GMAT Prep Now: Statistics Module (All Videos)

Sum of n numbers =

(mean)(n)

Variance

(standard deviation)²

Video 10 - Lesson: More Standard Deviation

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Video 9 - Question: Comparing Standard Deviations Is the standard deviation of set A greater than the standard deviation of set B? 1) Every number in set A is a multiple of 7 2) Every number in set B is a multiple of 11

1) {7,7,7,7} = SD of 0 {7, 70, 140} = SD > 0 Inconclusive 2) B could be {11, 11, 11, 11} (SD of 0) or { 11, 22, 33, 44} = SD > 0 Inconclusive Both = Inconclusive (could be equal, a > b, b > a)

{1,2,3,4} Find the mode

1,2,3,4

Video 4 Question: Greatest of 5 numbers Set S contains five positive integers. If the average (arithmetic mean) of set S is 8, the median is 5, and the mode is 4, then what is the greatest possible number in set S? A) 21 B) 22 C) 23 D) 24 E) 25

1. 5 spaces (least to greatest) 2. asterisk = greatest number 3. Mode is 4 = two 4's A.

Out of these data ranges A: {4, 4, 5, 6, 7, 7, 8} B: {5, 6, 6, 6, 6, 7, 7} C: {1, 1, 3, 6, 7, 11, 14} 1. Greatest standard deviation = 2. Least Standard deviation =

1. C. 2. B.

Example 1 of weighted averages

1. There are six 20-year-old men 2. There are six 40-year-old women What will be the average age of the combined population

Example of units of standard deviation Set A: {5, 7, 8, 9, 11, 14, 15, 15, 18, 18} If set A has a mean of 12 and a standard deviation of 4.4, how many numbers in set A are within 1 unit of standard deviation from the mean?

4.4 = 1 unit of standard deviation 1. Draw the number line 2. Mark the mean in the middle 3. Mark the spot 1 unit of standard deviation to the right of the mean (4.4 units over to the right) 16.4 = 1 unit of SD above the mean 20.8 = 2 units of SD above the mean 7.6 = 1 unit of SD below the mean 3.2 = 2 units of SD below the mean Final = How many numbers are between 7.6 and 16.4? (8, 9, 11, 14, 15, 15) = six numbers

Video 5 Lesson: When Mean = Median

:)

The term "average" on the GMAT can also be used interchangeably with _____ & _____

Arithmetic Mean Mean

Answer

Average age = 30

Video 3 Question: Ages of Ann, Bea and Cho If the average (arithmetic mean) age of Ann, Bea and Cho is 10 years, what is their median age? 1) Ann is 11 years old 2) Bea is 10 years old

B.

Video 8 - Question: Ordering Standard Deviations I. {85.3, 85.4, 85.5} II. {7, 10, 10} III. {124, 125, 126} Which of the following is the correct ordering of the above sets from the greatest standard deviation to the least? A) I, III, II B) II, III, I C) III, II, I D) I, III, II E) III, I, II

B.

Video 16 Question: Combined Test Scores In a certain school, the girls had an average (arithmetic mean) test score of 144, and the boys had an average score of 120. If the average score among the entire school was 128, what is the ratio of the number of boys to girls? A) 4 to 1 B) 3 to 1 C) 2 to 1 D) 3 to 2 E) 4 to 3

C.

Video 17 Question: Truth About Sets A & B Set A consists of 2 positive integers, and Set B consists of 3 positive integers. If the median of set A is 5, and the average (arithmetic mean) of set B is 3, which of the following must be true? I. The median of the combined sets is less than 5 II. The mean of the combined sets is less than 4 III. The median of set B is less than 5 A) II only B) III only C) I and II D) II and III E) I, II and III

D.

Video 2 Question: Adding k to a Set The average (arithmetic mean) of four numbers is 8. When k is added to the four numbers, the new average is 10. What is the value of k? A) 8 B) 12 C) 14 D) 16 E) 18

E.

Example: {2, 4, 6, 8, 10}

Evenly spaced by 2 Mean = 6 Median = 6

If the median and mean are equal, then the numbers in that set must be evenly spaced.

False The numbers may or may not be evenly spaced if the mean = median

How to find Standard Deviation (formula)

GMAT will never use this formula Questions with SD will test on what SD measures.

Units of standard deviation

If the standard deviation of a set of numbers is k, then k = 1 unit of standard deviation

Well, that's confusing. In general, what does (x₁ - m)² + (x₂ - m)² ..... mean? Also, why do we divide these numbers by n (the number of values)?

In short, it tells us how far each number in the set is away from the mean 1-4 = -3 units away from 4 3-4 = 1 unit away from 4 Then we square those numbers and divide it by 5 To undo the square, we square root everything

Bus Tour example

Let's say that the bus driver stated that there were - 10 people - average age = 22 Just knowing the average age doesn't give us a definitive way to know everyone's age individually.

Example of the informal definition approach for problem solving {1, 3, 4, 6, 6}

Mean = 4 1 - 4 = -3 (absolute value = 3) 4 -3 = 1 etc. Take all the distances from the mean and add them together. Now, divide it by 5 (the number of values in the data set)

Find the mode {7,4,6,8,6]

Mode = 6

Can a standard deviation be less than 0?

No It must be greater than or equal to 0

Set {1, 1, 7, 8 , 18}

Not evenly spaced, but median = mean

When n (the amount of numbers) is odd: the median = When n is even: median =

Odd = middle number Even = average of the 2 middle numbers

Video 6 Lesson: Weighted Averages

Pig destroyer

Informal definition of standard deviation

Standard Deviation = the average distance the data values are away from the mean

Mean formula

Sum of n numbers ÷ n

{4,5,5,5,6,6,6,6,7,7,9,300} Mean, Median, and Mode

The mean is greatly influenced by abnormally large/small numbers. 300 in this example 300 had no effect on median and mode

Median

The middlemost value when the numbers are arranged in ascending order

Mode

The number that occurs most frequently

When is the standard deviation 0?

When every number is the same {22, 22, 22, 22}

Properties of weighted averages

When you remove people from a population, it shifts the balance (which will effect the average)

Now let's say that the Bust tour guide stated the following information: - 10 people - average age = 22 - range = 79

With the range, while it gives us an accurate way to have a more condensed data set of possible ages, the numbers within the range set can vary.

If the numbers in a set are evenly spaced, then the mean and median of that set are _____

equal

Range

greatest vale - least value