Statistics - Calculating $60$th percentile from data given for $25$th, $50$th , $75$th and $90$th

Question

I am not a stats person. Help me.

If $25$th percentile is $3822$, $50$th is $4780$, $75$th is $5856$ and $90$th is $7106$, what is $60$th percentile?

Answer 1

As has been pointed out already, you can't be absolutely sure without knowing what the distribution is. Modelling with the Normal Distribution may not be accurate since the data do not appear to be symmetrical.

One method to estimate the 60th percentile could be to use linear interpolation, so you would have $$\frac{P_{60}-4780}{5856-4780}=\frac{60-50}{75-50}$$ which leads to $$P_{60}\simeq5210.4$$

It is possible that this is an underestimate since the cumulative frequency curve is likely to be concave over this interval.