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Summary Statistics I (STA1000) R99,00
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Summary

Summary Statistics I (STA1000)

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These notes fort test 1 in STA 1000 are a quick and easy summary of everything you might possibly need to know during the test. This document provides all the formulas necessary to ace your test and many in depth explanations of these formulas.

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  • March 26, 2023
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Week 1
𝑛𝑜. 𝑜𝑓 𝑒𝑞𝑢𝑎𝑙𝑙𝑦 𝑙𝑖𝑘𝑒𝑙𝑦 𝑤𝑎𝑦𝑠 𝑜𝑓 𝑔𝑒𝑡𝑡𝑖𝑛𝑔 𝑜𝑢𝑡𝑐𝑜𝑚𝑒
Pr 𝑂𝑢𝑡𝑐𝑜𝑚𝑒 =
𝑛𝑜. 𝑜𝑓 𝑒𝑞𝑢𝑎𝑙𝑙𝑦 𝑙𝑖𝑘𝑒𝑙𝑦 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠

Probability Versus Odds

Probability reflects the number of ways of getting specific outcome relative to the
total number of ways of conducting the experiment.

Odds reflect the number of ways that give you the event of interest relative to the
number of ways that don’t give you the event of interest.

Statistical Distributions

Statistical distributions are long-run patterns of various outcomes – used to predict
etc.

Excel Formulas

= rand()
® Generates a random number between 0 and 1. By pressing F9, random
numbers are re-generated.
= countif (A1:A20;1)
® “A1:A20” refers to range of data.
® “1” refers to what you’re looking for.
By pressing F4, you lock the data set to specific numbers.


Fair Game

Nobody is expected to win and nobody is expected to lose in the long run.

(Example):

I have a stall where people come and bet on the numbers from die throws. Each
bet is R1. If Amy bets R1 on all 6 numbers, in order for it to be a fair game, she
should win R6 if she’s correct – what she pays = what she wins.
Win Percentage

𝑡𝑜𝑡𝑎𝑙 𝑝𝑎𝑦𝑜𝑢𝑡 𝑓𝑜𝑟 𝑤𝑖𝑛𝑛𝑖𝑛𝑔
𝑊𝑖𝑛 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 = 𝑋 100
𝑎𝑚𝑜𝑢𝑛𝑡 𝑏𝑒𝑡 𝑎𝑐𝑟𝑜𝑠𝑠 𝑎𝑙𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠




Downloaded by Dumisile Biyela ()

, Indicates the percentage of what we have received in the form of bets that we pay
back in winnings.

The amount we pay back of what we take in.


House Advantage

This = the amount we [the stall owners] retain.

𝐻𝑜𝑢𝑠𝑒 𝐴𝑑𝑣 = 100 − 𝑊𝑖𝑛 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒

Expected Gain/Loss

𝐸 𝐺 𝑜𝑟 𝐿 = 𝑇𝑜𝑡𝑎𝑙 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐵𝑒𝑡 − (Pr 𝑊𝑖𝑛𝑛𝑖𝑛𝑔 × 𝑇𝑜𝑡𝑎𝑙 𝑃𝑎𝑦𝑜𝑢𝑡)




𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐵𝑒𝑡 = 𝑅2
1
Pr 𝑊𝑖𝑛𝑛𝑖𝑛𝑔 = ( )×2
12
𝑇𝑜𝑡𝑎𝑙 𝑃𝑎𝑦𝑜𝑢𝑡 = 𝑅11 × 𝑅2

Therefore:
1
𝐸 𝐺 𝑜𝑟 𝐿 = 2 − (( )×22)
12
𝐸 𝐺 𝑜𝑟 𝐿 = 0.166

*If E(G or L) <1, then it’s a loss!




Downloaded by Dumisile Biyela ()

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