Cumulative frequencyArchived ContentInformation identified as archived is provided for reference, research or recordkeeping purposes. It is not subject to the Government of Canada Web Standards and has not been altered or updated since it was archived. Please contact us to request a format other than those available. Show
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. The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors. The last value will always be equal to the total for all observations, since all frequencies will already have been added to the previous total. Discrete or continuous variablesVariables in any calculation can be characterized by the value assigned to them. A discrete variable consists of separate, indivisible categories. No values can exist between a variable and its neighbour. For example, if you were to observe a class attendance registered from day-to-day, you may discover that the class has 29 students on one day and 30 students on another. However, it is impossible for student attendance to be between 29 and 30. (There is simply no room to observe any values between these two values, as there is no way of having 29 and a half students.) Not all variables are characterized as discrete. Some variables (such as time, height and weight) are not limited to a fixed set of indivisible categories. These variables are called continuous variables, and they are divisible into an infinite number of possible values. For example, time can be measured in fractional parts of hours, minutes, seconds and milliseconds. So, instead of finishing a race in 11 or 12 minutes, a jockey and his horse can cross the finish line at 11 minutes and 43 seconds. It is essential to know the difference between the two types of variables in order to properly calculate their cumulative frequency. Example 1 – Discrete variablesThe total rock climber count of Lake Louise, Alberta was recorded over a 30-day period. The results are as follows: 31, 49, 19, 62, 24, 45, 23, 51, 55, 60, 40, 35 54, 26, 57, 37, 43, 65, 18, 41, 50, 56, 4, 54, 39, 52, 35, 51, 63, 42.
Answers:
The following information can be gained from either graph or table:
When a continuous variable is used, both calculating the cumulative frequency and plotting the graph require a slightly different approach from that used for a discrete variable. Example 2 – Continuous variablesFor 25 days, the snow depth at Whistler Mountain, B.C. was measured (to the nearest centimetre) and recorded as follows: 242, 228, 217, 209, 253, 239, 266, 242, 251, 240, 223, 219, 246, 260, 258, 225, 234, 230, 249, 245, 254, 243, 235, 231, 257.
Answers:
The following information can be gained from either graph or table:
Other cumulative frequency calculationsAnother calculation that can be obtained using a frequency distribution table is the relative frequency distribution. This method is defined as the percentage of observations falling in each class interval. Relative cumulative frequency can be found by dividing the frequency of each interval by the total number of observations. (For more information, see Frequency distribution in the chapter entitled Organizing data.) A frequency distribution table can also be used to calculate cumulative percentage. This method of frequency distribution gives us the percentage of the cumulative frequency, as opposed to the percentage of just the frequency. What kind of correlation indicates that two sets of scores tend to rise and fall together?A positive correlation is a relationship between two variables that tend to move in the same direction. A positive correlation exists when one variable tends to decrease as the other variable decreases, or one variable tends to increase when the other increases.
What term describes the extent to which performance on a type of measure is related to what?He management ch6. Which measure of validity is based on showing a substantial correlation between an evaluation's test scores and job performance scores?Criterion-related validation requires demonstration of a correlation or other statistical relationship between test performance and job performance. In other words, individuals who score high on the test tend to perform better on the job than those who score low on the test.
Which of the following validity processes correlates employee test scores with their current performance ratings?There are two main types of criterion validity: concurrent validity and predictive validity. Concurrent validity is determined by comparing tests scores of current employees to a measure of their job performance.
|