C2 Frequency Distribution

• Frequency distribution is an organized tabulation/graphical representation of the number of individuals in each category on the scale of measurement. It allows the researcher to have a glance at the entire data conveniently.
• A frequency table is an arrangement of numbers into classes with their corresponding frequencies
• The class interval or class width (h) refers to the difference between two consecutive limits of any given class, i.e., upper limit minus lower limit.
• The grouped frequency distribution is a type of frequency distribution where the data are arranged according to predetermined intervals called classes. The range of values within these classes is known as the class interval.
• Measures of central tendency - measures used to describe the center of a set of numerical data
• Class mark = midpoint of the class interval
• Measures of central tendency - measures used to describe the center of the data set
• Mode - most frequently occurring score
• Mode - the most frequently occurring score in a dataset
• Median - the middle value when all scores are listed from least to greatest
• Mean - the average of all scores in a dataset
• Mode - most frequently occurring number in a set of data
• Median - middlemost number in a set of data
• Mean - average of all the numbers in a set of data
• Mode - most frequently occurring number in a set of numbers
• Mean - average of all the observations in a set of numbers
• Median - middle number when the numbers are listed from smallest to largest or vice versa
• Range - difference between highest and lowest scores
• A relative frequency distribution lists the data values along with the percent of all observations belonging to each group. These relative frequencies are calculated by dividing the frequencies for each group by the total number of observations.
• The absolute frequency (f) for each class interval in a frequency distribution can easily be translated to a relative frequency by converting the absolute frequency to a proportion or percentage of the total number of cases. This results in a relative frequency distribution.
• Exact limits also are referred to as the real or true limits of a class interval.
• Class width is the length of one class interval, which is equal to the upper limit minus the lower limit of that interval.
• Midpoint is the exact center point of an interval. It is determined by adding the lower and upper limits together and then dividing their sum by 2.
• the real limit in statistics and psychology, is the lower or upper value for a continuous variable measured on a ratio scale. For example, a test score of 95 has the lower real limit of 94.5 and the upper real limit of 95.4 since any value within that range will equal 95 when rounded to a whole number.
• In statistics, the term "class" refers to a specific category into which individual scores fall based upon some characteristic being studied. The word “interval” is used instead of “class.”
• cumulative percentage frequency distribution shows the percentage of cases that falls below the upper exact limit of each class interval.
• A percentile rank reflects the percentage of cases falling below a given score point.
• The median divides the data set into two halves such that half of the values are above it and half are below it.
• Mode is the most frequently occurring score in a group of numbers.
• Pₙ = percentile rank
• quartiles refers to specific score points
• Q₁ - first quartile (lower middle)
• Q₂ - second quartile (median or midpoint)
• Q₃ - third quartile (upper middle)
• Outliers are scores that fall outside the normal distribution, which can be identified by using box plots.
• Percentile Rank Caveats (2/3):

  
  

  First, do not confuse percentile ranks, which reflect relative performance, with “percentage correct,” which reflects absolute performance.

  
  

  Second, percentile ranks always are based on a specific group and, therefore, must be interpreted with that group in mind.
• Cumulative frequency is used to determine the number of observations that lie above (or below) a particular value in a data set. The cumulative frequency is calculated using a frequency distribution table, which can be constructed from stem and leaf plots or directly from the data.