Thoughts on weighing observations
Suppose you have a set of observations (measurements) and want to assess how well they fall into an ideal target range. Here are a few thoughts on how to go beyond the most obvious measure: percentage of “inrange values”.
Suppose our observations lie in <$ (X, \rho) $>, a metric space, and our target range is a subset <$ S \subset X $> closed in <$ X. $> For each observation <$ x \in X $> we want to calculate its weight <$ \omega(x) \in \lbrack 0, 1 \rbrack. $> The total weight of a set of observation will then naturally be
<$$ \omega(\Xi) := \frac{1}{\Xi} \sum_{x \in \Xi} \omega(x), \quad \Xi \subset X. $$>Properties of <$ \omega $> weights
Feel free to skip to examples of specific weighting functions if you are not interested in an abstract discussion of their possible properties.
Note on notation. For <$ x \in X, A \subset X $> let <$ \rho(x, A) := \inf \{ \rho(x, y): y \in A \} $> be the distance of <$ x $> from the set <$ A. $> Let <$ \overline{A} $> denote the closure of <$ A \subset X $> in <$ X, $> let <$ \mathrm{int}\; A $> denote the interior of <$ A $> and let <$ \partial A := \overline{A} \setminus \mathrm{int}\; A $> be the boundary of <$ A. $>
Let us consider some properties we would expect this <$ \omega: X \to \lbrack 0, 1 \rbrack $> to have. First, I regard these as essential:

<$ \forall s \in S: \omega(s) = 1. $>
All observations within the target range have maximum weight. 
<$ \forall x, y \in X: \rho(x, S) = \rho(y, S) \Rightarrow \omega(x) = \omega(y). $>
<$ \omega(x) $> is in fact a function of the distance of <$ x $> from <$ S. $> We could be thinking about a real function <$ \omega_{\rho}: \lbrack 0, \infty ) \to \lbrack 0, 1 \rbrack, $> <$ \rho(x, S) \mapsto \omega_{\rho}(\rho(x, S)) $> instead of the abstract <$ \omega: X \to \lbrack 0, 1 \rbrack. $> 
<$ \forall x, y \in X: \rho(x, S) \lt \rho(y, S) \Rightarrow \omega(x) \ge \omega(y). $>
Observations farther from target have smaller weight. 
<$ \forall x \in X: \omega(x) \to 0 $> as <$ \rho(x, S) \to \infty. $>
The weight of outliers approaches zero.
Some properties are rather desirable:

<$ \omega \in C_0(X). $>
<$ \omega $> is continuous on <$ X. $> Prevents sudden drops in weight. 
<$ \omega \in C_0(\partial S). $>
Weaker form of (v). Guarantees smoothish dropoff at least around the boundary of the target. Obviously (v) <$ \Rightarrow $> (vi). 
<$ \omega \in C_1(X). $>
<$ \omega $> is differentiable on <$ X. $> Guarantees smooth weight transitions. Obviously (vii) <$ \Rightarrow $> (v). 
<$ \omega \in C_1(\partial S). $>
Weaker form of (vii). Guarantees smooth weight transition at least on the boundary of the target. Obviously (vii) <$ \Rightarrow $> (viii).
And finally, some properties are application dependent.

<$ \forall x \in X: \omega(x) \gt 0. $>
All weights are positive. 
<$ \rho(x, S) \mapsto \omega_{\rho}(\rho(x, S)) $> is (strictly) concave on <$ X. $>
Decrease in weight speeds up with growing distance from the target.
Examples of <$ \omega $> functions
I used the following setup for the example plots. This target range just happens to be specific to my application.
<$$ X = \mathbb{R}, \\ \rho = \rho_e \quad\mathrm{(Euclidean)}, \\ S = \lbrack 3.6, 7.8 \rbrack. $$>Discrete weight (inrange indicator)
<$$ \omega_d(x) := \begin{cases} 1, & x \in S, \ 0, & x \not\in S. \end{cases} $$>The most basic binary indicator. Has the essential properties but that is all. Because it is discontinuous at <$ \partial S, $> it is too sensitive. For example, an observation of 7.9, mere 1.2% above the upper bound of 7.8, is immediately discarded with zero weight.
Polynomial weight
<$$ \omega_{P(\alpha, \beta)}(x) := \begin{cases} 1, & x \in S, \ \max \left\lbrace 1  \left( \frac{\rho(x, S)}{\beta \mathrm{diam}\; S} \right)^{\alpha}, 0 \right\rbrace, & x \not\in S, \end{cases} $$>where <$ \alpha, \beta \gt 0 $> and <$ \mathrm{diam}\; S := \sup \{ \rho(x, y): x, y \in S \} $> is the diameter of <$ S. $>
This looks complicated but is not. The distance of <$ x $> from <$ S $> is scaled by a <$ \beta $>multiple of the “size” of <$ S $> and raised to the power of <$ \alpha. $> Negative weights are normalized to zero.
This weight function has properties the (i)–(vi) and (viii) (it is not differentiable <$ \forall x: \rho(x, S) = \beta \mathrm{diam}\; S $> where the polynomial hits the ground). It is concave <$ \forall x: \rho(x, S) < \beta \mathrm{diam}\; S $> when <$ \alpha \gt 1 $> but does not have property (ix) (it does assign zero weights).
The parameters <$ \alpha $> and <$ \beta $> will depend on your application and requirements. For example, let <$ \alpha = 2 $> and <$ \beta = \frac{1}{2} $> (weight is zero for points farther than one half of the target’s diameter):
Or <$ \alpha = 3 $> and <$ \beta = 1: $>
Instead of scaling by multiples of <$ \mathrm{diam}\; S $> we could perhaps scale by <$ \beta \sqrt{\strut\mathrm{Var}\;\Xi} $> or a <$ \beta $>quantile for a sample of observations <$ \Xi \subset X. $>
Exponential weight
<$$ \omega_{\exp(\alpha)}(x) := \begin{cases} 1, & x \in S, \ \exp \left( \alpha\rho(x, S) \right), & x \not\in S, \end{cases} $$><$ \alpha > 0. $> This function is interesting by being strictly positive. It is everywhere continuous and differentiable everywhere except for <$ \partial S. $> The sharp dropoff around <$ \partial S $> and its convexity might be problematic. <$ \alpha $> controls the speed of convergence to zero.
For example, <$ \alpha = \frac{1}{2}: $>
Much more could be written and explored in this area; these are just a few methods I have been playing with in a certain project. Other weighting functions can be considered and there is always the question of choosing parameters (they can either be fixed a priori or based on stochastic properties of the observation sample).