**Descriptive Statistics**

Descriptive statistics may last helpful for 2 purposes: 1) to furnish basic information regarding variables inwards an exceedingly information fix as well as 2) to focus on potential relationships betwixt variables. The three commonest descriptive statistics may last displayed diagrammatically or pictorially as well as expanse unit of measurement measures of:

**Graphical/Pictorial ways**

There expanse unit of measurement many graphical as well as pictorial ways that heighten researchers’ agreement of private variables as well as thence the relationships betwixt variables. Graphical as well as pictorial ways laissez passer a visible illustration of the info. a publish of these ways include:

- Histograms
- Scatter plots
- Geographical information Systems (GIS)
- Sociograms

**Histograms**

- Visually stand upwards for the frequencies amongst that values of variables occur
- Every toll of a variable is displayed on all-time depression of a bar graph, as well as a bar is drawn for every price.
- The peak of the bar corresponds to the frequency amongst that that toll happens

**Scatter plots**

- Show the link betwixt 2 quantitative or numeric variables past times plotting i variable against the worth of only about other variable.
- as an example, i axis of a scatter plot powerfulness stand upwards for peak as well as thence the dissimilar powerfulness stand upwards for weight. everyone inside the information would have i information on the scatter plot that corresponds to his or her peak as well as weight

**Geographic Info Systems (GIS)**

- A GIS could last a automatic information processing organization capable of capturing, storing, analyzing, as well as displaying geographically documented information; that’s, information known consistent amongst location.
- Employing a GIS program, a query worker volition make a map to stand upwards for information relationships visually

**Sociograms**

- Show networks of relationships amidst variables, sanctioning researchers to location the grapheme of relationships that may rather last also complicated to gestate.

**Measures of Central Tendency**

Measures of fundamental style expanse unit of measurement the initiative off basic and, often, the initiative off informative description of a population’s characteristics. They depict the “average” fellow member of the population of interest. There expanse unit of measurement three measures of fundamental tendency:

- Mean — the add together of a variable’s values divided past times the total make of values
- Median — the pump toll of a variable
- Mode — the worth that happens close frequently

The incomes of 5 indiscriminately elect individuals inside the u. s. expanse unit of measurement $10,000, $10,000, $45,000, $60,000, as well as $1,000,000.

Mean fiscal gain = (10,000 + 10,000 + 45,000 + 60,000 + 1,000,000) / 5 = $225,000

Median fiscal gain = $45,000

Modal fiscal gain = $10,000

The hateful is that the close ordinarily used alive of fundamental tendency. Medians expanse unit of measurement ordinarily used in i lawsuit only about values expanse unit of measurement extraordinarily completely dissimilar from the residual of the values (this is termed a inclined distribution). every bit an example, the median fiscal gain is ordinarily the close effective alive of the typical fiscal gain every bit a final result of, whereas close people earn betwixt $0 as well as $200,000, a couplet of people earn millions.

**Measures of Dispersion**

Measures of dispersion laissez passer information regarding the unfold of a variable’s values. There expanse unit of measurement 4 key measures of dispersion:

- Range
- Variance
- Standar Deviation
- Skew

*is only the distinction betwixt the tiniest as well as largest values inside the information. The interquartile vary is that the distinction betwixt the values at the 70 5th score as well as thence the xx 5th score of the info.*

**Range*** Variance* is that the close ordinarily used alive of dispersion. it’s calculated past times taking the typical of the foursquare variations betwixt every toll as well as thence the mean.

* Standard deviation*, only about other ordinarily used datum, is that the origin of the variance.

* Skew* could last a alive of whether or non only about values of a variable expanse unit of measurement extraordinarily completely dissimilar from the mass of the values. every bit an example, fiscal gain is inclined every bit a final result of the bulk practise betwixt $0 as well as $200,000, all the same a couplet of individuals earn millions. Influenza A virus subtype H5N1 variable is completely inclined if the intense values expanse unit of measurement on top of the mass of values. Influenza A virus subtype H5N1 variable is negatively inclined if the intense values expanse unit of measurement nether the mass of values.

Example:

The incomes of 5 indiscriminately elect individuals inside the u. s. expanse unit of measurement $10,000, $10,000, $45,000, $60,000, as well as $1,000,000:

Range = 1,000,000 – 10,000 = 990,000

Variance = [(10,000 – 225,000)2 + (10,000 – 225,000)2 + (45,000 – 225,000)2 + (60,000 – 225,000)2 + (1,000,000 – 225,000)2] / 5 = i hundred fifty,540,000,000

Standard Deviation = origin (150,540,000,000) = 387,995

Skew = fiscal gain is completely inclined.

**Measures of Association**

Measures of association betoken whether or non 2 variables expanse unit of measurement connected. 2 measures expanse unit of measurement ordinarily used:

- Chi-square
- Correlation

**Chi-Square**

- As a alive of association betwixt variables, chi-square tests expanse unit of measurement used on nominal information (i.e., information that expanse unit of measurement house into classes: e.g., sex [male, female] as well as form of project [unskilled, semi-skilled, skilled]) to run across whether or non they expanse unit of measurement associated.
- A chi-square is termed of import if there’s associate grade association betwixt 2 variables, associate grade non pregnant if there’s non an association

*The chi-square cheque may last used every bit a alive of goodness of match, to cheque if information from a sample render from a population amongst a item distribution, every bit an alternate to Anderson-Darling as well as Kolmogorov-Smirnov goodness-of-fit tests. As such, the chi sq. cheque isn’t restricted to nominal information; amongst non-binned data, however, the results depend upon all the same the bins or categories expanse unit of measurement created as well as thence the size of the sample

**Correlation**

- A correlation is employed to alive the forcefulness of the link betwixt numeric variables (e.g., weight as well as height)
- The initiative off mutual correlation is Pearson’s r, which may vary from -1 to +1.
- If the constant is betwixt nix as well as one, united variable volition increase, the reverse additionally volition increase. this tin last known every bit a instantly correlation. every bit an example, peak as well as weight expanse unit of measurement completely correlate every bit a final result of taller individuals sometimes weigh additional.
- If the correlation is betwixt -1 as well as zero, united variable volition increment the reverse decreases. this tin last known every bit a indirect correlation. every bit an example, historic menstruation as well as hours slept per nighttime expanse unit of measurement negatively correlate every bit a final result of older individuals sometimes slumber fewer hours per night