give the exact target values or the original dataset.