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# Statistical Methods I Test 1 [REVIEW]

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Department
Statistics
Course Code
STA 2023
Professor
All

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Statistics Spring 2014
January 8, 2014
Ch.1
A) Types of statistical problems
a. Descriptive- Describing a set of measurements
using graphs and numbers
b. Inferential- use a simple to say something about a population
B) Elements of inferential problems
a. Population- set of objects of interest
b. Variable- measurements that are recorded for each object
c. Sample- subset of the population
d. Inference- decision, estimate or prediction
e. Measure of reliability- based on probability
C) Types of data
a. Qualitative- values of x are categories
i. Examples- gender, race
b. Quantitative- values of x are numerical measurements
Ch.2
Describing data
Graphical techniques sec 2.2
1. Histogram- bar graph
a. Relative frequency is the proportion of the data (data point over the total population).
2. Stem and leaf display
10 16 25 40
12 17 28 60
15 25 38 80
Stem leaf
102567
2558
3 8
4 0
5
6 0
8 0
*This is skewed to the right.
Example
What is the stem unit? (Answer: Tenths)
0.348 0.536
0.349 0.548
0.467 0.621
0.498 0.638
Statistics Spring 2014
0.521 0.708
* you can round or you can make a two part leaf.
Example
What is the stem unit? (Answer: hundredths)
0.328 0.378
0.329 0.379
0.356 0.382
0.358 0.385
0.369 0.39
Stem Leaf
32 8 9
35 6 8
36 9
37 8 9
38 5
39 0
Numerical measure of central tendency sec 2.4
1. mean: average
a. m=population mean
b. (X bar) =sample mean
c. n- sample size
2. median
a. the very middle age of all ages (middle of data)
i. first arrange data in numerical order
ii. then find the middle.
iii. n is odd: median=middle number
iv. n is even: median- average of the 2 middle numbers
Example of mean
To estimate the average cost of a new home in Orlando, 25 homes are selected and their average cost is found to
be \$240,000
- Sample is 25 home
-Population is all homes
-Variable(x)is the cost of each house
-inference is to estimate the average cost of the homes in Orlando.
-m = unknown
Stem Leaf
344
469
5234
663
7 0
Statistics Spring 2014
-(X bar) is 240,000
-n=25
Shapes of distributions
-symmetric
-skewed right
-skewed left
How do the mean and median compare for each of these shapes?
-Mean and median are the same with the distribution is symmetric
mean=median
mound shaped uniform
Skewed right: Skewed left:
Example
X= age of student at UCF (skewed to the right)
X= grade on an easy test (skewed to the left)
X=number of days a UCF student hospitalized in the last year. (skewed to the right)
Sec. 2.5 measure of variability
1. Range= maximum-minimum
a. Data set: 1,3,3,3,10
i. Range= 9
ii. (X bar)= 4
iii. median= 3
b. Data set: 1,1,3,5,10
i. Range=9
ii. (x bar)=4
iii. median=3
2. Variance
a. S2 = sample variance
b. σ2 = population variance
3. Standard Deviation: positive square root of the variance
a. s= sample standard deviation
b. = population standard deviation. σ

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