Lesson 3

• Data presentation such as textual, tabular and graphical is essential to easily comprehend information that a researcher wants to input, however, these are nor enough for a comprehensive discussion of the data. To completely describe the data, numerical measures are necessary to give information on the specific characteristics of the data distribution
• Frequency distributions provide useful behaviour of the data. However, they do not provide with measures, which could quantitatively summarize the characteristics of the population. Hence, we further need to come up with other measurable characteristics of the data to describe the population
• Quantities that describe statistical data are numerical descriptive measures. They are quantities computed from a given set of observations and are used to derive information from data collected by the researcher. There are several descriptive measures. The most commonly used are the measures of location, dispersion, skewness, and kurtosis.
• Measures of Central Location

  • Minimum
  • Maximum
• Measures of Central Location

  It is a value within the range of the data, which describes its location or position relative to the entire set of data. The three measures of central location are the Mean, Median and Mode
• Minimum


  is the smallest value in the data set.
• Maximum


  is the largest value in the data set.
• Measures of Central Tendency


  describes the "center" of a given set of data. It is a single value about which the observations tend to cluster. The common measures of central tendency are the arithmetic mean or simply mean, median and mode.
• Arithmetic Mean (Mean)


  It is the average of the measurements in a set of data or the sum of a set of measurements divided by the number of measurements in the set.
• The mean is denoted by 𝑡ℎ𝑒 𝑠𝑦𝑚𝑏𝑜𝑙 𝑋̅ “read as x-bar for sample mean and 𝑎𝑛𝑑 𝑡ℎ𝑒 𝑔𝑟𝑒𝑒𝑘 𝑠𝑦𝑚𝑏𝑜𝑙 𝜇 for population mean.
• The mean of the data set 3,2,3,4,5,4,7,6,8. Is

  4.67
• Median


  the middle value of an array, denoted by X ~
• Median


  To compute the median of ungrouped data, the set of observations are arranged in an increasing or decreasing order of magnitude. Then, the point such that half the observations fall above it and half below it is the median. The median is the middle value when the number of observations is odd or the average of the two middle values when the number of observations is even.
• The Arrangement is either increasing or decreasing for ungrouped data
• Mode


  is the observation which occurs most frequently in the data set. From the French word moda which means fashion.
• The median and mode respond only to some changes in the terms, while the mean responds to every change in the terms. It is for this reason that the mean is the most used measure of central tendency because it is the average value of the distribution.
• The Mode


  The class interval with the highest frequency is the modal class.
• Quantiles

  1. Quartile
  2. Decile
  3. Percentile
• Quartiles


  The computation of quantiles is similar to median. Median is divided the dat set in to two
• Quartile


  the data set is divided in to 4
• Decile

  • data set is divided into ten
• Percentile


  –data set is divided into 100
• Measure of central tendency means to describe the given set of data. These measures indicated the point where the items are centrally located. However, they do not show whether the terms in the distribution are far from or close to each other.
• Range


  Is the simplest of the measures of spread or variability? It is the difference between the highest and the lowest score
• Range


  it is the easiest to compute and easiest to understand, it is also least satisfactory since its values is dependent only upon the two extremes and does not consider the scatter of the values in between these two extremes.
• Range


  It is not considered a stable measure of variability because its values can fluctuate greatly with the change in just a single score-either the highest or the lowest
• Mean Absolute Deviation


  to arrive at a more reliable indicator of reliability or spread in the distribution we should consider the value of each individual score and determine the amount by which each varies the mean of the distribution.
• Although it gives a better approximation of the spread of the distribution than the range or the quartile deviation it does not lend itself readily to mathematical treatment for further analysis.
• Standard Deviation


  Is a special form of average deviations from the mean, it is therefore also affected by all the individual values of the items in the distribution
• Coefficient of Variation


  is the ratio of the standard deviation to its mean, expressed in percent. It is relative measure of dispersion useful when comparing dispersion of two or more data sets with different units.