Create README.md

16 - NumPy Problems/11 - Mean - Var and Std/README.md

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+<h1 align='center'>Mean - Var - and - Std</h1>
+
+## Problem Statement
+
+**Problem URL :** [Mean, Var and Std](https://www.hackerrank.com/challenges/np-mean-var-and-std/problem?isFullScreen=true)
+
+![image](https://github.com/user-attachments/assets/a6dee4d7-6d32-4e35-9419-5e706945ad68)
+![image](https://github.com/user-attachments/assets/e1701a3a-fd7c-4a72-b8e9-5c2f004c71ca)
+![image](https://github.com/user-attachments/assets/3653265e-bcc5-4500-aa84-95e0a8201870)
+
+## Problem Solution
+```py
+import numpy as np
+
+N, M = map(int, input().split())
+
+np_array = np.array([[*map(int, input().split())] for i in range(N)])
+
+mean_values = np.mean(np_array, axis=1)
+var_values = np.var(np_array, axis=0)
+std_value = np.std(np_array, axis=None)
+
+print(mean_values)
+print(var_values)
+print(round(std_value, 11))
+```
+
+## Problem Solution Explanation
+Let's break down the code and explain the process step-by-step, using an example.
+
+
+1. **Importing Libraries:**
+   ```python
+   import numpy as np
+   ```
+   - `numpy` is imported to handle array operations efficiently.
+
+2. **Reading Input:**
+   ```python
+   N, M = map(int, input().split())
+   ```
+   - This reads two integers from the input: `N` (number of rows) and `M` (number of columns).
+
+3. **Creating the NumPy Array:**
+   ```python
+   np_array = np.array([[*map(int, input().split())] for i in range(N)])
+   ```
+   - This creates a 2D NumPy array.
+   - For each row (`N` rows in total), it reads a line of space-separated integers, converts them to integers, and forms a list.
+   - These lists are then combined into a 2D NumPy array.
+
+4. **Calculating Mean Values:**
+   ```python
+   mean_values = np.mean(np_array, axis=1)
+   ```
+   - Computes the mean of each row (across columns).
+   - `axis=1` specifies that the mean should be calculated along the columns for each row.
+
+5. **Calculating Variance Values:**
+   ```python
+   var_values = np.var(np_array, axis=0)
+   ```
+   - Computes the variance for each column.
+   - `axis=0` specifies that the variance should be calculated along the rows for each column.
+
+6. **Calculating Standard Deviation:**
+   ```python
+   std_value = np.std(np_array, axis=None)
+   ```
+   - Computes the standard deviation of all elements in the array.
+   - `axis=None` specifies that the standard deviation is calculated over the entire array.
+
+7. **Printing Results:**
+   ```python
+   print(mean_values)
+   print(var_values)
+   print(round(std_value, 11))
+   ```
+   - Prints the mean values (one value per line for each row).
+   - Prints the variance values (one value per line for each column).
+   - Prints the standard deviation rounded to 11 decimal places.
+
+### Example
+
+Let's use the example input:
+
+```
+2 2
+1 2
+3 4
+```
+
+- `N = 2`, `M = 2`
+- The 2D NumPy array will be:
+  ```
+  [[1, 2],
+   [3, 4]]
+  ```
+
+**Calculations:**
+
+1. **Mean Values (per row):**
+   - For the first row `[1, 2]`, mean = `(1 + 2) / 2 = 1.5`
+   - For the second row `[3, 4]`, mean = `(3 + 4) / 2 = 3.5`
+   - Result: `[1.5, 3.5]`
+
+2. **Variance Values (per column):**
+   - For the first column `[1, 3]`, variance = `[(1-2)^2 + (3-2)^2] / 2 = [1 + 1] / 2 = 1.0`
+   - For the second column `[2, 4]`, variance = `[(2-3)^2 + (4-3)^2] / 2 = [1 + 1] / 2 = 1.0`
+   - Result: `[1.0, 1.0]`
+
+3. **Standard Deviation:**
+   - All elements combined: `[1, 2, 3, 4]`
+   - Mean of all elements = `(1 + 2 + 3 + 4) / 4 = 2.5`
+   - Variance = `[(1-2.5)^2 + (2-2.5)^2 + (3-2.5)^2 + (4-2.5)^2] / 4`
+     = `[2.25 + 0.25 + 0.25 + 2.25] / 4`
+     = `5 / 4 = 1.25`
+   - Standard deviation = `sqrt(1.25) ≈ 1.118033988749895`
+   - Result: `1.11803398875` (rounded to 11 decimal places)
+
+### Output
+
+Given the example input, the code will produce:
+
+```
+[1.5 3.5]
+[1. 1.]
+1.11803398875
+```
+
+This output matches the expected results for mean values, variance values, and standard deviation, respectively.