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AMS 102 > Midterm 1 > Flashcards

Midterm 1 Flashcards

1
Q

How do I find the interquartile range?

HINT: ASTST

A
  1. Arrange the numbers into least to greatest
  2. Separate into Quarter 1 (Upper half) and Quarter 3 (lower half)
  3. Take the average of 2 numbers in the middle of each half
  4. Subtract the Lower half’s average from the Upper half’s average.
  5. This is the inner quartile range (IQR)

ASTST (Assholes Seem To Stink Terribly)

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2
Q

What does this symbol mean?
∑X

A

It means to find the summation of X, which is to add up all the numbers in the data set

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3
Q

When asked for ∑X, sometimes you will be asked to find N. What does this letter mean?

A

It is the number of data in the set

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4
Q

What does this symbol mean?
x̄ (X bar)

A

It is the average of the numbers in a sample set (data set).

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5
Q

What does this symbol mean?
μ

A

It is the population average.

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6
Q

What does this symbol mean?
σ

A

It is the standard deviation.

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7
Q

What is the Z score?

A

It is the number of standard deviations a value falls above or below the mean?

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8
Q

How do I find the Z score in a sample?

A

x - x̄ / (s)

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9
Q

How do I find the Z score in a population?

A

x - μ / (σ)

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10
Q

How do I find the Variance of sample data?

HINT: CFADT

A
  1. Use this formula: ∑ ( x - x̄ ) ^ 2 / (n) =σ^2
  2. Create a Table with the following values: X, x̄, (x - x̄), (x - x̄) ^ 2
  3. Fill in the Table (All data has the same sample mean)
  4. Add all values in the last column of the table (x - x̄) ^2 together
  5. Divide it by N
  6. This is the Variance of the sample data.

CFADT
Cows Feel And Dance Terrifically

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11
Q

How do I find the Standard Deviation of Sample Data?

PT 2 of Acronym
FT

A
  1. Find the Variance
  2. Take the Square Root of Variance

CFADT FT
Cows Feel And Dance Terrifically For Turtles

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12
Q

How do I find Percentiles?

HINT: AAUUT + IT

A
  1. Arrange the Data from least to greatest
  2. Assign a number to tell the location of the Data
    For Example:
    If you had
    (5, 8, 3)
    5 would be assigned as 1
    8 would be assigned as 2
    3 would be assigned as 3
  3. Use this Formula: L (subscript p) = (n+1) * (p/100)
  4. Use the answer to this formula to see which data value is in that location or the 2 data values it is between
  5. This is the percentile.

For example:
If you had
5.52 as your answer, it would be between the 5th and 6th values

  1. If there is a decimal part of your answer, add the LESSER data value + decimal part of answer, and multiply it by the difference between the 2 values
  2. This is the Percentile in that case.

Assholes Actually Understand Unicorns Tremendously + If Thirsty

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13
Q

What is the formula to find the location of a data’s percentile?

A

Lp = (n+1) * (p/100)

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14
Q

In which type of problem, does order MATTER?

A

permutations

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15
Q

In which type of problem, does order NOT MATTER?

A

combinations

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16
Q

what is the formula for PERMUTATIONS?

A

nPr= (n!)/ (n-r)!

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17
Q

what is the formula for COMBNATIONS?

A

nCr = (n!) / (n-r)! * R!

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18
Q

How does the permutation and combination formula equal each other?

A

nCr = nPr/ R!

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19
Q

what type of graphs are used for quantitative data?

A

Histograms

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20
Q

what 2 types of graphs are used for categorical data?

A
  1. bar graphs
  2. circle graphs
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21
Q

What 2 things can bar graphs show?

A
  1. Percents
  2. Frequency
22
Q

What 2 types of data is the mode appropriate for?

A
  1. categorical
  2. quantitative
23
Q

What is the formula for the Coefficient of Variation?

A

standard deviation/ sample mean * 100%

24
Q

What is the key difference between proportionate allocation and disproportionate allocation (optimum)?

A
  1. What is the key difference between the allocations?
    Proportionate allocation is when a number is selected from each stratum of data, so that it is proportional to the breakdown of these groups in the population.

Disproportionate allocation is when the number of selected from each stratum of data, so that it is disproportional. Suppose you know that more variability exists in a particular stratum, you will want a larger sample from that stratum to capture the phenomenon.

25
Q

This is an example of disproportionate (optimum) allocation.

A

Example:
Question: What % of students are in favor of multiple-choice exams?
There are 350 students in the exam. Let’s break down the population of students into 4 groups. This is so they are dissimilar to each other.

The 4 groups are: Freshmen (50) , Sophomores (50) , Juniors (100), and Seniors (150)

Let’s say we take a sample of this population:, in where we sample 10 Freshmen, 15 Sophomores, 20 Juniors, and 10 Seniors.

This is a disproportionate allocation, because we have the same amount of Freshmen and Sophomores, yet we have 10 Freshmen sampled and 15 Sophomores sampled. This is Because there is more variability within the opinions of Sophomores, thus we need to take a larger sample.

26
Q

In stratified random sampling, what 2 things should you assume about strata?

A

In stratified random sampling, what 2 things should you assume about strata?

27
Q
A
28
Q

What is the formula for the Coefficient of Variant?

