After inspecting the Series, we may want to perform calculations on the marks. Pandas provides several methods for mathematical and statistical operations.

• sum(): The sum() method returns the sum of the non-missing values in the Series.
  For example:

• marks = pd.Series([85, 72, 90, 65])

• marks.sum()

output:

312

The method adds all the values together:
85 + 72 + 90 + 65 = 312

• mean(): The mean() method returns the average of the values in the Series.
  For example:

marks = pd.Series([80, 90, 70])

marks.mean()

output:

80.0

The average is (80 + 90 + 70) / 3 = 80.
So, whenever we want to find the average of numerical data, we can use mean().

• median(): The median() method returns the middle value after arranging the values in ascending order.
  For example:

marks = pd.Series([60, 70, 80, 90, 100])

marks.median()

output:

80.0

The values are already arranged as 60, 70, 80, 90, 100, so the middle value is 80.

• mode(): The mode() method returns the value or values that occur most frequently in the Series.
  For example:

marks = pd.Series([70, 80, 80, 90, 80])

marks.mode()

output:

0    80

dtype: int64

Here, 80 occurs most frequently, so mode() returns 80.

• min(): The min() method returns the smallest value from the Series.
  For example:

marks = pd.Series([85, 72, 90, 65])

marks.min()

output:

65

So, the smallest mark is 65.

• max(): The max() method returns the largest value from the Series.
  For example:

marks = pd.Series([85, 72, 90, 65])

marks.max()

output:

90

So, the largest mark is 90.

• count(): The count() method returns the number of non-null values present in the Series.
  For example:

marks = pd.Series([85, 72, 90, 65, None])

marks.count()

output:

4

There are 5 total items, but one value is missing. So, count() returns 4 because it does not count the missing value.
If we want the total number of items, including missing values, we can use the size attribute.

marks.size

output:

5

So remember:
size → total number of items
count() → number of non-null items

• std(): The std() method returns the standard deviation of the values.
  For example:

marks = pd.Series([60, 70, 80, 90, 100])

marks.std()

output:

15.811388300841896

Standard deviation helps us understand how much the values are spread out from their average.
For beginners, you can simply remember:
std() → tells us how much the data varies.

• var(): The var() method returns the variance of the values.
  For example:

marks = pd.Series([60, 70, 80, 90, 100])

marks.var()

output:

250.0

Variance is also used to understand how much the values are spread out.

• quantile(): The quantile() method returns the value at a particular quantile.
  For example:

marks = pd.Series([60, 70, 80, 90, 100])

marks.quantile(0.5)

output:

80.0

Here, 0.5 represents the 50th percentile, which is closely related to the median.
We can also use:

marks.quantile(0.25)

output:

70.0

Here, 0.25 represents the 25th percentile.

• cumsum(): The cumsum() method returns the cumulative sum of the values.
  For example:

marks = pd.Series([10, 20, 30, 40])

marks.cumsum()

output:

0     10

1     30

2     60

3    100

dtype: int64

Here, each value is added to the sum of the previous values.
The calculation is:
10
10 + 20 = 30
30 + 30 = 60
60 + 40 = 100

• cumprod(): The cumprod() method returns the cumulative product of the values.
  For example:

marks = pd.Series([2, 3, 4])

marks.cumprod()

output:

0     2

1     6

2    24

dtype: int64

The calculation is:
2
2 × 3 = 6
6 × 4 = 24

• cummax(): The cummax() method returns the maximum value seen so far as we move through the Series.
  For example:

marks = pd.Series([60, 80, 70, 90])

marks.cummax()

output:

0    60

1    80

2    80

3    90

dtype: int64

At each position, Pandas keeps the highest value encountered so far.

• cummin(): The cummin() method works similarly to cummax(), but it keeps track of the minimum value seen so far.
  For example:

marks = pd.Series([60, 80, 50, 90])

marks.cummin()

output:

0    60

1    60

2    50

3    50

dtype: int64