319 - Chapter 1

  • A population is the entire collection of objects or outcomes about which information is sought.

  • A sample is a subset of a population, containing the objects or outcomes that are actually observed.

  • A simple random sample of size n is a sample chosen by a method in which each collection of n population items is equally likely to make up the sample, just as in a lottery.

  • A sample of convenience is a sample that is obtained in some convenient way, and not drawn by a well-defined random method.

  • Tangible populations are populations consisting of physical objects, and are always finite.

  • A simple random sample may consist of values obtained from a process under identical experimental conditions. In this case, the sample comes from a population that consists of all the values that might possibly have been observed. Such a population is called a conceptual population.

  • The items in a sample are said to be independent if knowing the values of some of them does not help to predict the values of the others

  • when sampling from a finite population, the items may be treated as independent so long as the sample contains 5% or less of the population.

  • Sampling with replacement. With this method, the population is exactly the same on every draw, and the sampled items are truly independent.

  • The standard deviation is a quantity that measures the degree of spread in a sample.gives an indication of the variation in the data

  • To compute the median of a sample, order the values from smallest to largest. The sample median is the middle number. If the sample size is an even number, it is customary to take the sample median to be the average of the two middle numbers.

  • If the sample size is denoted by n, and a p% trimmed mean is desired, the number of data points to be trimmed is np∕100. If this is not a whole number, the simplest thing to do when computing by hand is to round it to the nearest whole number and trim that amount

  • Variables that take numerical values are quantitative

  • Variables that take categorical values are qualitative. Each item is classified under a category.

  • A controlled experiment is one in which the experimenter controls the values of the factors

  • An observational study is one where the experimenter simply observes the factors as they are ,without having any control over them

  • A statistic is a number that reveals a characteristic of a sample. Numerical summaries of a sample

  • Numerical summaries of a population are called parameters

  • The sample mean, gives an indication of the centre of data

  • Quartiles divide the data as nearly as possible into quarters

  • The first quartile is the median of the lower half of the data to find the first quartile compute 0.25(n+1)

  • The third quartile is the median of the upper half of the data to find it compute 0.75(n+1)

  • the median is the second quartile

  • The pth percentile of a sample divides the sample so that as nearly as possible, p% of the sample values are less than the pth precentile , and (100-p) % are greater

  • The frequency for a given category is simply the number of sample items that fall into that category

  • The sample proportion or relative frequencies is the frequency divided by the sample size

  • No of classes = sqrt(n)

  • Class frequency = number of sample values in a class interval

  • Relative frequency = Frequency/sample size = proportion of sample values in
    a class interval

  • Density = Relative frequency/class width

  • Class width = (Upper limit of the class(highest rounded up) – Lower limit of the class(smallest rounded down)/sqrt(n)

  • A histogram with only one peak is what we call unimodal.

  • If a histogram has two peaks then we say that it is bimodal. Bimodal histograms often indicate subsamples.

  • Lower outlier boundary = Q1 – 1.5*IQR

  • Upper outlier boundary = Q3 – 1.5*IQR

  • Data for which items consist of pairs of values is called bivariate