Data analysis notes - idk what it is PDF

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Displaying and 1A classifying data

 Data and Variables In a data set, we call the qualities or quantities about which we record information variables  Categorical variables Represent characteristic or qualities of people or things (eye colour fitness levels) - Nominal variables Have data values that can be used to group individuals according to particular characteristic (sex) - Ordinal variables Have data values that can be used both groups and other individuals according to a particular characteristic (fitness level)  Numerical variables Are used to represent quantities, things that we count or measure - Discrete variables Represent quantities that are counted (number of car) - Continuous variables Represent quantities that are measured rather than counted (length, weight)  Comparing numerical and categorical variables

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1B Displaying and describing the distribution of categorical variables  The frequency tables A frequency table is a listing of values a variable taken in a dataset, along with how often (frequently) each value occurs. Frequency can be recorded as a: - Number; the of times a value occurs, or - Percentage; the percentage of time a value occurs (percentage frequency) Percent = count/total count x 100%

Solution: Percentage = group/category x 100 = % total

6 ×100 =54.5 11

5 ×100 =45.5 11

CAS = ctrl + enter to get 0.0 instead of

0  How has forming a frequency table helped?  The process of forming a frequency table for a categorical variable: - displays the data in a compact form - tells us something about the way the data values are distributed (the pattern of the data). Solution:

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1B Displaying and describing the distribution of categorical variables  Stacked or segmented bar charts In a segmented bar chart, the bars are stacked one on top of another to give a single bar with several parts or segments. The lengths of the segments are determined by the frequencies. The height of the bar gives the total frequency Solution:

 The mode The mode is the most frequently occurring value or category.  Some guidelines for writing a report describing the distribution of a categorical variable Briefly summarise the context in which the data were collected including the number of individuals involved in the study. If there is a clear modal category, ensure that it is mentioned. Include frequencies or percentages in the report. Percentages are preferred. If there are a lot of categories, it is not necessary to mention every category, but the modal category should always be mentioned.

solution: The climate types of 23 countries were classified as being, ‘cold’, ‘mild’ or ‘hot’. The majority of the countries, 60.9%, were found to have a mild climate. Of the remaining countries, 26.1% were found to have a hot climate, while 13.0% were found to have a cold climate. 3

1C Displaying and describing the distributions of numerical variables  The grouped frequency distribution

Solution:

 The histogram and its construction The histogram is a graphical display of the information in the grouped frequency table. Solution:

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 Range = largest value- smallest value  Median’s the middle number  What to look for in a histogram - Shape and outliers Symmetric distribution

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skewed distributions

Outliers Is any data values that stand out from the main body of data Centre Centre of a distribution or the median Spread

Solution: A)

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C)  Using a histogram to describe the distribution of a numerical variable in the context of its data

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1D Using a log scale to display data  Properties of logs to the base 10 1 If a number is greater than one, its log to the base 10 is greater than zero. 2 If a number is greater than zero but less than one, its log to the base 10 is negative. 3 If the number is zero, then its log is undefined.

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