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Auto-generated via `{sandpaper}`
Source  : d7ec13d
Branch  : main
Author  : Christian Knudsen <[email protected]>
Time    : 2024-11-08 09:39:40 +0000
Message : Merge pull request KUBDatalab#167 from chrbknudsen/main

flere mindre rettelser
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actions-user committed Nov 8, 2024
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4 changes: 2 additions & 2 deletions clt.md
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Expand Up @@ -45,7 +45,7 @@ mean(random_numbers)
```

``` output
[1] 0.5107301
[1] 0.4834503
```
The important point of the Central Limit Theorem is, that if we take a large
number of random samples, and calculate the mean of each of these samples,
Expand All @@ -59,7 +59,7 @@ mean(runif(100))
```

``` output
[1] 0.4658433
[1] 0.4370272
```
And we can use the `replicate()` function to repeat that calculation several times, in this case 1000 times:

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9 changes: 7 additions & 2 deletions descript-stat.md
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Expand Up @@ -339,18 +339,23 @@ by the variance as defined here, and we would really like to get a
connection between what we observe here, and the normal distribution.
:::

The mathematical notation would be:
For the population variance, the mathematical notation would be:

$$
\sigma^2 = \frac{\sum_{i=1}^N(x_i - \mu)^2}{N}
$$

:::: callout

## Population or sample?

Why are we suddenly using $\mu$ instead of $\overline{x}$? Because this
definition uses the population mean. The mean, or average, in the entire
population of all penguins everywhere in the universe. But we have not
weighed all those penguins.
::::

Instead we will normally look at the sample variance:
And the sample variance:

$$
s^2 = \frac{\sum_{i=1}^N(x_i - \overline{x})^2}{N-1}
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38 changes: 19 additions & 19 deletions kmeans.md
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Expand Up @@ -144,31 +144,31 @@ clustering
```

``` output
K-means clustering with 3 clusters of sizes 62, 47, 69
K-means clustering with 3 clusters of sizes 47, 69, 62
Cluster means:
Alcohol Malicacid Ash Alcalinityofash Magnesium Totalphenols Flavanoids
1 12.92984 2.504032 2.408065 19.89032 103.59677 2.111129 1.584032
2 13.80447 1.883404 2.426170 17.02340 105.51064 2.867234 3.014255
3 12.51667 2.494203 2.288551 20.82319 92.34783 2.070725 1.758406
1 13.80447 1.883404 2.426170 17.02340 105.51064 2.867234 3.014255
2 12.51667 2.494203 2.288551 20.82319 92.34783 2.070725 1.758406
3 12.92984 2.504032 2.408065 19.89032 103.59677 2.111129 1.584032
Nonflavanoidphenols Proanthocyanins Colorintensity Hue
1 0.3883871 1.503387 5.650323 0.8839677
2 0.2853191 1.910426 5.702553 1.0782979
3 0.3901449 1.451884 4.086957 0.9411594
1 0.2853191 1.910426 5.702553 1.0782979
2 0.3901449 1.451884 4.086957 0.9411594
3 0.3883871 1.503387 5.650323 0.8839677
OD280OD315ofdilutedwines Proline
1 2.365484 728.3387
2 3.114043 1195.1489
3 2.490725 458.2319
1 3.114043 1195.1489
2 2.490725 458.2319
3 2.365484 728.3387
Clustering vector:
[1] 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 1 1 2 2 1 1 2 2 1 2 2 2 2 2 2 1 1
[38] 2 2 1 1 2 2 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 3 1 3 3 1 3 3 1 1 1 3 3 2
[75] 1 3 3 3 1 3 3 1 1 3 3 3 3 3 1 1 3 3 3 3 3 1 1 3 1 3 1 3 3 3 1 3 3 3 3 1 3
[112] 3 1 3 3 3 3 3 3 3 1 3 3 3 3 3 3 3 3 3 1 3 3 1 1 1 1 3 3 3 1 1 3 3 1 1 3 1
[149] 1 3 3 3 3 1 1 1 3 1 1 1 3 1 3 1 1 3 1 1 1 1 3 3 1 1 1 1 1 3
[1] 1 1 1 1 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 3 3 3 1 1 3 3 1 1 3 1 1 1 1 1 1 3 3
[38] 1 1 3 3 1 1 3 3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 2 3 2 2 3 2 2 3 3 3 2 2 1
[75] 3 2 2 2 3 2 2 3 3 2 2 2 2 2 3 3 2 2 2 2 2 3 3 2 3 2 3 2 2 2 3 2 2 2 2 3 2
[112] 2 3 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 3 2 2 3 3 3 3 2 2 2 3 3 2 2 3 3 2 3
[149] 3 2 2 2 2 3 3 3 2 3 3 3 2 3 2 3 3 2 3 3 3 3 2 2 3 3 3 3 3 2
Within cluster sum of squares by cluster:
[1] 566572.5 1360950.5 443166.7
[1] 1360950.5 443166.7 566572.5
(between_SS / total_SS = 86.5 %)
Available components:
Expand All @@ -188,9 +188,9 @@ table()
``` output
true
quess 1 2 3
1 13 20 29
2 46 1 0
3 0 50 19
1 46 1 0
2 0 50 19
3 13 20 29
```

The algorithm have no idea about the numbering, the three groups are numbered
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70 changes: 35 additions & 35 deletions md5sum.txt
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2 changes: 1 addition & 1 deletion normal-distribution.md
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Expand Up @@ -196,7 +196,7 @@ rnorm(5, mean = 0, sd = 1 )
```

``` output
[1] -0.5012600 0.6792018 0.9950838 -1.4185692 -0.4106442
[1] -0.06628293 -0.94233783 1.54180816 1.33387672 1.14548414
```
Den returnerer (her) fem tilfældige værdier fra en normalfordeling med (her)
middelværdi 0 og standardafvigelse 1.
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