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GMAT > 14 - Statistics > Flashcards

14 - Statistics Flashcards

1
Q

Counting consecutive integers, inclusive of the first and last numbers in a set

A

(Highest number - lowest number + 1)

50 to 101, inclusive

101 - 50 + 1 = 52

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2
Q

Counting the number of consecutive inegers inclusive of either only the first or last number in a set, not both.

Tom is 10th in Line , and Sara is 50th in line. How many people are there from Tom to Sara, including Tom but not Sara?

A

Counting the number of consecutive inegers inclusive of either only the first or last number in a set, not both.

Last/highest number - given first number

Tom is 10th in Line , and Sara is 50th in line. How many people are there from Tom to Sara, including Tom but not Sara?

50 - 10 = 40

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3
Q

Counting the number of integers in a set between 2 numbers

A

Counting the number of integers in a set between 2 numbers

Last/highest - first number - 1

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4
Q

Counting multiples of integer A AND B, but not of both, in a set of consecutive integers where remainder is needed

What is the sum of all two-digit numbers that leave a remainder of 1 when divided by both 3 and 4?

A

Counting multiples of integer A AND B, but not of both, in a set of consecutive integers

What is the sum of all two-digit numbers that leave a remainder of 1 when divided by both 3 and 4?

Find the LCM and add one because you need a remainder of 1

LCM (3,4) = 12 + 1 = 13

sum = average * quantity

average = (first integer + last integer / 2)

first integer = LCM (3,4) + remainder = 12 + 1 = 13

last integer = LCM * n + remainder needed where n will give you the product closest to the highest boundary (in this case 99) 12*8=96 + 1 = 97

13 + 97 / 2 = 55

Quantity = ((last integer - first integer) / common difference) + 1

(97 - 13) / 12 = 7 + 1 = 8

55*8 = 440

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5
Q

Counting multiples of integer A or B, but not of both, in a set of consecutive integers

A

Counting multiples of integer A or B, but not of both, in a set of consecutive integers

Number of multiples of A - Number of Multiples of B - 2(Number of Multiples of LCM)

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6
Q

Counting the multiples of integer A or B in a set of consecutive integers

A

Counting the multiples of integer A or B in a set of consecutive integers

(Number of multiples of A + Number of Multiples of B) - (Number of Multiples of the LCM A,B)

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7
Q

Counting consecutive multiples in a set

A

Counting consecutive multiples in a set

((Highest number divisible by given number - lowest number divisible by given number) /given number)) + 1

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8
Q

If the smallest or largest value in a data set is the mean, then

A

If the smallest or largest value in a data set is the mean, then

all values in the data set are the same

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9
Q

If range = 0 for a data set, then

A

If range = 0 for a data set, then

all values in the data set are the same

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10
Q

Using the average formula to find the sum of a set of numbers

A

Using the average formula to find the sum of a set of numbers

Sum = (Average * Number of Terms)

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11
Q
A
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12
Q

Finding the arithmetic mean with evenly spaced integers

A
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13
Q

Weighted Average Formula

A

Weighted Average Formula

(data point 1 * frequency of data point 1) + (data point 2 * frequency of data point 2) /total frequency of data points

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14
Q

Boundaries of Weighted Average

A

Boundaries of Weighted Average

The weighted average of two different data points will be closer to the data point with the greater number of observations with the greater weighted percentage.

