Introduction to Statistics

Statistics is a branch of mathematics that has applications in almost every facet of our daily life. Statistical methods provide powerful tools to collect, analyze, summarize, and interpret data to reach informed decisions.

Descriptive statistics is the science of summarizing and describing the important characteristics of a set of data.

Inferential statistics is the science of using information obtained from a sample to infer about the characteristics of a population of interest.

<p>A population is a set of the entire collection of units (individuals, objects).</p> Signup and view all the answers

<p>A sample is a subset of the population selected in some prescribed manner.</p> Signup and view all the answers

<p>A variable is a characteristic that changes or varies over time and/or for different individuals or objects under consideration.</p> Signup and view all the answers

<p>An experimental unit is the individual or object on which a variable is measured.</p> Signup and view all the answers

<p>A single measurement or data value is obtained when a variable is actually measured on an experimental unit.</p> Signup and view all the answers

<p>Univariate data (B)</p> Signup and view all the answers

<p>Bivariate data (C)</p> Signup and view all the answers

<p>Multivariate data (B)</p> Signup and view all the answers

<p>Qualitative variable (A)</p> Signup and view all the answers

<p>Political affiliation: Liberals, Conservatives, NDP, Green, Independent, The colour of a car, The size of T-shirts: XS, S, M, L, XL, Racers classified as coming in 1st, 2nd, 3rd, etc.</p> Signup and view all the answers

<p>Quantitative variable (A)</p> Signup and view all the answers

<p>Continuous and Discrete (A)</p> Signup and view all the answers

<p>Discrete variables can assume only a finite or countable number of values; x=0,1,2,3,.....</p> Signup and view all the answers

<p>Continuous variables can assume the infinitely many values corresponding to the points on a line interval; 0&lt;x&lt;5.</p> Signup and view all the answers

<p>Qualitative (B)</p> Signup and view all the answers

<p>Quantitative (B)</p> Signup and view all the answers

<p>Qualitative (A)</p> Signup and view all the answers

<p>Quantitative (A)</p> Signup and view all the answers

<p>Quantitative (A)</p> Signup and view all the answers

<p>Continuous (A)</p> Signup and view all the answers

<p>Discrete (B)</p> Signup and view all the answers

<p>Continuous (B)</p> Signup and view all the answers

<p>Discrete (B)</p> Signup and view all the answers

<p>Continuous (A)</p> Signup and view all the answers

<p>Bar Chart and Pie Chart (C)</p> Signup and view all the answers

<p>A statistical table is a list of the categories along with a measure of how often each category occurred.</p> Signup and view all the answers

<p>Frequency, Relative Frequency, and Percentage (A)</p> Signup and view all the answers

<p>Frequency refers to the number of measurements in each specified category.</p> Signup and view all the answers

<p>Relative frequency is the proportion of measurements in each specified category.</p> Signup and view all the answers

<p>Percentage is the amount of a given quantity as a fraction of a hundred.</p> Signup and view all the answers

<p>A bar chart shows the distribution of measurements in categories, with the height of the bar measuring how often a particular category was observed..</p> Signup and view all the answers

<p>The bar chart would show each rating category on the x-axis and the frequency (number of administrators) on the y-axis, with each bar height representing the corresponding frequency. For example, a bar for 'A' would reach to the height of 35 on the y-axis. The pie chart would divide a circle into four sections, each representing a rating. The size of each section would be proportional to the frequency of that rating. For example, the section for 'B' would be much larger than the section for 'D' because 'B' has a much higher frequency.</p> Signup and view all the answers

<p>The bar chart would have six bars representing the colors: brown, green, red, yellow, orange, and blue. The height of each bar would represent the number of times each color appears in the data. For example, the bar for &quot;Brown&quot; would be the tallest, reaching to a height of 6 (since &quot;Brown&quot; appears 6 times in the data).</p> Signup and view all the answers

<p>Pie charts and bar charts are used for quantitative data that are measured on different segments of the population, or different categories of classification.</p> Signup and view all the answers

<p>An example would be the average income for people of different age groups, different genders, or living in different geographic areas of the country.</p> Signup and view all the answers

<p>The bar chart would have bars representing each category on the x-axis and the amount (in billions of dollars) on the y-axis. The height of each bar would correspond to the amount allocated to that category. The pie chart would divide a circle into sections representing each category, with the size of each section proportional to the amount allocated to that category. For example, the section for &quot;Land forces&quot; would be the largest, as it has the highest amount allocated.</p> Signup and view all the answers

