Class notes
BUS 310 Chapter 3 Notes
- Course
- BUS 310
- Institution
- University Of Hawaii - Manoa
This is a comprehensive and detailed note on chapter 3 for Bus 310. *Essential Study Material!!
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3.1 Central Tendency● Central tendency-extent to which the values of a numerical variable group around a
typical, or central, value. Variation-measures the amount of dispersion away from a
central value that the values of a numerical variable show. Shape-variable is the pattern
of the distribution of values from lowest to highest
○ Median=( (rank)n+1)/2
○ A simple measure of variation around the mean might take the diff btw each
value and the mean and then sum these diffs. However, if you did that, you’d find
that the diffs sum to 0 bc the mean’s the balance point for every numerical
variable. A measure of variation that differs from one data set to another squares
the diff btw each value and the mean and then sums these squared diffs=sum of
squares (SS). Sample variance (s^2)-sum of suares divided by sample sz minus
1. Sample standard deviation (S)’s the sqrt of the sample variance.
■ Sum of all squared diffs btw Xi values and X (X=sample mean)(n=sample
size)(Xi=ith value of the variable X)
(sqrt(Xi-X)^2/(n-1))
3.2 Variation and Shape
● Coefficiant of variation (CV)-measures the scatter in the data relative to the mean.
Always a %. (Sample SD/sample mean)100%
○ Z score-diff btw value and the mean, divided by the SD. Helps identify outliers.
○ Skewness-measures the extent to which the data values aren’t symmetrical
around the mean
■ Mean < median: negative/left-skewed distrib
■ Mean = median: symmetrical distribution
■ Mean > median: positive/right-skewed distrib
○ Kurtosis-measures peakedness of the curve of distribution. Lepokurtic-distrib that
has a sharper-rising center peak than the peak of a normal distribution has
positive kurtosis; a kurtosis value that’s greater than zero. Platykurtic-flatter w a
negative kurtosis value.
3.3 Exploring Numerical Data
● Quartiles-split values into 4 equal parts--the first quartile (Q1) divides the smallest 25%
of values. Q2 goes from 26-50%. Q3 51-75% ((3(n+1))/4). Q4 76-100%.
○ Rule 1: If the ranked value is a whole #, the quartile is equal to the measurement
that corresponds to that ranked value. Ex: If sample size n=7, Q1 is equal to the
measurement associated w the (7+1)/4 = second ranked value
○ Rule 2: If the ranked value is a fractional half (2.5,4.5), the quartile is equal to the
measurement that corresponds to the avg of the measurements corresponding to
the 2 ranked values involved. Ex: If sample sz n=9, Q1 is equal to the (9+1)/4 =
2.5 ranked value, halfway btw the second ranked value and third ranked value
○ Rule 3: If the ranked value’s neither a whole # nor fract half, you round the result
to the nearest integer and select the measurement corresponding to that ranked
value. Ex: if n=10, Q1=(10+1)/4 =2.75 ranked value. Round 2.75 to 3 and use the
third ranked value.
● Interquartile range (aka midspread) measures the diff in the center of a distribution btw
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