Frequency Distributions Flashcards
array?
An array is an arrangement of raw numerical data in ascending or descending order of magnitude.
range?
The difference between the largest and smallest numbers is called the range of the data.
frequency distribution or frequency table
A tabular arrangement of data by classes together with the corresponding class frequencies is called a frequency distribution, or frequency table.
class interval & class limits
A symbol defining a class, such as 60-62, is called a class interval.
The end numbers, 60 and 62, are called class limits; the smaller number (60) is the lower class limit, and the larger number (62) is the upper class limit.** **
class boundaries or true class limits?
lower class boundary?
upper class boundary?
If heights are recorded to the nearest inch, the class interval 60-62 theoretically includes all measurements from 59.5000 to 62.5000 in. These numbers, indicated briefly by the exact numbers 59.5 and 62.5, are called class boundaries, or true class limits; the smaller number (59.5) is the lower class boundary, and the larger number (62.5) is the **upper class boundary. **
How to calculate the class boundaries?
The class boundaries are obtained by adding the upper limit of one class interval to the lower limit of the next-higher class interval and dividing by 2.
*Note: Class boundaries should not coincide with actual observations. *
How to calculate the size, or width, of a class interval?
The size or width of a class interval is the difference between the lower and upper class boundaries and is referred to as the class width, class size, or class length.
class mark?
The class mark is the midpoint of the class interval and is obtained by adding the lower and upper class limits and dividing by 2.
Thus the class mark of the interval 60-62 is (60 + 62) / 2 = 61.
The class mark is also called the class midpoint.
General Rules for Forming Frequency Distributions:
1)
2)
3)
General Rules for Forming Frequency Distributions:
1) Determine the largest and smallest numbers in the raw data and thus find the range (the difference between the largest and smallest numbers).
2) Divide the range into a convenient number of class intervals having the same size. If this is not feasible, use class intervals of different sizes or open class intervals. The number of class intervals is usually between 5 and 20, depending on the data. This tends to lessen the so-called grouping error involved in further mathematical analysis. However, the class boundaries should not coincide with the actually observed data.
3. Determine the number of observations falling into each class interval; that is, find the class frequencies. This is best done by using a tally, or score sheet.
A histogram or frequency histogram, consists of a set of rectangles having
a) bases…..
b) areas……
A histogram or frequency histogram, consists of a set of rectangles having
a) bases on a horizontal axis (the X axis), with centres at the class marks and lengths equal to the class interval sizes, and
b) areas proportional to the class frequencies.
frequency polygon?
A frequency polygon is a line graph of the class frequencies plotted against class marks.
It can be obtained by connecting the midpoints of the tops of the rectangles in the histogram.
The relative frequency of a class is the ….?
*The relative frequency of a class is the frequency of the class divided by the total frequency of all classes and is generally expressed as a percentage. *
For example, the relative frequency of the class 66-68 in Table 2.1 is 42/100 = 42%. The sum of the relative frequencies of all classes is clearly 1, or 100%.
cumulative frequency?
The total frequency of all values less than the upper class boundary of a given class interval is called the cumulative frequency up to and including that class interval.
For example, the cumulative frequency up to and including the class interval 66-68 in Table 2.1 is 5+18+42=65, signifying that 65 students have heights less than 68.5 in.
cumulative-frequency polygon or ogive?
A graph showing the cumulative frequency less than any upper class boundary plotted against the upper class boundary is called a cumulative-frequency polygon or **ogive. **
Find examples: pages 52-56
relative cumulative frequency, or percentage cumulative frequency?
*The relative cumulative frequency, or percentage cumulative frequency, is the cumulative frequency divided by the total frequency. *
For example, the relative cumulative frequency of heights less than 68.5 in is 65/100 = 65%, signifying that 65% of the students have heights less than 68.5 in.
Find Examples: pages 52-56
Symmetrical or bell-shaped curves?
Symmetrical or bell-shaped curves are characterized by the fact that observations equidistant from the central maximum have the same frequency.
Adult male and adult female heights have bell-shaped distributions.
Examples: p.57
Skewed to the left?
Curves that have tails to the left are said to be skewed to the left.
The lifetimes of males and females are skewed to the left. A few die early in life but most live between 60 and 80 years.
Example: p. 57
Skewed to the right?
Curves that have tails to the right are said to be skewed to the right.
The ages at the time of marriage of brides and grooms are skewed to the right. Most marry in their twenties and thirties but a few marry in their forties, fifties, sixties and seventies.
Example: p.57
uniformly distributed (type of frequency curve) ?
*Curves that have approximately equal frequencies across their values are said to be uniformly distributed. *
Certain machines that dispense liquid colas do so uniformly between 15.9-16.1 ounces, for example.
Example: p.57
J-shaped or reverse J-shaped frequency curve?
*In a J-shaped or reverse J-shaped frequency curve the maximum occurs at one end or the other. *
U-shaped frequency distribution curve?
*A U-shaped frequency distribution curve has maxima at both ends and a minimum in between. *
bimodal frequency curve ?
A bimodal frequency curve has two maxima.
multimodal frequency curve ?
*A multimodal frequency curve has more than two maxima. *
