Chapter 2 Statistics: Frequency Distributions
a grouped frequency distribution is most efficient with about ______ class intervals
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EXAMPLE: A score on a test is x = 43. 60% of the class had scores of 43 or lower. The score of x + 43 has a percentile rank of ________, and the score is called the _________.
60% 60th percentil
what is a frequency distribution
a common procedure for organizing a set of data. Takes a disorganized set of scores and (usually) places them in order from highest to lowest. Provides an organized picture of data.
explain the concept of interpolation
estimating intermediate values on the scale of measurement that are not represented in a frequency distribution table or graph. Such intermediate value is located between two specific numbers listed within the frequency distribution.
how do you calculate percentages (%) for the distribution of scores
find the proportion (%) and then multiply by 100 this looks like p(100) or f/N(100)
explain the interpolation process
first you find the width of the two intervals that bind the intermediate value at hand. You must find the width of the intervals of both scales : the width of the y and x axis intervals. The position corre
scores measurement of an interval or ratio scale can be constructed into a ______ or _____ for a frequency distribution
histogram or polygon
what is the variability
measures the degree to which scores are spread over a wide range or clustered
what is the central tendency
measures where the center of the distribution is located
percentile rank refers to ________ and percentile refers to a _______. They describe the exact position of a value/score in a distribution.
percentage score
percentile is when a score is identified by its ________
percentil rank
Raw scores are more useful when they're in the form of ______
percentiles
a _________________ has its tail pointing to the positive end of the x-axis while a __________ has its tail pointing to the negative end of the x-axis
positively skewed distribution negatively skewed distribution
____ and ____ are commonly incorporated into frequency distributions because they help describe the distribution of scores
proportion and percentage
you can't usually find the absolute frequency of scores for a population, but you can often obtain the _________. This is useful if you don't have exact numbers, and more info on the relationship between categories
relative frequency
what are apparent limits and provide an example
applied by the concept of real limits, this is for establishing the boundaries within class intervals. They form the upper and lower boundaries for the class intervals, and serve as 'apparent limits' despite the real limits IE: class interval of 40 - 49 has a lower apparent limit of 40 and a higher apparent limit of 49, while the lower real limit is 39.5 and the upper real limit is 49.5
when accounting for accumulative frequency, remember that we cannot count it unless it is _________________
at or below the UPPER REAL LIMIT of that interval
how do you calculate cumulative percentage
calculated as: c% = cf/N (100) AKA cumulative frequency divided the number of individuals in the population sample times 100 to get the cumulative percentage
Interpolation assumes that there is a __________ from one interval to the next
constant rate of change
x values for frequency distributions are usually measurement of a _______________ and therefore represent ________________. Therefore, real limits are applied to this concept.
continuous variable intervals on the scale of measurement
what is a histogram
scores listed along the x-axis (which serves as the scale of measurement). The y-axis height at the scores indicate the frequency of that category. there are no gaps between the bars of each category. You can also stack blocks to represent frequencies of scores and to provide info in a more organized and simple way.
what is a bar graph
scores that are typically non-numerical. They are very similar to a histogram, but has spaces between bars. This emphasizes that the scale consists of separate, distinct categories (discrete variable)
instead of drawing a complete frequency distribution graph, researchers often describe a distribution by listing its characteristics, which ALWAYS include at least the _____, _______, and ______
shape, central tendency, and variability
when a continuous variable is measures, the resulting measurements correspond to intervals on the number line rather than ________. With this, each individual score represents an interval bounded by _____________. An example of this is a score of x = 8 seconds is bounded by the lower real limit of __ and the upper real limit of __
single points real limits (a lower real limit and an upper real limit) LRL = 7.5 secs URL = 8.5 secs
nearly all smooth curve frequency distributions can be described as ______, _______, or _______
symmetrical, right-skewed, or left-skewed
a frequency distribution can be represented by a ______ and/or a ______, but regardless aims to present the set of categories that make up the __________ and the record of frequency - AKA ___________
table and/or graph original measurement scale the number of individuals in each category
the x values in a frequency distribution table represent the scale of measurement and not __________
the actual score
what are proportions (p)
the fraction of the total group that is associated with each score. The proportion associated with each score is calculated by p = f/N. Proportions are often called relative frequencies and are represented by a lower case p.
explain what a rank (AKA "percentile rank") is
the percentage of individuals in the distribution with scores at or below the value/score at hand
what is the tail of the distribution
the section where scores taper off towards one end of the distribution
by adding up the frequencies, you can determine ________
the total number of scores or individuals in the population or sample
what are smooth curves
this is for populations which consist of numerical scores from a numerical or ratio scale. This shows the relative changes from one score to the next. Includes normal curves
what is a polygon
used for grouping distributions of numerical scores from an interval or ratio scales of measurement. Categories of measurement are along the x -axis with a dot above each to correspond to the frequency on the y-axis. A continuous line connects the series of dots. The graph starts and finishes at a zero frequency. Each dot is at the midpoint between each class interval.
explain what a cumulative frequency is
values that are at and below a score/percentile. They represent an accumulation of individuals as you move up the scale.
the distance between two real limits of an interval is called the ________
width
frequencies are always listed at the ____ while the scale of measurement is always listed at the _____
y axis x axis
How do you calculate cumulative frequency
you calculate it by adding up the frequencies in and below that score. To find percentiles, convert frequencies into percentages. Resulting values are cumulative percentages - they show the percentage of accumulating individuals as you move up the scale.
Explain grouped frequency distribution table
you present groups of scores rather than individual scores. This is used with a set of data that has a large range It is then grouped into intervals so that it is more simple and organized. This is better than having a giant range, like a high of 75 and a low of 15, making the range 60. This group of intervals are called class intervals
explain how you would calculate ΣX
you would first calculate x for each score. Sometimes x can be more complicated such as (x - 1)^2, or something much simpler ((but for this example well use (x - 1) ^ 2)) But next, you solve whats IN THE PARENTHESIS FIRST. You then square this value. This is the new x value. THEN, multiply each x value by the frequency which it appears in the data. For example, if x is calculated as 1, 4, and 9, and their frequencies are 1, 2, and 3, then 1 X 1 = 1, 4 X 2 = 8, and 9 X 3 = 27. Multiplying the x value by its frequency thus eliminates the need to calculate x multiple times for the same x values. Lastly, you add up all the numbers to get the solution to Σ(x - 1) ^2.
