{"id":2456,"date":"2024-07-01T12:06:55","date_gmt":"2024-07-01T16:06:55","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/?post_type=chapter&p=2456"},"modified":"2024-07-01T14:37:21","modified_gmt":"2024-07-01T18:37:21","slug":"means-vs-proportions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/1130sandbox\/chapter\/means-vs-proportions\/","title":{"raw":"Means vs Proportions","rendered":"Means vs Proportions"},"content":{"raw":"
\r\n

Learning Objectives<\/p>\r\n\r\n<\/header>\r\n

\r\n\r\nIn this section, we will introduce the concept of estimating population proportions and understand how these different from population means.\r\n\r\n<\/div>\r\n<\/div>\r\n

Two Population Parameters to Estimate<\/h2>\r\nln this chapter, there are two population parameters that we will be investigating using sampling. They are:\r\n
    \r\n \t
  1. The true mean (or average) of a population, also symbolically known as [latex]\\mu[\/latex], and<\/li>\r\n \t
  2. The true proportion of a population, also symbolically represented by [latex]p[\/latex].<\/li>\r\n<\/ol>\r\nIn the first five sections, we estimated the true mean of a population when [latex]\\sigma[\/latex] was known and unknown. The remaining sections in this chapter refer to estimating the true proportion of a population ([latex]p[\/latex]).\r\n

    The Difference Between a Population Mean and Proportion<\/h2>\r\nThe difference between a population mean and population proportion is quite simple. We are calculating a true mean, \u00b5, when d<\/span>ealing with a measured variable, i<\/span>.e., something that can be physically measured to a desired degree of precision. Variables of this type are called quantitative variables<\/a>.<\/span>\r\n\r\nWe are trying to understand the true percentage, [latex]p[\/latex], when trying to measure a fraction of population or\u00a0true proportion of a population. Variables or columns in the data where we record which trait, or category, a person or item belongs to, are called categorical variables<\/a>.\r\n

    Mean or Proportion? (Exercise #1)<\/h1>\r\nSelect which type each measurement is from the list below. Is it an example of quantitative (mean) data or categorical (proportion) data?<\/span>\r\n
    \r\n
    [h5p id=\"177\"]<\/div>\r\n<\/div>\r\n
    \r\n

    Click here to review the solutions to the above exercise<\/h1>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Quantitative Variable (mean or \u03bc)<\/th>\r\nCategorical Variable (proportion or [latex]p[\/latex])<\/th>\r\n<\/tr>\r\n
    Amount of rainfall in Vancouver (in mms<\/a>)<\/td>\r\nPercent of rainy days per annum in Vancouver<\/td>\r\n<\/tr>\r\n
    Number of defective items in inventory<\/td>\r\nPercent of defective parts in inventory<\/td>\r\n<\/tr>\r\n
    Number of late deliveries per month<\/td>\r\nPercent of late deliveries per month<\/td>\r\n<\/tr>\r\n
    Number of absent employees per day<\/td>\r\nPercent of absent employees per day<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nThe table above provides the obvious distinction between the two forms of problems you will encounter: estimating a true mean of a population versus estimating a true proportion of population.\r\n\r\n<\/div>\r\n

    Mean or Proportion? (Exercise #2)<\/h1>\r\nIn the exercise below, move the metric to the correct side - categorical or quantitative. All of the statistics reported in the exercise above are reported by Hostinger Tutorials in the following article<\/a>.\r\n
    \r\n
    [h5p id=\"176\"]<\/div>\r\n<\/div>\r\n
    \r\n

    Click here to review the solutions to the above exercise<\/h1>\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
    Categorical Variable (proportion or [latex]p[\/latex])<\/th>\r\nQuantitative Variable (mean or \u03bc)<\/th>\r\n<\/tr>\r\n
    More than 50% of company's marketing budgets go to paid media and new technologies<\/td>\r\nGlobal Digital Advertising Market is Expected to Reach $740 Billion in 2024<\/td>\r\n<\/tr>\r\n
    Around 84% of B2B marketers create brand awareness through content marketing<\/td>\r\nUses spend 6 hours and 48 minutes, on average, watching online videos each week<\/td>\r\n<\/tr>\r\n
    On average, the first result on Google generates 39.8% of all clicks<\/td>\r\nThe global market size of television advertising was worth $235 billion in 2023<\/td>\r\n<\/tr>\r\n
    With featured snippets, the click-through rate increases to 42.9%<\/td>\r\nIn 2023, the market value of digital marketing reach $366 billion<\/td>\r\n<\/tr>\r\n
    Nearly half of millenials believe influencer recommendations more than regular ads when buying a product<\/td>\r\nOn average, companies invest $34.50 per internet user to create and promote video ads<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nAll of the statistics reported in the exercise above are reported by Hostinger Tutorials in the following article<\/a>.\r\n\r\n<\/div>","rendered":"
    \n
    \n

    Learning Objectives<\/p>\n<\/header>\n

    \n

    In this section, we will introduce the concept of estimating population proportions and understand how these different from population means.<\/p>\n<\/div>\n<\/div>\n

    Two Population Parameters to Estimate<\/h2>\n

    ln this chapter, there are two population parameters that we will be investigating using sampling. They are:<\/p>\n

      \n
    1. The true mean (or average) of a population, also symbolically known as [latex]\\mu[\/latex], and<\/li>\n
    2. The true proportion of a population, also symbolically represented by [latex]p[\/latex].<\/li>\n<\/ol>\n

      In the first five sections, we estimated the true mean of a population when [latex]\\sigma[\/latex] was known and unknown. The remaining sections in this chapter refer to estimating the true proportion of a population ([latex]p[\/latex]).<\/p>\n

      The Difference Between a Population Mean and Proportion<\/h2>\n

      The difference between a population mean and population proportion is quite simple. We are calculating a true mean, \u00b5, when d<\/span>ealing with a measured variable, i<\/span>.e., something that can be physically measured to a desired degree of precision. Variables of this type are called quantitative variables<\/a>.<\/span><\/p>\n

      We are trying to understand the true percentage, [latex]p[\/latex], when trying to measure a fraction of population or\u00a0true proportion of a population. Variables or columns in the data where we record which trait, or category, a person or item belongs to, are called categorical variables<\/a>.<\/p>\n

      Mean or Proportion? (Exercise #1)<\/h1>\n

      Select which type each measurement is from the list below. Is it an example of quantitative (mean) data or categorical (proportion) data?<\/span><\/p>\n

      \n
      \n
      \n