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15
Q

Weighted Average Data Sufficiency Warning

A

Weighted Average Data Sufficiency Warning

You don’t need a total number when comparing weighted percentages

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16
Q

Weighted Time Average

A

Weighted Time Average

Total Distance/Total Time

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17
Q

Using Ratios and Fractions when solving Algebra

A
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18
Q

Median

A

Odd

Middle Number in a Set

Odd number of terms in a set - middle number

Even number of terms in a set - average of two middle numbers

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19
Q

Shortcut to finding median’s position in a large set

A

Shortcut to finding median in a large set

Odd number of terms in a set: (n+1/2) = position in set

Even number of terms in a set: (n+2/2) = position of the 2nd number in the set

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20
Q

Relationship between mean and median in an even set of numbers

A

Relationship between mean and median in an even set of numbers

mean = median in an even set of numbers

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21
Q

Mode

A

Mode

Number that occurs most frequently

Can be multiple if more than one number has the highest frequency

No mode if no number appears more than the other numbers

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22
Q

Range formula

A

Range formula

(highest number in a set - lowest number in a set)

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23
Q

Standard Deviation

A
  • Standard Deviation measures how far a set of values are from the mean
    • higher SD when further from mean
    • lower SD when closer to the mean
    • if numbers = mean, SD = 0
    • typically look at SD = 1 or 2 or 3, beyond that is very unlikely to occur
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24
Q

Adding or subtracting one constant value to each term in a data set does what to the standard deviation?

A

Adding or subtracting one constant value to each term in a data set does what to the standard deviation?

Nothing, but it does change the mean

Caveat: if SD = mean, it will decrease

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25
Q

If you multiply or divide the elements in a data set by a constant amount, the standard deviation will

A

If you multiply or divide the elements in a data set by a constant amount, the standard deviation will also be multiplied or divided by that same amount

26
Q

Adding numbers to a data set equal to the mean will to what to a positive standard deviation?

A

Adding numbers to a data set equal to the mean will to what to a positive standard deviation?

Decrease the standard deviation

27
Q

Comparing standard deviations through estimation

A

Comparing standard deviations through estimation

Given sets of numbers

  1. Find the mean in a set
  2. Determine absolute value of each number from the mean
  3. Add together
  4. Do this for each set, higher number = higher SD
28
Q

If given a data set of equal values, the standard deviation is

A

If given a data set of equal values, the standard deviation is zero.

29
Q

The standard deviation will be zero when

A
  1. Range of a set = 0
  2. Largest value of a set = mean
  3. Smallest value of a set = mean
30
Q

Relationship between mean and median in an even set of numbers

A

mean = median in an even set of numbers

31
Q

Solving for standard deviation and mean given two standard deviations and values:

Ata track meet, a measurement in the standing long jump of 12.5 feet was 3.5 standard deviations above the mean; a measurement of 2.5 feet was 1.5 standard deviations below the mean. What was the mean measuremnet of the standing long jump?

A

Solving for standard deviation and mean given two standard deviations and values:

Ata track meet, a measurement in the standing long jump of 12.5 feet was 3.5 standard deviations above the mean; a measurement of 2.5 feet was 1.5 standard deviations below the mean. What was the mean measuremnet of the standing long jump?

m = mean, s= standard deviation.

Equation 1: m + 3.5s = 12.5

^It is addition because it is above the standard deviation.

Equation 2: m - 1.5s = 2.5

^It is subtraction because it is below the standard deviation.

32
Q

Data Sufficiency: Averages with variables

A
33
Q

Sum of Arithmetic Progression of Consecutive Integers (a sequence of numbers that all differ by a given number)

A

Sum of Arithmetic Progression of Consecutive Integers (a sequence of numbers that all differ by a given number)

sum = average * quantity

average = (first integer + last integer)/2

quantity = (last integer - first integer/common difference) +1

Don’t forget the +1!

34
Q

What number should be removed from the list 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 so that the average of the remaining number is 6.9?

A

What number should be removed from the list 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 so that the average of the remaining number is 6.9?

12 - 2 + 1 = 11 numbers in the list

Average =7

Average is the median since it’s an odd set of numbers.

7*11 = 77

(77 - 8) / 10 = 6.9 so 8 needs to be removed

35
Q

Arithmetic mean of a consecutive set (bookend approach)

A

Arithmetic mean of a consecutive set (bookend approach)

(smallest integer + largest integer) / 2

36
Q

The cost of two items and the average price are sufficient to calculate the ratio or percentage.

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