AS FM

as.ipynb

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+{
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+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "%matplotlib widget\n",
+    "from collections.abc import Iterable\n",
+    "\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "from scipy.stats import chi2\n",
+    "import math\n",
+    "from fractions import Fraction as F"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# AS\n",
+    "This contains automations for A-level (AS) Maths stats ordered in the same way as they are on [integral maths](https://my.integralmaths.org/)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Collecting and Interpreting Data\n",
+    "### Sampling\n",
+    "- Simple random sampling\n",
+    "  - Random procedure\n",
+    "    - e.g. drawing tickets, random number generator\n",
+    "  - In a finite sample space, all candidates have an equal chance of being selected\n",
+    "  - Sampling is done without replacement\n",
+    "  - Selections are independent\n",
+    "- Cluster sampling\n",
+    "  - Only some subgroups of a sample space are selected\n",
+    "  - Only appropriate when subgroups are reasonably representative of the entire sample space\n",
+    "- Opportunity sampling\n",
+    "  - Selection by opportunity\n",
+    "    - e.g. interviewing passers by on a street\n",
+    "- Stratified sampling\n",
+    "  - Used when sample space can be divided into subgroups (strata)\n",
+    "    - ... to ensure all strata are sampled\n",
+    "  - Weighting needs to be used if numbers of samples from each strata are not proportional to the size of the strata\n",
+    "- Quota sampling\n",
+    "  - Same as stratified sampling with a quota for each strata\n",
+    "- Self-selected sample\n",
+    "  - Individuals chose to be sampled\n",
+    "  - e.g. online poll\n",
+    "- Systematic sampling\n",
+    "  - Systematic procedure\n",
+    "  - e.g. every 10th person on alphabetically sorted list"
+   ]
+  }
+ ],
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