Module 3 Notes - Numerical Descriptive Measures Flashcards
The _______ ________ is the extent to which the values of a numerical variable group around a typical or central value.
central tendency
the _________ is the amount of dispersion or scattering away from a central value that the values of a numerical variable show
variation
the _____ is the pattern of a distribution of values from the lowest to the highest value
shape
Arithmetic Mean
A= \frac {1}{n} \sum \limits_{i=1}^n a_i
Middle value in the ordered array
Median
Most frequently observed value
Mode
the __________ ____ (often just called “mean”) is the most common measure of central tendency.
*For a sample of size n (lower case n):
arithmetic mean
*The most common measure of _______ ________.
*____ = sum of values divided by the number of values
*Affected by extreme values (outliers).
Mean
*In an ordered array, the ______ is the “middle number (50% above, 50% below)
*less sensitive than the mean to extreme values
median
Locating the Median
*The location of the median when the values are in numerical order (smallest to largest):
*If the number of values is odd, the media is the middle number
*If the number of values is even, the media is the average of the two middle numbers
Median Position = n+1/2 position in the ordered data
*Value that occurs most often
*Not affected by extreme values.
Mode
Range, Variance, Standard Deviation, Coefficient of Variation
-Measures of _________ give information on the spread or variability or dispersion of the data values
Measures of Variation
*Simplest measure of variation.
*Difference between the largest and smallest value
Range.
*Does not account for how the data are distributed.
*Sensitive to outliers
“Why the _____ can be misleading”
range
*Average (Approx.) of squared deviations of values from the mean.
Sample Variance
*Most commonly used measure of variation.
*Shows variation about the mean.
*Is the square root of the variance.
*Has the same units as the original data.
Sample standard deviation
Steps for computing _________ _________
1. Computer the difference between each value and the mean.
2. Square each difference.
3. Add the squared differences.
4. Divide this total by n-1 to get the sample variables.
5. Take the square root of the sample variance to get the sample ________ _________
standard deviation.
*Measures relative variation.
*Always in percentage (%)
*Shows variation relative to mean.
*Can be used to compare the variability of two or more sets of data measured in different units.
The Coefficient of variation (Standard Deviation / Mean) * 100
Locating Extreme Outliers: _-_____
Z=X-x̄/S
Where X represents the data value
x̄ is the sample mean
S is the sample standard deviation
Z-score
*Suppose the mean math SAT score is 490, with a standard deviation of 100.
*Computer the Z-score for a test score of 620.
(Z=x-x̄/s)=(620-490/100)=(130/100)=1.3
-A score of 620 is 1.3 standard deviations above the mean and would not be considered an outlier.
*A data value is considered an extreme outlier if its Z-score is less than -3.0 or greater than +3.0
Z-score
The more data are spread out, the greater the _____, ________, and ________ __________.
range, variance, standard deviation
The more data are concentrated, the smaller the _____, ________, and ________ _________.
range, variance, and standard deviation
If the values are all the same (no variation) all these measures will be zero
range, variance, and standard deviation
None of these measures are ever in negative.
range, variance, and standard deviation
