# Statistics with numeric lists of integers, fractions, and decimals.

The built-in and statistics modules provide all the necessary methods to calculate summary stats for lists of numbers as integers, floats, high precision decimal, or rational fractions.

## Page contents

- Builtin min, max, sum
- Statistics module mean, median, mode, stdev, variance
- Soft error caused by key=abs
- Statistics on a list of precision decimals
- Statistics on a list of fractions

## Builtin min, max, sum

Summarizing numeric list data using built-in methods

Py3: Min, max and sum

```
nums = [-1,5,2,-7,3,6,2,5,8,5,-4,3,-8,3,5,-1]
# min, max
nums_min = min(nums) #= -8
nums_max = max(nums) #= 8
# sum, number of elements
nums_sum = sum(nums) #= 26
nums_len = len(nums) #= 16
```

Notes: Min, max and sum of lists

List data can be sorted into custom order. If only the min and max values are needed - then built-in methods and provide quick access to the values. There is a summation function for numbers too. To find average, the sum can be divided by the length of the sequence.

## Statistics module mean, median, mode, stdev, variance

Simple stats for numeric lists

Py3: Statistics module

```
import statistics as st
nums = [-1,5,2,-7,3,6,2,5,8,5,-4,3,-8,3,5,-1]
# calculate statistical parameters
nums_mean = st.mean(nums) #= 1.625
nums_medn = st.median(nums) #= 3.0
nums_mode = st.mode(nums) #= 5
nums_stdv = st.stdev(nums) #= 4.6457...
nums_vars = st.variance(nums) #= 21.5833...
```

Notes: Mean, median, mode and variance

The statistics module in the standard library can operate on numeric lists to provide basic statistical measures for data. Version 3.8 also adds quantiles, geometric mean, and multimodes where multiple values occur at similar frequencies.

## Soft error caused by key=abs

Multi-valued key match chooses first item.

Py3: Min, max using absolute values

```
nums = [-1,5,2,-7,3,6,2,5,8,5,-4,3,-8,3,5,-1]
# compute absolute valued min and max
key_min = min(nums, key=abs) #= -1
key_max = max(nums, key=abs) #= 8
abs_min = min(*map(abs, nums)) #= 1
abs_max = max(*map(abs, nums)) #= 8
# key = [1,5,2,7,3,6,2,5,8,5,4,3,8,3,5,1]
# calculating absolute valued statistics
nums = [-1,1]
key_min = min(nums, key=abs) #= -1
key_max = max(nums, key=abs) #= -1
nums = [1,-1]
key_min = min(nums, key=abs) #= 1
abs_min = min(*map(abs, nums)) #= 1
```

Notes: Custom keys and care

The min and max methods provide support for custom keys like sort. However care needs to be taken in using them as keys. Here the abs function creates a redundancy for min and max. The better way is to convert to absolute values and not to use a key.

## Statistics on a list of precision decimals

Statistics for high precision decimals.

Py3: Decimal statistics

```
import decimal as dc
import statistics as st
txt = '1.2, 1.4, 1.9, 2.4, 1.7, 1.9, 2.1, 1.0'
nums = [dc.Decimal(t) for t in txt.split(',')]
# statistics on decimal object
dc_min = min(nums) #= 1.0
dc_max = max(nums) #= 2.4
dc_sum = sum(nums) #= 13.6
dc_mean = st.mean(nums) #= 1.7
dc_stdv = st.stdev(nums) #= 0.4720...
```

Notes: Working with decimals

Just like integers and floats, the statistics module gracefully handles high precision decimal numbers.

## Statistics on a list of fractions

Fractional and rational number statistics.

Py3: Fraction statistics

```
import fractions as fr
import statistics as st
frc_tup = [(3,7), (1,4), (2,5), (3,7), (1,2)]
nums = [fr.Fraction(n, d) for n,d in frc_tup]
# statistics with fractions
dc_min = min(nums) #= 1/4
dc_max = max(nums) #= 1/2
dc_sum = sum(nums) #= 281/140
dc_mean = st.mean(nums) #= 281/700
dc_stdv = st.stdev(nums) #= 0.09236...
```

Notes: Fractions module working with stats

Fractions expressed as numerator and denominators are processed by the stats module and the values are mostly returned as rational fractions. A few cases like stdev and variance cannot maintain a rational fraction format.