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MAT 110 Vocabulary Ch 14
14.1
STATISTICS: an area of mathematics in which we gather, organize, analyze and make predictions from
numerical information called DATA or a DISTRIBUTION
SAMPLE: a subset of a population
BIASED: does not accurately reflect the population as a whole – 2 types: SELECTION and LEADINGQUESTION BIAS
FREQUENCY DISTIBUTION: a set of data listed with their frequencies
RELATIVE FREQUENCY DISTRIBTION: showing the percent of time that each item occurs in a frequency
distribution (usually expressed as a decimal)
REPRESENTATION OF DATA: See pages 703-710 for specific examples: FREQUENCY TABLE, BAR GRAPH,
HISTOGRAM, and STEM AND LEAF DISPLAY
14.2
MEASURES OF CENTRAL TENDENCY: mean, median, mode and quartiles
MEAN: average of the data (notation 𝑥̅ or µ)
MEDIAN: the middle number in a list of data when arranged in order. If there are two middle numbers,
then they must be averaged
MODE: the number that appears most frequently. (There can be two modes if two numbers appear the
most or no mode if more than two scores appear most frequently.)
FIVE-NUMBER SUMMARY: Lowest value, Q1 (Median of the lower half), MEDIAN, Q3 (Median of the
upper half), Highest value
BOX AND WHISKER PLOT: a graph that represents the five-number summary:
Q1
Q2
Q3
source: ellerbruch.nmu.edu
14.3
RANGE: the difference between the largest and smallest data values (Largest # minus smallest #)
DEVIATION FROM THE MEAN: distance a number is form the mean (negative if below the mean,
positive if above) ( x - 𝑥̅ )
MAT 110 Vocabulary Ch 14
STANDARD DEVIATION : a measure based on the distance each data value is from the mean (s or σ)
∑(𝑥− 𝑥̅ )2
𝑠= √
Formula:
1.
2.
3.
4.
5.
𝑛−1
which is to:
Find the mean for the data
Find the deviation from the mean for each
Square the values in 2.
Add up the squares and then divide by n – 1 (the value at this point is called VARIANCE)
Calculate the square root of the answer to step 4
𝑠
COEFFICIENT OF VARIATION: CV = 𝑥̅ ∙ 100 %
14.4
NORMAL CURVE or NORMAL DISTRIBUTION: the most common distribution and describes many reallife data sets; Bell-shaped curve; mean median and mode the same; symmetric with respect to the
mean; area under the curve equals 1
34%
2.5%
13.5%
34%
13.5%
2.5%
Source: www.syque.com
Roughly 68% of data is with 1 standard deviation from the mean, 95% are within 2 standard deviations
from the mean and 99.7% are within 3 standard deviations of the mean.
Z – SCORE: the number of standard deviations a data value is from the mean.
If a normal distribution has a mean of µ and a standard deviation of σ then you can convert a
𝑥− 𝜇
data value, x, to a z-score with the formula: 𝑧 = 𝜎