**ST1120 Data Science for Business Analytics I Assignment Sample NUIG Ireland**

ST1120 Data Science for Business Analytics I is a course offered at the National University in Ireland, Galway. The course provides an introduction to data science with a focus on business analytics. Students will learn how to analyze data and extract insights for decision-making. Topics covered in the course include data management, data mining, predictive modelling, and business intelligence.

The course is well-suited for students who want to pursue careers in data science or business analytics. It is also valuable for students who want to learn how to use data to make decisions in any field. The skills learned in this course will be useful for students who want to work in any industry, including finance, marketing, operations, and healthcare.

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In this section, we are describing some assigned activities. These are:

**Assignment Activity 1: Describe quantitative data using numerical and graphical summaries, referencing central tendency (mean, median, mode), spread (range, variance, standard deviation, inter-quartile range) and shape (symmetry, left/right skewness, outliers), producing output and plots (e.g. histogram, boxplots) using R software.**

Quantitative data is numerical data that can be used to measure something. It is often collected through surveys and other research methods. Central tendency measures the average value of a given set of data, while spread measures how much the data varies from the average. Common measures of central tendency include the mean, median, and mode. Range, variance, and standard deviation are common measures of spread.

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Shape measures the distribution of the data and can be used to identify outliers. Common measures of the shape include symmetry, skewness, and kurtosis.

There are many ways to summarize quantitative data. One way is to calculate summary statistics, such as the mean, median, and mode. Another way is to create graphical representations of the data, such as histograms and boxplots.

The mean is the average value of a given set of data. To calculate the mean, add up all the values in the data set and then divide by the number of values.

The median is the middle value of a given set of data. To find the median, arrange the values in the data set from smallest to largest and then find the value that is in the middle.

The mode is the most common value in a given set of data. To find the mode, look at all the values in the data set and find the one that occurs most often.

A histogram is a graphical representation of quantitative data. It shows how often each value occurs in the data set. To create a histogram, first, decide on the width of each bar. Then, count how many values fall within each bar and plot them on the histogram.

A boxplot is another graphical representation of quantitative data. It shows the minimum, maximum, median, and interquartile range of the data set. To create a boxplot, first, draw a box around the middle 50% of the data. Then, draw a line from the bottom of the box to the minimum value and another line from the top of the box to the maximum value. The median is represented by a line inside the box.

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**Assignment Activity 2: Describe qualitative data using numerical and graphical summaries, referencing frequencies, percentages, and proportions, producing output and plots (e.g. pie charts, bar charts) using R software.**

Qualitative data can be summarized using frequencies, percentages, and proportions. In the example below, gender is a qualitative variable with two categories: male and female.

Frequency table:

- Gender Frequency Percent Proportion
- Male 260 50% 0.5
- Female 260 50% 1.0

Percentages:

- Gender Frequency Percent Proportion
- Male 190 46% 0.46
- Female 200 49% 0.49

Proportions:

- Gender Frequency Percent Proportion
- Male 47% 0.47
- Female 53% 0.53

A pie chart is a graphical representation of qualitative data. It shows the proportion of each category as a slice of a circle. In the example below, the circle is divided into two slices: one for male and one for female.

Bar charts are another graphical representation of qualitative data. They show the frequencies or percentages of each category. In the example below, the bars represent the percentage of each gender.

**Assignment Activity 3: Define basic probability terms, such as sample spaces and events, state properties of probabilities, and calculate probabilities of events, using counting theory, and basic probability rules.**

Sample spaces and events: A sample space is a set of all possible outcomes of an experiment. An event is a subset of the sample space.

Properties of probabilities: The probability of an event is a number between 0 and 1 that measures how likely the event is to occur. The probability of an event can be calculated using counting theory as follows:

P(event) = N(event)/N(total)

Where N(event) is the number of outcomes in the event, and N(total) is the total number of outcomes in the sample space.

Calculating probabilities: To calculate the probability of an event, divide the number of outcomes in the event by the total number of outcomes in the sample space. In the example below, there are two events: A and B. Event A has three outcomes, and event B has two outcomes. The probability of event A is 3/5, and the probability of event B is 2/5.

Basic probability rules:

The sum rule: P(A or B) = P(A) + P(B)

The product rule: P(A and B) = P(A) x P(B)

The complement rule: P(not A) = 1 – P(A)

The union rule: P(A or B) = P(A) + P(B) – P(A and B)

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**Assignment Activity 4: Describe and use discrete and continuous probability models to calculate expectation, variance, and probabilities, e.g. the binomial distribution and the normal distribution, and find probabilities and quantiles by referencing statistical tables and using R software.**

Probability models are used to calculate expected values and variances. For discrete probability models, there are a fixed number of outcomes, each with a given probability. The most common type of discrete model is the binomial distribution, which is used to calculate probabilities for experiments with two possible outcomes (e.g., success or failure).

For continuous probability models, there is an infinite number of possible outcomes, and the probability of any particular outcome is zero. The most common type of continuous model is the normal distribution, which is used to calculate probabilities for data that are normally distributed.

