Is pandas showing the wrong percentile?

Question

I'm working with this WNBA dataset here. I'm analyzing the Height variable, and below is a table showing frequency, cumulative percentage, and cumulative frequency for each height value recorded:

From the table I can easily conclude that the first quartile (the 25th percentile) cannot be larger than 175.

However, when I use Series.describe(), I'm told that the 25th percentile is 176.5. Why is that so?

wnba.Height.describe()
count    143.000000
mean     184.566434
std        8.685068
min      165.000000
25%      176.500000
50%      185.000000
75%      191.000000
max      206.000000
Name: Height, dtype: float64

Answer 1

There are various ways to estimate the quantiles.
The 175.0 vs 176.5 relates to two different methods:

1. Includes the Q1 ( this gives 176.5) and
2. Excludes the Q1( gives 175.0).

The estimation differs as follows

#1
h = (N − 1)*p + 1 #p being 0.25 in your case
Est_Quantile =  x⌊h⌋ + (h − ⌊h⌋)*(x⌊h⌋ + 1 − x⌊h⌋)

#2
h = (N + 1)*p   
x⌊h⌋ + (h − ⌊h⌋)*(x⌊h⌋ + 1 − x⌊h⌋)