<p>Line charts are used when a quantitative variable is measured over time at equally spaced intervals (daily, weekly, monthly, quarterly, or yearly).</p> Signup and view all the answers

<p>Time series are data that are measured over time at equally spaced intervals.</p> Signup and view all the answers

<p>The line chart would have the year on the x-axis and the population (in thousands) on the y-axis. Each year would have a corresponding point representing the population for that year, and the points would be connected by a line. This line would demonstrate the trend in population projections over time for age group 65-69.</p> Signup and view all the answers

<p>Dotplots are used for small data sets which cannot easily be separated into categories or intervals of time.</p> Signup and view all the answers

<p>For large data sets, dotplots can be difficult to interpret because of potential overcrowding and an excessive number of dots, making it hard to discern patterns.</p> Signup and view all the answers

<p>The dotplot would have a number line from 2 to 9. There would be a dot above the number 2, two dots above the number 6, one dot above the number 3, one dot above the number 9, and one dot above the number 7, visually representing the frequency of each data value.</p> Signup and view all the answers

<p>Order the data from smallest to largest, Divide each observation/measurement into a stem (all digits of the observation except the least significant digit) and a leaf (the least significant digit of the observation), List the stems in a column, with a vertical line to their right, Put the leaf portion for each observation in the same row as its corresponding stem, and State your leaf unit.</p> Signup and view all the answers

<p>The stem-and-leaf plot for the data presented has stems representing the whole parts of the completion times (1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2), and leaves indicating the decimal parts of the completion times. For example, the first entry, 1.89, would have a stem of 1 and a leaf of 8. So, the plot would arrange the data like this: 1 | 3 4 5 5 5 5 6 7 8 9 9 9 9 9 2 | 0 0 0 0 0 0 0 0 0</p> Signup and view all the answers

<p>If a stem-and-leaf plot has too few stems and too many leaves, the data may be difficult to visualize and interpret. This is because the plot may become too crowded or spread out, making it hard to analyze the distribution of the data.</p> Signup and view all the answers

<p>Stems can be divided in one of two ways: into two lines, with leaves 0-4 and 5-9, or into five lines, with leaves 0-1, 2-3, 4-5, 6-7, 8-9.</p> Signup and view all the answers

<p>These two stem-and-leaf plots are constructed for the same data set because the stems are divided differently in each plot to address the issue of having too few stems and too many leaves. The first plot has stems divided into three lines, while the second plot has stems divided into five lines. This different division of stems results in different representations of the data.</p> Signup and view all the answers

<p>A histogram is a graphical representation of the distribution of quantitative data, where the data is grouped into categories or classes, and the height of each bar represents the frequency or relative frequency of values in that class.</p> Signup and view all the answers

<p>Classes in a histogram should be mutually exclusive, meaning no data point belongs to more than one class, and they should be exhaustive, meaning all data points belong to one of the classes.</p> Signup and view all the answers

<p>As a rule of thumb, the number of classes in a histogram should range between 5 and 12, but the optimal number may vary depending on the specific data and the size of the dataset.</p> Signup and view all the answers

<p>To construct a histogram with frequencies, group the GPA data into classes of equal size (e.g., 9.5-10.0, 10.0-10.5, 10.5-11.0, 11.0-11.5), count the number of GPAs within each class, and represent those counts as bars on the histogram. For relative frequencies, calculate the frequency of each class as a proportion of the total number of students. For example, the class 10.5-11.0 would have a frequency of 12 and a relative frequency of 12/30.</p> Signup and view all the answers

<p>The height of each bar in a histogram represents the frequency or the relative frequency of values falling into that particular class.</p> Signup and view all the answers

<p>When adjacent bars in a histogram share sides, it means that the leftmost value of each bar is included in that class, indicating that there is no gap between the categories.</p> Signup and view all the answers

<p>Outliers are individual values that fall outside the overall pattern of the data. These are unusually large or small data values.</p> Signup and view all the answers

<p>The three key aspects of a graph's overall pattern are its shape, centre, and spread.</p> Signup and view all the answers

<p>A distribution is symmetric if the right and left sides of the distribution form mirror images.</p> Signup and view all the answers

<p>A distribution is skewed to the right if a greater proportion of the measurements lie to the right of the distribution peak, while a distribution is skewed to the left if a greater proportion of the measurements lie to the left of the distribution peak.</p> Signup and view all the answers

<p>A distribution is unimodal if it has one peak.</p> Signup and view all the answers