Chapter 1: Sampling and Data
Chapter 1 Review
Chapter Review from 1.1
The mathematical theory of statistics is easier to learn when you know the language. This module presents important terms that will be used throughout the text.
Chapter Review from 1.2
Data are individual items of information that come from a population or sample. Data may be classified as qualitative, quantitative continuous, or quantitative discrete.
Because it is not practical to measure the entire population in a study, researchers use samples to represent the population. A random sample is a representative group from the population chosen by using a method that gives each individual in the population an equal chance of being included in the sample. Random sampling methods include simple random sampling, stratified sampling, cluster sampling, and systematic sampling. Convenience sampling is a nonrandom method of choosing a sample that often produces biased
data.
Samples that contain different individuals result in different data. This is true even when the samples are well-chosen and representative of the population. When properly selected, larger samples model the population more closely than smaller samples. There are many different potential problems that can affect the reliability of a sample. Statistical data needs to be critically analyzed, not simply accepted.
Chapter Review from 1.3
Some calculations generate numbers that are artificially precise. It is not necessary to report a value to eight decimal places when the measures that generated that value were only accurate to the nearest tenth. Round off your final answer to one more decimal place than was present in the original data. This means that if you have data measured to the nearest tenth of a unit, report the final statistic to the nearest hundredth.
In addition to rounding your answers, you can measure your data using the following four levels of measurement.
- Nominal scale level: data that cannot be ordered nor can it be used in calculations
- Ordinal scale level: data that can be ordered; the differences cannot be measured
- Interval scale level: data with a definite ordering but no starting point; the differences can be measured, but there is no such thing as a ratio.
- Ratio scale level: data with a starting point that can be ordered; the differences have meaning and ratios can be calculated.
When organizing data, it is important to know how many times a value appears. How many statistics students study five hours or more for an exam? What percent of families on our block own two pets? Frequency, relative frequency, and cumulative relative frequency are measures that answer questions like these.
Exercises
What type of measure scale is being used? Nominal, ordinal, interval or ratio.
- High school soccer players classified by their athletic ability: Superior, Average, Above average
- Baking temperatures for various main dishes: 350, 400, 325, 250, 300
- The colors of crayons in a 24-crayon box
- Social s