Summary Statistics - Revision history

Admin at 01:12, 19 March 2024

2024-03-19T01:12:23Z

← Older revision		Revision as of 01:12, 19 March 2024
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	When we investigate ~~a [[Variable (Statistics)\|variable]] in~~ a dataset, two things are ~~great at~~ ''summarizing'' the dataset: the ''center'' and the ''spread''.		When we investigate a dataset, two things are used to ''summarizing'' the dataset: the ''center'' and the ''spread''.

	= Measuring Center =		= Measuring Center =
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	Non-robust statistics include mean, range, and standard deviation.		Non-robust statistics include mean, range, and standard deviation.

			= Others =
			Besides the listed above, there are other statistics used to measure center and spread:

			'''Spread:'''

			* [[Bivariate\|Bivariate data]]: covariance, correlation

	[[Category: Statistics]]		[[Category: Statistics]]

Rice: /* Variance */

2024-03-19T00:23:26Z

Variance

@@ Line 42: / Line 42: @@
 == Interquartile Range (IQR) ==
-The '''interquartile range''' (IQR) is the middle 50% of the dataset.
+The '''interquartile range''' (IQR) is the middle 50% of the dataset. It is just from Q<sub>1</sub> to Q<sub>3</sub>.
 == Variance ==
@@ Line 52: / Line 52: @@
 <math>s^2 = \frac{1}{n - 1} \sum (x_i - \bar{x})^2 =  \frac{1}{n - 1} \left( \sum x_i^2 - n \bar{x}^2 \right)</math>
 [[Category: Statistics]]

Rice at 00:01, 19 March 2024

2024-03-19T00:01:32Z

← Older revision		Revision as of 00:01, 19 March 2024
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	== Mean ==		== Mean ==

	The '''mean''' is the average/expected value of a variable. The sample mean is denoted as <math>\bar{X}</math>, whereas the population mean is denoted as <math>\mu_X</math>.		The '''mean''' is the average/expected value of a variable. The sample mean is denoted as <math display="inline">\bar{x}</math>, whereas the population mean is denoted as <math>\mu_X</math>.

	<math>		<math>
	\bar{X} = \frac{1}{n} \sum x_i		\bar{x} = \frac{1}{n} \sum x_i
	</math>		</math>

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	= Measuring Spread =		= Measuring Spread =
			There are three main ways to measure the spread of the dataset: range, interquartile range, and variance.

			== Range ==
			The '''range''' of a variable is the interval between the first statistic and the last statistic (after being ordered).

			== Interquartile Range (IQR) ==
			The '''interquartile range''' (IQR) is the middle 50% of the dataset.

			== Variance ==
			The '''variance''' measures how much the dataset deviate from the ''mean''. To be exact, it measures the average ''squared difference'' from the mean.

			The reason we take the ''squared'' difference is because we want both statistics smaller than the mean and those greater than the mean to contribute to the variance.

			The same variance is denoted as <math>s^2</math> and the population variance is denoted as <math>\sigma^2</math>. We have

			<math>s^2 = \frac{1}{n - 1} \sum (x_i - \bar{x})^2 = \frac{1}{n - 1} \left( \sum x_i^2 - n \bar{x}^2 \right)</math>
	[[Category: Statistics]]		[[Category: Statistics]]

Rice: Created page with "When we investigate a variable in a dataset, two things are great at ''summarizing'' the dataset: the ''center'' and the ''spread''. = Measuring Center = There are two ways to measure center: the mean and the median. == Mean == The '''mean''' is the average/expected value of a variable. The sample mean is denoted as $\bar{X}$ , whereas the population mean is denoted as $\mu_X$ . $\bar{X} = \frac{1}{n} \sum x_i$
2024-03-18T23:53:25Z

Created page with "When we investigate a variable in a dataset, two things are great at ''summarizing'' the dataset: the ''center'' and the ''spread''. = Measuring Center = There are two ways to measure center: the mean and the median. == Mean == The '''mean''' is the average/expected value of a variable. The sample mean is denoted as <math>\bar{X}</math>, whereas the population mean is denoted as <math>\mu_X</math>. <math> \bar{X} = \frac{1}{n} \sum x_i </ma..."

New page
When we investigate a [[Variable (Statistics)|variable]] in a dataset, two things are great at ''summarizing'' the dataset: the ''center'' and the ''spread''.

= Measuring Center =

There are two ways to measure center: the mean and the median.

== Mean ==

The '''mean''' is the average/expected value of a variable. The sample mean is denoted as <math>\bar{X}</math>, whereas the population mean is denoted as <math>\mu_X</math>.

<math>
\bar{X} = \frac{1}{n} \sum x_i
</math>

where <math>n</math> is the sample size.

== Median/Percentiles/Quartiles ==

The '''median''' tell us the literal center of the dataset: 50% of statistics are on the left, 50% on the right. It is denoted with <math>\widetilde{X}</math>

The '''quartiles''' is the same, except at 25% for the first quartile, 50% for the second (also the median), and 75% for the third. They are denoted with <math>Q_1, Q_2, Q_3</math>

The '''percentiles''' is also the same, except at a particular percentage. For example, the 80th percentile has 80% of data before it.

To calculate the P-th percentile (and thereby calculating all the other something-tiles), we have

<math>
\left( \frac{P}{100} \right) (n + 1)
</math>

where <math>n</math> is the sample size.

== Mode ==

The '''mode''' is the most frequently occurring value. It's pretty neglected lol.

= Measuring Spread =

[[Category: Statistics]]