Is this the correct way to get the $25^{th}$, $50^{th}$, and $75^{th}$ percentile?

Question

From the frequency distribution in the image below,

$P_{25} = 0.25(53) = 13.25$

$13.25$ falls between index $1$ and $2$, so then $\dfrac{1+2}{2} = 1.5$, round up, $2$.

$P_{25} = 35.8\%$

---

$P_{50} = 0.50(53) = 26.5$

$26.5$ falls between index $2$ and $3$, so then $\dfrac{2+3}{2} = 2.5$, round up, $3$.

$P_{50} = 52.8\%$

---

$P_{75} = 0.75(53) = 39.75$

$39.75$ falls between index $4$ and $5$, so then $\dfrac{4+5}{2} = 4.5$, round up, $5$.

$P75 = 75.5\%$

Here is the frequency distribution:

Please help

Thank you

Answer 1

It is hard to understand your calculations. You shoud focus on the column of Cumulative Pct., last one, and see on which ranges fall the 25%, 50% and 75%, namely:

25% -> (<85-90)
50% -> (80.5-85)
75% -> (70.5-75)

Edit: reviewing it, I think you are looking at the column of the isolated percentage of each range. Notice that a percentile is the value below which a given percentage of observations in a group of observations fall. So in your case a 75% of the observations are located in the range 70.5-75 or before