Question

A student doing this experiment obtained the data shown in the table above. The value of the constant, k, for this data is

Answer 1

I don't see the table you mention. Could you either paste the data here or upload a picture of the table?

If you prefer to check/compute it yourself, here are the common ways to find k depending on the model:

1) If the model is y = kx (line through the origin)
- Best-fit k (least-squares) = Σ(xi yi) / Σ(xi^2).
- Estimate of uncertainty (standard error) = sqrt[ RSS/(N−1) ] / sqrt[ Σ(xi^2) ], where RSS = Σ(yi − k xi)^2.

2) If the model is y = kx + b (general straight line)
- Best-fit slope k = [ N Σ(xi yi) − (Σxi)(Σyi) ] / [ N Σ(xi^2) − (Σxi)^2 ].
- Intercept b = (Σyi − k Σxi)/N.
- Standard error of slope: se_k = sqrt[ RSS/(N−2) ] / sqrt[ Σ(xi − x̄)^2 ] with RSS = Σ(yi − k xi − b)^2.

3) If the relationship is reciprocal or power law, transform first (e.g., log(y) vs log(x) for y = k x^n) then fit a line.

If you paste the table (xi and yi columns or whatever variables are used), I will compute k and its uncertainty for you.