Statistics Test

MGMAT Statistics Test (12/15) - 80%

Statistics

• Arithmetic mean:
  Average = Sum / # of terms
  Sum = Average x (# of terms)
  To keep track of two average formulas in the same problem, you can set up an RTD style table.
• The average of an evenly spaced set is the middle number (or the arithmetic mean of two middle numbers). All you need to do to find the middle number is to find the arithmetic mean of the first and last terms.
• Weighted averages:
  Weighted average = (weight/sum of weights) x (data point) + (weight/sum of weights) x (data point) + ..
  or
  Weighted average = (weight)(data point) + (weight)(data point) / sum of weights
• Having just the ratios of the weights will allow you to find a weighted average. Simply write the ratio as a fraction, and use the numberator and the denominator as weights. If you know the weighted average you know the ratio of weights.
• If you know the two sub-group averages and you know the overall weighted average, then you can solve for the relative weightings of the two sub-groups. 
• If you are finding a weighted average of rates (whose units are fractions), then the "weights" correspond to the units appearing in the denominator of the rate.
• Median is the unique middle value of a set containg an odd number of values arranged in increasing (or decreasing) order, or the arithmetic mean of the two middle values of a set containing an even number of values arranged in increasing (or decreasing) order.
  You may be able to determine a specific value for the median of a set even if one or more unknowns are present.
• Solve problems involving both the arithmetic mean and the median by writing expressions for both.
• You may be required to construct and manipulate a completely abstract set, you can use alphabetical order to make it a little more concrete, or you can place the variables on an abstract number line in order to visualize their relationships, or you can create a column chart.
• Standard deviation indicates how far from the average (mean) the data points typically fall. The more spread out the numbers, the larger the SD.
  If you see a problem focusing on changes in the SD, ask yourself whether the changes move the data closer to the mean, farther from the mean, or neither. If the problem requires comparisons, ask yourself which set is more spread out from its mean.
  The term "variance" is the square of the SD.
• The mode of a set of numbers is the number that occurs most often.
• The range of a set of numbers is the difference between the largest number and the smallest number.
  
  

Sentence Correction

• Subject and verb must agree in number
  - find the subject and the verb through filler
  - verb might come before subject, ask what?
  - identify each subject and verb in the underlined part and pair them
• Unusual subjects
  - compound subjects - and means plural (two things)
  - collective nouns (i.e. group, team) are singular
  - verbals that function as nouns (gerunds aka -ing words or infinitives) are singular
• Fragments
  - looks like a complete sentence, but doesn't express a complete thought
  - check to see that the sentence has a main verb
• Run-on sentence
  - combines two sentences that could stand on their own without proper punctuation, must be separated by a semicolon or a comma and a fanboys word:
  For
  And
  Nor
  But
  Or
  Yet
  So
  - Make sure there are full sentences on both sides of these conjunctions
• Pronouns
  - have to refer to a specific antecedent
  - must agree in number with the antecedent
  - both is plural; each is singular
  - watch out for answer choices that introduce new pronouns
• Modifiers
  - When a sentence starts with a modifier, the object that it is modifying should be the first word after the comma
  - Modifiers should be close to what they modify
• Verb tense indicates the time of verb's action
  - Auxiliary verbs express more complex tenses:
    Past perfect (had) - event in the past preceding another event in the past, (X had before Y was)
    Present perfect (has) - started in the past continuing to present (doesn't need to continue to into the future)
  - Actions in the same time frame should be expressed in the same tense
  - Keywords: as, until, before, since
• Parallel construction:
  - Lists
  - Correlative conjunction: not only.. but also, neither.. nor.. 
  - Comparisons and contrasts - unlike, just as...so, like, as...as, than.., compared with.., in contrast..,
  - "like..., word directly after the comma" 
  - Make sure items are logically comparable

Checklist

• Phrases and clauses
  Find subject and main verb of sentence
  Do subject and verb agree in number?
  Is the sentence a fragment?
  Do phrases/clauses create wordiness?
• Lists 
  Is each item parallel?
• Verbals
  Do verbals violate parallelism?
  Any misplaced/dangling modifiers?
  Are verbals wordy/awkward?
• Pronouns
  Match pronouns to antecedents
  Does each pronoun have one ant.?
  Do pronouns and ant. agree? 
  Is pronoun unnecessary and wordy?
• Comparisons
  Identify items that are compared
  Are items logically able to be compared?
  Are compared items parallel?
  Are comparison idioms correct?
• Quantity Words
  Is correct word used (e.g. fewer/less)? Any redundancy in quantity words?
• “Tell” Words“
  Had” / “if” – tense errors?
  “Being” / “having been” – wordiness?
  Passive verbs – awkward style?
  “There are” / “there is” – wordiness?

