Cookbook Measures of Central Tendency

data/calculate-the-median/00-stdlib.ml

@@ -0,0 +1,35 @@
+---
+packages: []
+discussion: |
+  - **Description:** The [Median](https://statistics.laerd.com/statistical-guides/measures-central-tendency-mean-mode-median.php) measure of central tendency
+  is the middle value in an ordered set of data. It is useful for statistical analysis as it isn't easily influenced by extreme values (outliers)
+  - **Data Assumption:** This code assumes the data is of type float. While we can calculate the median for any numeric value, it makes sense to use floats in OCaml since all
+  integers i.e 1 can be represented as floats 1. but not all floats can be represented by integer data types i.e. 1.5 does not equal 1 or 2
+  - **Note:** When there is an even number of elements in the data, the median will be the average of the two middle values.
+---
+
+(* `median` returns the middle value of the elements of `data`.
+    An empty list will return `invalid_arg "empty list"`.
+
+    To find the median, the data needs to be sorted. `List.sort` comes with the OCaml standard library 
+    and is used to create the `sorted_data` object.
+
+    We then check if we have an even or odd number of elements in `data`. This determines how we find the middle value.     
+*)
+let median data =
+  let n = List.length data in
+  if data = []
+  then invalid_arg "empty list"
+  else (
+    let sorted_data = List.sort compare data in
+    if n mod 2 = 0
+    then (
+      let mid1 = List.nth sorted_data ((n / 2) - 1) in
+      let mid2 = List.nth sorted_data (n / 2) in
+      (mid1 +. mid2) /. 2.0)
+    else List.nth sorted_data (n / 2))
+
+(* Example usage *)
+let data = [ 1.0; 2.0; 3.0; 4.0; 5.0; 6.0; 1.0 ]
+
+Printf.printf "The median value is %f" (median data)

data/cookbook/calculate-the-mean/00-stdlib.ml

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+---
+packages: []
+discussion: |
+  - **Description:** One of most commonly used measure of central tendency is the [Mean](https://statistics.laerd.com/statistical-guides/measures-central-tendency-mean-mode-median.php)
+  - **Calculation:** Using the Ocaml Standard Library
+  - **Data Assumption:** This code assumes the data is of type float. While we can calculate the mean for any numeric value, it makes sense to use floats in Ocaml since all
+  integers i.e 1 can be represented as floats 1. but not all floats can be represented by integer data types i.e. 1.5 does not equal 1 or 2
+---
+
+
+(* sample data for testing *)
+let data = [ 2.; 3.; 4.; 5.; 3. ]
+
+(* `mean` accepts a list of floats `data` and returns the mean or average of that data.
+
+  The total number of elements `total_elemnts` in the list is found using the `List.length` method from the standard libary.
+
+  `List.length` returns an integer, so we use the `float_of_int` function
+   to convert the `length` to a float so it can be used in the next calculation.
+
+   `summed_elements` is the sum of all elements in the list `data`. 
+   It is calculated using the built-in `fold_left` method with the float addition operator `+.`
+*)
+let mean data =
+  match data with
+  | [] -> invalid_arg "list must not be empty"
+  | _ ->
+    let total_elements = float_of_int (List.length data) in
+    let summed_elements = List.fold_left ( +. ) 0. data in
+    summed_elements /. total_elements
+;;
+
+(* Example usage. Note the final value is rounded to the second decimal place in the print statment. *)
+Printf.printf "The mean value is %.2f" (mean data)

data/cookbook/tasks.yml

@@ -188,6 +188,12 @@ categories:
     tasks:
     - title: Calculate Geodistance Between Two Points
       slug: calculate-geodistance-between-points
+  - title: Measures of Central Tendency
+    tasks:
+    - title: Calculate the Mean 
+      slug: calculate-the-mean
+    - title: Calculate the Median
+      slug: calculate-the-median
 - title: Operating System
   tasks:
   - title: Run an External Command and Process Stdout