Chapter 1
Statistics – science of data – collection of, organization, analysis and interpretation.
Population – entire group of individuals
Variable – a characteristics of an individual
Variables are
Quantitative – numerical
Qualitative – non-numerical
Statistics are:
Descriptive – get the informational and report
Inferential – get the information and draw parts of it and interpret it.
Sample – subset of population
Should be random, but how do we get a random sample?
1000 people, sample of 100 that needs to be random.
Number the sample, then take 100 out of that (draw them out of a hat so to speak)
We can also use a random table. (p. 6 in book)(instructions are there)
Chapter 2
Central Tendency
- Mean
- Medium
- Mode
Range, variance and standard deviation
p. 44
Stem and leaf know what it is
whole number as the stem. the decimal points become the leafs.
sometimes the stems must be broken in to seperat parts.
30 could be .0 to .4 and then .5 to .9
Frequency distribution -
- tabular summery
- frequency of observation in each class
p. 46
65 invoices
need to figure out how many classes are needed.
you do not want to have too large a sample or too many samples.
general rule is 2^k > N where k is number of classes
2^6 = 64
2^7 = 128
2^7 is greater than the 65 observations
so we use 7 classes. Now class length
high number - low number / number of classes
29 - 10 /7 = 2.7147 take next highest number 3
make your table
10 - 12
13 - 15
16 - 18
19- 21
22 - 24
25 - 27
28 - 30
then add the frequencies in the table
10 - 12 3 3/65 =
13 - 15 14 14/65
16 - 18 23 23/65
19- 21 12
22 - 24 8
25 - 27 4
28 - 30 1
this would be 65 and the last collumn relativity , should be 1 totaled
Class bounteries, take .5 on either side of the number. this makes sure that you get all the numbers
next a histogram (p. 48 in book)
connect the midpoints on the blocks to get a distribution
population parameter - a number calculated from a population and discribes a population.
population mean - mu
standard deviation - sigma
sample statistics - calculated for a sample and describes them
x-bar - sample means
S -sample standard deviation
point estimates.
measure of central tendencies -
- mean
- medium
- mode
paper notes 1
sample means - if you have n as size of sample, then
xBAR = EXi/n sumation size...
30. 8 31.7 30.1 31.6 32. 1
n = 5
xBAR = add them all/devide by 5 = 156.5/5 = 31.31
46 54 42 46 32 sample observation
xBAR = all/5
= 44
X mean - average
2) median
midpoint of distribution
- arrange the numbers in some order (ascending or decending)
- if n is odd then median is the middle observation
- if n is even then middle two observations are devided by 2
42, 32, 54, 46, 46
32 42 46 46 54
n= 5 2.5 is 54
2210 2255 2350 238- 2390 24320 2440 2450 2350 2630 2825
n is 12
numbers are ordered, middle two are 2390 + 2420/ 2 = 2405 medium
Mode
Mode is the observation that has greater frequency
in the 5 2 digit numbes above it would be 46
mediam and mode are not affected by extreme values
the mean will be affected by extreme values
Normal distribution the symetric curve around the mean. 1/2 above and 1/2 below.
if normal mean = medium = mode
skewed distribution
skewed right left to right mean medium mode
skewed right mode medium mean
measure of central tendencies we have just looked at.
measure of variations
1. range
2. variance
range take the largest and subtract the smallest is the range
variance - population variance sigma^2
paper notes 2
Sample variance S^2 = sum of (Xi - xBAR)^2 / n - 1
this n - 1 gives us an unvbiased estimate of sigma^2
sigma is population standard variation
s is sample
sigma is sqrt of sigma^2
s = sqrt of s^2
from book profit margin of french fries (p. )
8 % 10% 15% 12 % 5%
mu = sumx/5
mean
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