Intro to Statistics

• Statistics is a mathematical science dealing with experimental design.

Descriptive Statistics

• Descriptive statistics involves methods for collecting, organizing, and summarizing data.

Inferential Statistics

• Inferential statistics is the process of drawing conclusions from data.

Parameter vs. Statistic

• A parameter describes a characteristic of a population.
• A statistic describes a characteristic of a sample.

Array

• An array is an arrangement of data from lowest to highest, highest to lowest, or any other defined order.

Ungrouped Frequency Distribution

• Ungrouped frequency distribution is an arrangement of data where the frequency of each individual data point is shown separately.
• Tally marks (I, II, III, etc.) can be used when manually counting frequency.

Grouped Frequency Distribution

• Grouped frequency distribution is an arrangement of data where data is grouped into categories or classes.

Range

• Range indicates how spread out or dispersed the data is.
• Range is calculated as the highest value minus the lowest value.

Types of Range

• Exclusive range formula: HS - LS (Highest value minus Lowest value)
• Inclusive range formula: HS - LS + 1 (Highest value minus Lowest value plus 1)

Class

• A class is a group of values organized together for the purpose of calculating a frequency distribution.
• Class is estimated using the formula: 1 + 3.3 log(n), where n is the number of data points.

Class Size

• Class size is the number of data points within each class.
• Class size is calculated as: i = range/class.

Cumulative Frequency

• Cumulative frequency is the total frequency up to a certain point in a distribution.

Measure of Central Tendency

• Measure of central tendency is a value that represents a set of data.

Mean

• The mean is the average of the values in a sample.
• Mean of ungrouped data set formula: Σxi / n (summation of all values divided by the number of values).
• Mean of ungrouped frequency distribution formula: Σ(frequency * value) / n where n is the total number of data points.
• Mean of grouped frequency distribution: assumed mean + (Σ(frequency * class deviation) / n) * i, where i is the class size.

Median

• The median is the value that falls in the middle position of a data set.
• Median of Grouped Frequency Distribution Formula: Lower limit + (N/2 - Cumulative Frequency) / frequency * I.

Mode

• The mode is the most frequently occurring score in a data set.

Types of Mode

• Unimodal: one mode.
• Bimodal: two modes.
• Multimodal: more than two modes.

Measure of Variability

• Measure of variability indicates the spread of scores in a distribution.

Mean Deviation

• Mean deviation is a rough estimate of the average distance of values from the mean.
• Formula: Σ|Xi - mean| / n (summation of the absolute difference between each value and the mean, divided by the number of values).

Variance

• Variance is the square of the mean deviation.

Types of Variance

• Population variance formula: σ² = Σ(values - mean)² / N (summation of squared differences between each value and the population mean, divided by the population size).
• Sample variance formula: s² = Σ(values - mean)² / (n - 1) (summation of squared differences between each value and the sample mean, divided by the sample size minus 1).

Standard Deviation

• Standard deviation is the square root of the variance.

Types of Standard Deviation

• Population standard deviation: √σ² (square root of the population variance).
• Sample standard deviation: √s² (square root of the sample variance).

Focuses on descriptive and inferential statistics, differentiating parameters from statistics. Covers data arrangement in arrays and frequency distributions, both grouped and ungrouped. Also including the range of values.