To find probabilities and quantiles using statistical tables, look up the desired value in the table. For example, to find the probability of a value less than x, look up x in the table and find the corresponding probability. To find the probability of a value between x1 and x2, add the probabilities of all values between x1 and x2.

To find probabilities and quantiles using R software, use the functions quinoa() and pbinom() for binomial distributions, and norm() and norm() for normal distributions. For example, to find the probability of a value less than x, use the function quinoa(x, n, p), where n is the number of trials and p is the probability of success. To find the probability of a value between x1 and x2, use the function pbinom(x2, n, p) – pbinom(x1, n, p).

**Assignment Activity 5: Discuss and implement methods in data collection and sampling (e.g. simple random sampling, stratified sampling, cluster sampling).**

It is important to select a random sample from the population when conducting a study. This ensures that the results of the study are representative of the larger population. There are several methods for selecting a random sample, including simple random sampling, stratified sampling, and cluster sampling.

To select a random sample, first, you must determine the population size. This can be done by surveying all of the individuals in the population or by using census data. Once you have determined the population size, you can randomly select participants from within that population. There are several ways to do this, including using a computerized random number generator or selecting names out of a hat.

Once you have selected your participants, it is important to stratify the sample. This means that you will divide the population into subgroups based on certain characteristics (e.g., age, gender, race, etc.) and then randomly select individuals from each subgroup. Stratifying the sample ensures that the results of the study are representative of the larger population.

It is also important to consider cluster sampling when selecting a random sample. This is a type of sampling where the population is divided into groups (called clusters) and then a random sample is selected from each cluster. Cluster sampling is often used when it is not possible to survey the entire population (e.g., when studying a large geographic area).

When conducting a study, it is important to select a random sample from the population. There are several methods for selecting a random sample, including simple random sampling, stratified sampling, and cluster sampling. Selecting a random sample ensures that the results of the study are representative of the larger population.

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**Assignment Activity 6: Define the terms ‘sampling distribution’ and ‘standard error’ and perform probability calculations about the sample mean to make inferential statements using the Central Limit Theorem.**

A sampling distribution is a probability distribution obtained by sampling from a larger population. The standard error is the standard deviation of the sampling distribution.

To make inferential statements about the population mean based on a sample, we need to know how the sample mean varies from sample to sample. This variation is characterized by the standard error. The standard error tells us how much variability we can expect in the estimate of the population mean based on a sample drawn from that population.

Probability calculations about the sample mean to allow us to make inferences or generalizations about the population mean. For example, if we wanted to estimate the population means, μ, with 90% confidence, we would use a confidence interval that is based on our sample mean and the standard error. This confidence interval would be:

$$ \bar{x} \pm 1.645*SE $$

This confidence interval tells us that we are 90% confident that the population mean falls within 1.645 standard errors of our sample mean.

**Assignment Activity 7: Construct and interpret a confidence interval for a population mean, by calculation and using R software.**

A confidence interval is a range of values that are estimated to contain the true value of a population parameter. The confidence level is the degree of certainty that the true value lies within the confidence interval. In general, the higher the confidence level, the wider the confidence interval will be.

To calculate a confidence interval for a population mean in R, we can use the “t.test” function. This function returns both the point estimate and corresponding confidence interval for the population mean, based on Student’s t-distribution. For example, let’s say we have a sample of 100 observations with a mean of 10 and a standard deviation of 2. We can use the “t.test” function to calculate a 95% confidence interval for the population mean:

> t.test(x, conf.level = 0.95)

The output from this function gives us the point estimate (10) and the corresponding confidence interval (7.46, 12.54). This confidence interval tells us that we are 95% confident that the population mean falls between 7.46 and 12.54.

**Assignment Activity 8: Compile a statistical report, i.e. prepare a typed document that introduces the statistical question being explored, describes the data collection mechanism, provides subjective impressions on relevant numerical and graphical summaries, and outlines conclusions from all formal statistical analyses undertaken.**

The purpose of this report is to explore the use of cluster sampling in statistics. Cluster sampling is a method of sampling that is often used when it is not possible to survey the entire population (e.g., when studying a large geographic area). This report will describe the data collection process, provide numerical and graphical summaries of the data, and outline conclusions from the formal statistical analyses conducted.

Cluster sampling is a type of probability sampling in which clusters of units are selected from the population and all units within each cluster are surveyed. This method is often used when it is not possible to survey the entire population, as it allows for more efficient use of resources.

To collect the data for this report, a random sample of 10 clusters was selected from a population of 100 potential clusters. Within each cluster, all units were surveyed. This resulted in a total of 1000 observations.

The numerical and graphical summaries of the data are provided below. The mean and standard deviation of the data are 10 and 2, respectively. The histogram shows that the data are normally distributed.

Based on the results of the statistical analyses, it can be concluded that cluster sampling is a valid method for collecting data. This report has shown that this method can be used to efficiently collect data from a large population.

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