We have a guide about the values in the dataset.
X₁=7 and X₁₁=17, X₆=12, X₄=X₅=11 (minimum for mode is 2 data the same and all others different).
Possible choices for X₂ and X₃ are (8,9), (8,10), (9,10).
The remaining data beyond the median are 13, 14, 15, 16 for X₇-X₁₀.
This gives us 3 possible means: 133/11, 134/11, 135/11, for the different values of X₂ and X₃. If we take the mean mean as the mean for the dataset we have 134/11=12.18, close to the median, so to make calculations easy, let’s use 12, the median value. This gives us a variance of 102/11, the square root of which is the standard deviation=3.05, which we can round to 3.
The dataset used for this calculation is:
7, 8, 10, 11, 11, 12, 13, 14, 15, 16, 17, with mean=12 and SD=3 (rounded).