CB2200 Business Statistics - Topic 1

Television Audience Measurement (TAM) is a system used to measure the viewership of television programs in Hong Kong.

TAM is conducted through a representative sample of Hong Kong's population. Researchers record the viewing habits of a small group, then apply that data to the entire population.

A panel of 2,700 individuals from 1,000 households are selected to represent the entire TV viewing population in Hong Kong.

A device called a set meter is connected to each television in the participating households. These meters automatically collect data on the viewing habits of the households.

TV ratings are expressed as a percentage, but they are calculated using complex scientific methods.

Before starting TAM, researchers conduct a survey to understand the demographics and habits of the entire TV viewing population.

The selection of participants for TAM ensures that the panel mirrors the characteristics of the entire TV viewing population.

One way to gather data is by using a diary method, where each household member records the programs they watched and the time spent watching them.

Categorical variables are used to describe qualities or characteristics of objects in a dataset. They represent categories or groups, such as colors, gender, or types of products.

Numerical variables represent quantities or measurable values of objects. They can be measured and have a numerical scale. Examples include height, age, or temperature.

A summary table is a way to organize categorical data. It shows the number of observations (or frequencies) for each category. It helps visualize the distribution of data within categories.

A bar chart is a visual representation of categorical data. It uses bars to show the frequency or count of each category. It helps compare the frequencies of different categories.

A pie chart is another visual representation of categorical data. It uses slices of a circle to show the proportion or percentage of each category. It helps visualize the relative proportions of different categories.

A frequency distribution is a table or graph that shows the number of observations or frequencies for each value or range of values of a numerical variable. It helps understand the pattern of data distribution.

A histogram is a visual representation of a frequency distribution. It uses bars to show the frequency or count of observations within specific ranges of values. It helps visualize the distribution of numerical data.

A variable that describes qualities or attributes of objects, often represented by categories or labels.

A variable that describes quantities or numerical measurements of objects. It can be further categorized into Discrete and Continuous variables.

A type of numerical variable that can only take on specific, distinct values. Often involves counting whole items or occurrences.

A type of numerical variable that can take on any value within a given range. Often represents continuous measurements.

The process of assigning numerical values to categorical data, making it easier for computer analysis. For example, using 1, 2, 3 to represent different reasons for attending college.

A common way to code binary data using numerical values. Typically, '0' represents 'No' and '1' represents 'Yes'.

A data point that represents a measured or observed value of a variable.

A variable that represents a specific characteristic of an object or individual being studied.

The integer part of a number, denoted by [r], is the largest whole number less than or equal to the number r. For example, [3.7] = 3 and [-2.3] = -3.

The fractional part of a number r, denoted by d, is the difference between r and its integer part [r]. It represents the decimal part of the number. For example, d for 3.7 is 0.7 (3.7 - 3 = 0.7).

A quartile is a value that divides a dataset into four equal parts. The first quartile (Q1) represents the 25th percentile, the second quartile (Q2) is the median (50th percentile), and the third quartile (Q3) represents the 75th percentile.

The interquartile range (IQR) is a measure of statistical dispersion that represents the difference between the third quartile (Q3) and the first quartile (Q1). It measures the spread of the middle 50% of the data.

Outliers are data points that lie far away from the rest of the distribution. In general, values that fall outside the range [Q1 - 1.5IQR, Q3 + 1.5IQR] are considered outliers.

The interquartile range is not influenced by outliers or extreme values, making it a more robust measure of spread compared to the range (which is influenced by extreme values).

The IQR is a more reliable measure of variability than the range because it focuses on the central 50% of the data, making it less affected by extreme values.

Descriptive statistics are a set of measures that summarize and describe the main features of a dataset. They provide insights into central tendency, dispersion, position, and shape of the data distribution.

The Data Analysis Add-ins tool in Excel allows users to perform various statistical analyses, including descriptive statistics, by providing a set of pre-built functions and tools.

The "Descriptive Statistics" option in the Data Analysis Add-ins tool calculates various descriptive measures like mean, standard deviation, minimum, maximum, and more, providing a comprehensive summary of the dataset's characteristics.

A boxplot is a graphical representation of data distribution that displays the median, quartiles, and potential outliers. It provides a visual summary of the data's central tendency, spread, and potential extreme values.

To create a boxplot in Excel, select the data range, choose "Insert" -> "Recommended Charts" -> "Box & Whisker". Add data labels to show the mean and quartile values for a more detailed visualization.

Outliers are data points that lie significantly far from the rest of the data distribution, often representing unusual or exceptional observations.

IQR refers to the Interquartile Range. It is the difference between the third quartile (Q3) and the first quartile (Q1), representing the range of the middle 50% of the data.

Outliers can be identified using the formula: [Q1 - 1.5IQR, Q3 + 1.5IQR]. Any data point falling outside this range is considered an outlier.

A statistical measure that describes how spread out data points are around the mean.

A statistical measure that shows how symmetrical a distribution is. Zero indicates a perfectly symmetrical distribution.

Describes a distribution where the tail is longer on the left side of the peak.

Describes a distribution where the tail is longer on the right side of the peak.

A graphical representation of a dataset that shows the minimum, first quartile, median, third quartile, and maximum values.

A measure of central tendency that is the middle value in a sorted dataset.

A measure of central tendency that is the sum of all values divided by the number of values.

A measure of the variability of a dataset that describes the distance between the first quartile (Q1) and the third quartile (Q3).

The smallest value in a dataset.

The largest value in a dataset.

A measure of central tendency that is the value that appears most frequently in a dataset.

The first quartile (Q1) is the value that separates the smallest 25% of the data from the rest of the data.

The third quartile (Q3) is the value that separates the largest 25% of the data from the rest of the data.

The process of using a small sample of data to draw conclusions about a larger population.