Add summary of review of statistics.

_posts/2024-11-22-review-of-statistics.md

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+---
+layout: post
+title: "Review of Statistics"
+tags:
+  - statistics
+---
+
+In class today we reviewed statistics.
+
+You can see a recording of the class [here](https://cardiff.cloud.panopto.eu/Panopto/Pages/Viewer.aspx?id=cbac6507-2962-42ce-8336-b22b00a5781b)
+
+This week's quiz was won again by bc.
+
+6 usernames have won:
+
+- bc
+- Dmitry (2)
+- Homelander
+- Hacker
+- Matt
+- Michael
+
+After the quiz I tackled the coursework like question from the handout.
+You can see the notebook here:
+[statistics.ipynb]({{site.baseurl}}/assets/nbs/2024-2025/statistics-review.ipynb)

assets/nbs/2024-2025/statistics-review.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "367e7b7a-0872-42fa-96aa-f81ccb9a2dcf",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import statistics as st"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "c74231d9-2b40-42f2-a9bc-ebc733025221",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "NormalDist(mu=10.0, sigma=0.5)"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "distribution = st.NormalDist(mu=10, sigma=.5)\n",
+    "distribution"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "8f80c49d-98cf-40c6-b3f8-6c94c01f6216",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "3.167124183311998e-05"
+      ]
+     },
+     "execution_count": 5,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "probability_of_less_than_eight = distribution.cdf(8)\n",
+    "probability_of_less_than_eight"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "b64b155b-ad76-4d47-a1e4-5658657984fd",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "10.6407757827723"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "distribution.inv_cdf(.9)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b9773b8f-ed9b-40de-b14e-17000ff05482",
+   "metadata": {},
+   "source": [
+    "Question 6 from the coursework."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "4bb67df0-8752-44c8-b2d8-a5d5d753b2bf",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "NormalDist(mu=65.0, sigma=5.0)"
+      ]
+     },
+     "execution_count": 17,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "distribution = st.NormalDist(mu=65, sigma=5)\n",
+    "distribution"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e8832e88-c92d-4fcd-a4b2-31b4944c2f17",
+   "metadata": {},
+   "source": [
+    "The probability of failing (getting a score less than 40%) is given by the cdf:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "cbf46b9a-b324-42a6-bb6d-c956e7583f82",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "2.8665157186802404e-07"
+      ]
+     },
+     "execution_count": 18,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "distribution.cdf(40)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fad76ac8-848e-48ac-b756-c72eb78e77b7",
+   "metadata": {},
+   "source": [
+    "The probality of getting a first class mark is: $1-F(70)$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "83b8b528-d94a-46d1-9ef4-aa1c49617f74",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "0.15865525393145707"
+      ]
+     },
+     "execution_count": 19,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "1 - distribution.cdf(70)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "d6901c15-b13c-4725-9ba7-3e7b9d15ab8b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "71.407757827723"
+      ]
+     },
+     "execution_count": 21,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "distribution.inv_cdf(1 - .10)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a82176dc-aab2-4fb7-8532-978ac7ad9337",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
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+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.13.0"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}