Coordinate Plane Test

MGMAT Coordinate Plane Test (13/15) - 87%
One careless mistake.

Coordinate Plane

• Slope of a line is defined as "rise over run" - how much it rises vertically divided by how much it runs horizontally.
  rise / run = y₁-y₂ / x₁-x₂ 
• A point where a line intersects a coordinate axis is called an intercept.
  - The x-intercept is the point on the line at which y = 0
  - The y-intercept is the point on the line at which x = 0
  Plug in 0 for x or y to find the intercepts.
• All lines can be written as equations in the form of y = mx + b, where m represents the slope of the line and b represents the y-intercept of the line.
• Finding the equation of a line:
  1) Find the slope of the line by calculating the rise over run.
      Remember that y-intercept is a point as well
  2) Plug the slope in for m in the slope-intercept equation.
  3) Solve for b, the y-intercept, by plugging the coordinates of one point into the equation. Either point's coordinates will work.
  4) Write the equation in the form of y = mx + b
• Determining which quadrants a given line passes through can be done in two ways:
  1) First, rewriting the equation in form of y = mx + b and then sketching the line
  2) Finding two points on the line by setting x and y equal to zero in the original equation. 
• The perpendicular bisector has the negative reciprocal slope of the line segment it bisects.
  1) Find the slope of the line it bisects
  2) Find the negative reciprocal by flipping the fraction and changing the sign (product must be -1)
  3) Find the midpoint of the line, by finding the midpoints of the x and y coordinates separately.
  4) To find the value of b of the perpendicular bisector substitute the coordinates of the midpoint for x and y. 
• Parallel lines have equal slopes. 
• If two lines in a plane intersect in a single point, the coordinates of that point solve the equations of both lines. To find the find the intersection point of two equations, turn them into slope-intercept form and set them equal to each other.
• When faced with an inequality in the coordinate plane:
  1) Draw the line either by converting to slope-intercept form or using the x and y intercepts
  2) Plug in a point on one side of the line. If this point makes the inequality true, that point is in the solution set. If not, the solution set is on the other side of the line.
• Distance between two points
  Square root of (x₁-x₂)²+(y₁-y₂)²
  
  Need to finish this.
  

Probability

Probability = Number of desired or successful outcomes / Total number of possible outcomes

• All the outcomes must be equally likely - you can use a counting tree
• To determine the probability that independent events X and Y will both occur, multiply the two probabilities together.
• To determine the probability that mutually exclusive events X or Y will occur, add the two probabilities together.
  - if the events cannot occur together, add the probabilities of individual events
  - if the events can occur together, use the formula: P(A or B) = P(A) + P(B) - P(A and B)
• Probability of success + Probability of failure = 1
• If success contains multiple possibilities - especially if the wording contains phrases such as "at least" and "at most" - then consider finding the probability that success does not happen.
• Be careful of situations in which the outcome of the first event affects the probability of the second event, i.e. picking things out of a box.
• When you use a probability tree, multiply down the branches and add across the results.
  

Reading Comprehension

• Read for the big picture, don't dwell on the details, translate ideas and terms into simpler words, ask "why" for each new idea, create a Passage Structure
• Use PS and keywords in the passage to find:
  Main Idea: What? The point or idea that the author expresses in the passage.
  Attitude: How? The feeling or opinion the author expresses about the main idea.
  Purpose:Why? The author's reason for writing
• Pay attention to soft and extreme wordings: some vs all
• Keywords: must, if, then, like
• Read the passage first, don't look at the question before
• Main idea or title should capture the whole passage, not just one paragraph
  
• Global questions
  - Use MAPs
  - Prephrase an answer
  - Look for a match
• Detail question
  - Use MAPs to locate the detail
  - Paraphrase and scan answer choices for the paraphrasing of the passage language
  - Read the complete idea to provide context
• Inference question
  - Think must be true (and are concretely supported by the passage)
  - Eliminate answers one by one using the passage to invalidate
  - (Don't prephrase)
• Distinguish between the author's voice and others
• Common wrong answer choices - out of scope, too broad, distorted details, extreme.