Week 6

• Statistics


  The science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions
• Universe


  The set of all entities under study
• Population


  The total or entire group of individuals or observations from which information is desired by a researcher
• Individual


  A person or object that is a member of the population being studied
• Statistic


  A numerical summary of a sample
• Sample


  A subset of the population
• Descriptive statistics


  Consist of organizing and summarizing data. Descriptive statistics describe data through numerical summaries, tables, and graphs.
• Inferential statistics


  Uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result
• Parameter


  A numerical summary of a population
• Process of Statistics


  1. Identify the research objective

  2. Collect the information needed to answer the questions

  3. Organize and summarize the information

  4. Draw conclusion from the information
• If the entire population is studied, then inferential statistics is not necessary, because descriptive statistics will provide all the information that we need regarding the population
• Although ordinal scales indicate that some subjects are higher, or lower than others, they do not indicate how much higher or how much better.
• Interval Level


  This is a measurement level not only classifies and orders the measurements, but it also specifies that the distances between each interval on the scale are equivalent along the scale from low interval to high interval. A value of zero does not mean the absence of the quantity. Arithmetic operations such as addition and subtraction can be performed on values of the variable.
• Ratio Level


  A ratio scale represents the highest, most precise, level of measurement. It has the properties of the interval level of measurement and the ratios of the values of the variable have meaning. A value of zero means the absence of the quantity. Arithmetic operations such as multiplication and division can be performed on the values of the variable.
• Both interval and ratio data involve measurement. Most data analysis techniques that apply to ratio data also apply to interval data. Therefore, in most practical aspects, these types of data (interval and ratio) are grouped under metric data. In some other instances, these type of data are also known as numerical discrete and numerical continuous.
• Ranking of college athletic teams

  • Ordinal
• Employee number


  • Nominal
• Number of vehicles registered

  • Ratio
• Brands of soft drinks

  • Nominal
• Number of car passers along C5 on a given day

  • Ratio
• Zip code


  • Nominal
• Degree of pain


  • Ordinal
• A research objective is presented. For each, identify the (A) population and (B) sample in the study.
• A polling organization contacts 2141 male university graduates who have a white-collar job and asks whether or not they had received a raise at work during the past 4 months.
• Every year the PSA releases the Current Population Report based on a survey of 50,000 households. The goal of this report is to learn the demographic characteristics, such as income, of all households within the Philippines.
• Researchers want to determine whether or not higher folate intake is associated with a lower risk of hypertension (high blood pressure) in women (27 to 44 years of age). To make this determination, they look at 7373 cases of hypertension in these women and find that those who consume at least 1000 micrograms per day of total folate had a decreased risk of hypertension compared with those who consume less than 200.
• Indicate whether the following statements require the use of descriptive or inferential statistics.
• Identify the qualitative and quantitative variables and indicate the highest level of measurement required in each. If quantitative, classify whether discrete or continuous.
• The total population of students is 10,679, and the minimum sample is 2,450
• Schools


  • Antipolo National High School
  • Bagong Nayon National High School
  • Dela Paz National High School
  • Sta. Cruz National High School
  • Tubigan National High School
• Antipolo National High School has a population of 3,360 students
• Bagong Nayon National High School has a population of 2,540 students
• Dela Paz National High School has a population of 2,122 students
• Sta. Cruz National High School has a population of 1,290 students
• Tubigan National High School has a population of 1,367 students
• Computing mean of grouped data


  1. Fill out table with class interval, frequency (f), midpoint (x), and fx

  2. Compute mean as ∑fx/n
• Computing median of grouped data

  1. Fill out table with class interval, frequency (f), lower boundary (LB), and cumulative frequency (cf)

  2. Compute median as LB + ((n/2 - <cf)/f)i
• Computing quartiles, deciles, and percentiles of ungrouped data


  1. Arrange data from lowest to highest

  2. Use formulas: Qk = LB + ((nk/4 - <cf)/f)i, Dk = LB + ((nk/10 - <cf)/f)i, Pk = LB + ((nk/100 - <cf)/f)i
• Computing quartiles, deciles, and percentiles of grouped data


  1. Fill out table with class interval, frequency (f), lower boundary (LB), and cumulative frequency (cf)

  2. Use formulas: Qk = LB + ((nk/4 - <cf)/f)i, Dk = LB + ((nk/10 - <cf)/f)i, Pk = LB + ((nk/100 - <cf)/f)i
• A percentile rank of 74% means that 74% of SAT Mathematics scores are less than or equal to 600 and 26% of the scores are greater.