A

CV = s/x * 100%

29
Q
A
30
Q

What does the Coefficient of Variation do?

A

It allows us to compare 2 data sets when the units are different

31
Q

What type of sampling assumes differences BETWEEN are small and differences WITHIN are large?

A

Cluster Sampling

32
Q

How does Stratified Random Sampling Work?

A

Depending on the focus of the study, members of the population are divided into 2 or more homogenous subsets, called strata, that share a similar characteristic such as age, gender, ethnicity, political preference. A random sample is then selected from each strata.

33
Q

How does 1 in K Systematic Sampling Work?

A

First, each member of the population is assigned a number. A starting number is randomly selected from among the first K members, and then every kth member is selected from the starting number, in other words, every third, or every fifth, or ever hundrendth member is selected depending on the value of K.

34
Q

What is nominal data? What type of data is this used for?

A
  1. It is data that consists of name only or qualities with no implied criteria by which we can identify which data is greater than or less than another
  2. This is used for categorical data
    Example:
    Which of the following attributes of this restaurant do you find most attractive: services, prices, quality of food?
35
Q

What is ordinal data? What type of data is this used for?

A
  1. It is data that may be arranged in some order, but actual differences between data values either cannot be determined, or are meaningless.
  2. This is used for qualitative data
    Example:
    Would your overall rating of this restaurant be: Poor, Good, Excellent?
36
Q

What is interval data? What type of data is this used for?

A
  1. It is data where there are meaningful differences between data values. However there is no ‘0’ or start point, and ratios of data are not meaningful.
  2. This is used for quantitative data.
    Example:
    What time did you eat at the restaurant?
    HINT: Calendar and Clock times are this scale
37
Q

What is ratio data? What type of data is this used for?

A
  1. It is data where there are meaningful differences that exist between data values. It does have a ‘0’ or start point. ‘0’ reflects the absence of the measured characteristic.
  2. It is used for quantitative data.
    Example:
    Have you eaten at this restaurant previously?
    HINT: Time lapses are always this scale
38
Q

What is the measure of the variability of the data points from the mean?

A

The Standard Deviation

39
Q

Mutually Exclusive events are never dependent-True or False

A

FALSE. THEY ARE ALWAYS DEPENDENT

40
Q

How do I do random sampling?

A
41
Q

How are frequency polygons created?

A

They are obtained by connecting the midpoints of the bars of a histogram using straight lines

42
Q

What is a pareto chart?
(HINT: What 2 things make it distinctly a pareto chart)

A
  1. The bar height represents frequency of an event
  2. The bars are rearranged so they are in decreasing order of frequency
43
Q

How to do simple random sampling?

LSGIICT

A
  1. Look at the number of digits in the population size number

Ex. If N= 60, there is 2 digits

  1. Separate the random number table, into groups with the same number of digits as N,

Ex.
If N=60
5670 8293

You would separate the groups into: 56, 70, 82, 93

  1. Give multiple labels to the groups
    Ex. 61 62 63… could also be 01 02 03 04 05
  2. If the groups are greater than your N, REJECT THEM
  3. If they are lower than N, then subtract the number from N

Ex.
60-56= 4
This would be the first member of your group

  1. Continue this till your amount of members = your lowercase n

Ex. In this case, let’s say n = 4

  1. This is how you do simple random sampling.

Ladies Sashay Goodbye If It Continues Tastefully

44
Q

How to find the Class Lower Limit?

A

The Lower Limit is simply the lowest data entry.

45
Q

How do I find the classes’ lower limit?

HINT: LADT

A
  1. Look at the Minimum Lower Class Limit
  2. Add the Class Width to the Lower Class Limit,
  3. Do this you have added the same number of times as your number of classes
  4. This is your lower limit

Laugh Anyways Despite Time

46
Q

How do I find the classes’ lower boundaries and upper boundaries

HINT: SDSAWT

A

LOWER CLASS BOUNDARIES
1. Subtract the 1st Class’s Upper Limit from the 2nd Class’s Lower Limit
2. Divide this answer by 2
3. Subtract this value from ALL of the lower class limits
THEN FOR YOUR UPPER CLASS BOUNDARIES
4. Add this value to ALL of the upper class limits
5. Write it as now, lower class boundary (hyphen) - upper class boundary
6. These are your Class Boundaries

Sing Douchebag Songs Always When Tired

46
Q

What should I remember about intersections?

A

To always subtract the P (A) from the intersection to find the probability of ONLY A,
SAME WITH B

47
Q

How do I do a problem like this?
Given:
P (A) = .2 P(B) = .3 P(A and B)=.12 ,
What is P(A or B’)?

A

Subtract the intersection form the probabilities to find the probabilities by themselves
Create Venn Diagram
Use Demorgan’s Law
Hint: Intersection includes both A and B, so when it says only B, only look at B part
This is the Answer

48
Q

What is a dichotomous variable ?

A
  1. A dichotomous variable is a type of categorical variable where there is only 2 categories.
    Example: True or False, Absent or Present
49
Q

How would I compute the mean of a dichotomous variable?

A

You would get the portion of the sample that exists

50
Q

What are the 2 ways to pick a stratified sample?

A
51
Q
A

AMS 102 (2 decks)

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