Varibility Probability Z Scores Hypothesis Flashcards
Fairly variable distribution.
Heterogenous scores.
More similar distribution- specific range.
Homogeneous score
How do you compute range?
URL highest- LRL lowest
Determines the dispersion of data points.
Sum of squares
Measure of total variability of a set of scores around a particular number, usually the mean of the set of scores.
squared deviation scores.
What does variance measure?
The average squared deviation from the mean.
Measure of variability.
How do you compute variance for a population?
SUM OF SQUARE/df
How do you compute variance for a sample?
S^2= SS/ (N-1)
Used in descriptive statistics (instead of variance)
“Typical distance of a set of scores from their mean”
Standard deviation
Summarize the spread of scores in a population or a sample.
Measure degree to which scores differ from one another.
Measure the Variability
obtain a measure of how spread out the scores are in a distribution.
Goal of variability
Measuring Variability
• the range
• the interquartile range
• the standard deviation/variance.
total distance covered by the distribution, from the highest score to the lowest score
Range
distance covered by the middle 50% of the distribution (the difference between Q1 and Q3).
Interquartile range
is a statistical measurement that looks at how far a group of numbers is from the mean. Put simply, standard deviation measures how far apart numbers are in a data set.
Standard deviation
the average of the squared differences from the mean.
Variance
usually sufficient to complete most z-score transformations
Z-score
composed of scores that have been transformed ot create predetermined values for u and o. Also used ot make dissimilar distributions comparable.
standardized distribution
a method for measuring and quantifying the likelihood of obtaining a specific sample from a specific population
Probability
When a score is referred to by its rank, the score is called a
Percentile
a. z<0.25
b. Z>0.80
c. Z<-1.50
d. D. z>-0.75
P= 0.5987
0.2119
0.0668
0.7734
Separate the top 20% from the rest
Z= 0.84
natural discrepancy, or the amount of error, between a sample statistic and its corresponding population
parameter
Sampling error
standard deviation of the distribution of sample means
Standard error of M
The deviation of a value (x) from the mean of the sample divided by the standard deviation (s)of the sample is known as the “z” value or z-score.
True
False
True
A z-score of 1.0 corresponds to a value one standard deviation from the mean.
True
False
True
Since the normal curve is not symmetrical the area corresponding to a z-score of +1.0 will be different from that corresponding to -1.0.
False
A home business has an average income of $900.00 per month with a standard deviation of $15.00. If the income in a given month is $930.00, what
-score corresponds to this value?
2.0
Another home business has an average income of $1,200.00 per month with a standard deviation of $100.00. If the income in a given month is $1,030.00, what
-score corresponds to this value?
-1.7
Clyde Cement wants to analyze a shipment of bags of cement. He knows the weight of the bags is normally distributed so he can use the standard normal distribution. He measures the weight of 600 randomly selected bags in the shipment. Next, he calculates the mean and standard deviation of their weights. The mean is 50 lbs. and the standard deviation is 1.5 lbs.
What percentage of the bags of cement will weigh less than 50 lbs.?
50
Equation in z-score
z = (x-m)/s
z = (deviation/standard deviation)
What is the mean and SD of Standard Scores?
Mean 100 SD 15
Scores deviate from the mean in a predictable way. Most scores occur around the mean, fewer scores occur far from the mean
Normal distribution
For a sample with M = 60 and s = 8, what is the 7-score corresponding to X = 62?
0.25
Using z-scores, a population with u = 3/ and o
= 6 is standardized so that the new mean is u=
50 and o = 10. How does an individual’s z-score
in the new distribu[1]tion compare with his/her z-score in the
original population?
New z = old z
A distribution with u = 35 and o = 8 is being
standardized so that the new mean and standard
deviation will be u = 50 and o =
10. In the new, standardized distribution your score is
X = 60. What was your
score in the original distribution?
X= 45
