Textbook Notes (362,755)
York University (12,350)
MATH 1131 (2)
Cindy Fu (1)
Chapter 2

# Chapter 2- Statistics 1131.docx

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School
York University
Department
Mathematics and Statistics
Course
MATH 1131
Professor
Cindy Fu
Semester
Fall

Description
Chapter 2 2.1  Definitions 1: -Univariate: a data set consisting of observation of only a single characteristic of the individuals/ objects. -Bivariate: a data set consisting of observations of two characteristics of the individuals/objects. -Multivariate: data set consisting of observations of more than two characteristics of the individuals/objects.  Definitions 2: -A categorical/qualitative data set: consists of non-numerical observations that may be placed in categories. -A numerical/quantitative data set: consist of observations that are numbers. Examples: 1-Sneaker preference A sample of 12 people is asked what their favorite brand of sneakers is. This is a qualitative data set, since the responses are either Nike, Adidas ...etc. It is non-numerical univariate study. 2-Egg Weights Suppose a new enzyme is tested and 20 eggs are randomly selected and weighted, to test the nutritional benefits of the enzyme. Then the resulting weights are recorded in a table. Since the observations are numerical then this is a univariate quantitative data set. Definitions 3: -Discrete data: is data that values are finite. It is recognized with the word counting. Ex: The number of lightning that hits Ontario in one day can be 5 but not 5.5, and you can count it. -Continuous data: is data that its values fall on an interval. It is recognized with the word measuring. Ex: Barometric pressure can be any value between 960 and 1070 mmHg. It can be 970.67. Categorical data Univariate data Discrete data Numerical data Continuous data Questions: classify the following as categorical or numerical. If numerical, then classify as discrete or continuous. 1-The number of books read by middle-school students during the academic year. You are counting the number of books. Number=numerical, and counting=discrete. 2-The length of time (in minutes) it takes to get a haircut. Time is numerical, but it is measured since you can take 15.4 minutes. Therefore, it is continuous. 3-The type of candy received at house on Halloween. Type= quality= categorical. Therefore, this is a categorical data set. 2.2 Definitions: -Frequency distribution for categorical data: is a summary table that presents categories, counts, and proportions. Refer to table 2.1, on page 22 on textbook. -Class: the label of each categorical data set. -Frequency: is the count for each glass. -Relative frequency/sample proportion: is the frequency of the class divide by the total number of observations. Examples: Class Frequency Relative frequency Bahamas 2 2/25=0.08 Bermuda 4 4/25=.16 Caribbean 6 6/25=.24 Mediterranean 3 3/25=.12 Southampton 10 10/25=.4 Total 25 1.00 1-What is the proportion of cruise ships that did not go to Southampton? .4 went to Southampton, so 1-0.4=0.6 did not go to Southampton. 2- Draw a bar graph for the above table. 12 10 8 Series 3 6 Column1 Frequency 4 2 0 Bahamas Bermuda Caribbean Mediterranean Southampton The key here is that the class is at the x-axis, and the frequency is at the y-axis. 3- Draw a Pie chart. Sales Bahamas Bermuda Caribbean Mediterrean Southampton You take the frequency of a class and multiply it by 360 to get the angle/size of a class. Each piece of the pie is a class. 2.3 Definitions: -Outliers: values that are very far from the rest. -Variability: refers to the spread or compactness (crowdedness together, little variability) of the data.  A stem-and leaf plot is a graphical procedure used to describe the shape, centre, and variability of the distribution of numerical data.  How to draw a stem-leaf graph. 520 52 0 Leaf 46 6 Stem 47 48 49 8 7 3 8 7 - 0 is placed in the 52 stem row. 50 2 8 2 6 4 1 5 1 - Data is organized so one digit 51 5 3 1 3 2 is on the right, and the rest is 52 0 2 5 3 7 3 on the left, but up to 2 digits 53 3 on left. If for example, you 54 0 8 8 4 have 502 and 503, then the 2 55 7 6 7 and the 3 are in the same stem 56 7 4 row. 57 0 0 2 0 4 - Notice that the 2 digit 58 9 5 numbers are organized in 59 8 7 6 increasing order. 60 1 9 4 4 - The centre of data=typical 61 2 value=value in the middle=where the data is clustered is 52 or 53 here. - The outlying value here is 466 since it is far from the data cluster. - Data can be referred to as variable (spread) or outlier. Real World Analogy: -In
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