Statistics

Last golden tips

- we can find the weighted average by only having the two data points averages and the ratio of the quantities to each other. - median = the mean in evenly spaced set - adding or subtracting same value form a set does not change the standard deviation...HOWEVER Multiplying or dividing a set with the same number, will change the standard deviation - if we have 2 averages, and the weighted average, then we can find the quantities of the 2 variables using the scale method

is having value of 2 data points, and the ratio of the quantities of the two data points, enough to find the weighted average?

yes. Given the value of two data points and the ratio of the quantity of the two data points, we can calculate the weighted average of the two data points. that's because we will be able to express one variable in terms of the other.

Tom is 10th in line, and Sara is 50th in line. How many people are between Tom and Sara? 38 39 40 41 42

39 since the range is excluding of the endpoints, simply subtract the large from the small number and subtract 1 in the end, 50-10-1=39

What info do you need to have in order to solve weighted average Qs

Find -Weighted average -- 2 averages and ratio of the objects amounts. ---example 7 in TTP test 3 - amounts of objects --

Question 2 - "which is better to use, fractions or decimals..?" Set X = {0.5, 3/4, 1/2, 5/4, 0.6, 1.2}. When the median is subtracted from the average (arithmetic mean), the resulting value is 0.125 0.25 0.375 0.5 0.675

a i converted all terms to fractions and that made it more difficult. from ttp; The first thing we want to do is get all of our values in either decimal or fraction form. While we usually prefer to work with fractions, decimals may actually be easier in this case, especially because the fractions will easily convert to decimals.

Question 12 - "mean = medium when.." Set N consists of a number of consecutive multiples of 3. What is the median of set N? 1) The range of set N is 66. 2) The mean of set N is 36.

b In an evenly spaced set, the mean equals the median, so the median is also 36. Statement two alone is sufficient.

how can you find the position of the median in a odd or even set of numbers?

counts of the members in the set + 1 / 2 ex; numbers in set is 4, the median position will be 2.5, meaning sum the 2nd and 3rd position and divide them by half. numbers in set is 3, then position of median is 2.

---average formula for evenly spaced set--- How many multiples of 2 are there between 51 and 99, inclusive? 21 22 23 24 25

immediately apply the rule. saves much time.

how can you compare the standard deviation of two sets with equal number of data points without fully computing it?

you'll never actually need to calculate standard deviation on the GMAT To compare the standard deviation among data sets that have an equal number of data points, perform the following steps: Step 1: Determine the mean of each set. Step 2: For each individual set, determine the absolute difference between the mean of that set and each data point in that set. Step 3: Sum the differences obtained from each individual set. The set with the greater sum has the greater standard deviation.

The average (arithmetic mean) age of a group of 10 workers is 46. If the average (arithmetic mean) age of 6 of the workers is 30, what is the average (arithmetic mean) age of the other 4 workers? 50 55 60 65 70

⇒180+4x=460⇒4x=280⇒x=70

What are the main topics in Statistics Qs?

1) Average (Arithmetic Mean) 2) Median 3) Mode 4) Range 5) Standard deviation

What are two effecient ways to find the average in an evenly spaced set?

1- bookend method; sum the smallest and largest numbers of the range, then divide by 2 2- find the median; works better when we have the numbers in the middle

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? 38 39 40 41 42

40 since the range is inclusive only for one of the endpoints, simply subtract the large from the small number, 50-10=40

Maximization/Minimization Average Problems; At a particular state fair, out of 40 children, the average number of goldfish won was 6. Four children won 3 goldfish each, six won 8 goldfish each, five won 2 goldfish each, and four won no goldfish. If each remaining child won at least 4 goldfish, which of the following could be the maximum number of goldfish won by a particular child? 88 90 94 98 100

90 Note; If x and y are positive integers and x + y = 10, how can we be sure of assigning the maximum possible value to y? The answer is to make sure that x has the lowest possible value. Since x and y are positive integers, the smallest that x can be is 1. Correspondingly, 9 would be the largest possible value of y. Some average problems may require us to use this type of logic. It follows that 20 children × 4 goldfish per child = 80 goldfish = the minimum number of goldfish won by 20 children. We are now left with 170 goldfish - 80 goldfish = 90 goldfish (for the last child).

how to find the the high and low values of standard deviations?

High Value=mean+x(sd) Low Value=mean−x(sd) In these formulas, mean is the mean of the set, sd is the standard deviation of the set, and x is the number of standard deviations from the mean that we want to compute.

Question 11 - "common sense approach" The average (arithmetic mean) of 8 consecutive integers is 20.5. What is the average of the first 7 of these integers? 21 20 19 18 17

b This problem can also be solved without using algebra. We know that the average of a group of numbers is the balance point among those numbers. If we have 8 consecutive integers with an average of 20.5, then we know that 20.5 is the average of the two middle numbers in the series. Remember, when we have an even number of numbers, the average of those numbers is the average of the two middle numbers. We can work up and down from 20.5 to construct the set of numbers. 17 18 19 20 (20.5) 21 22 23 24 Now that we have our numbers, we can take the average of the first 7 of them: 17 18 19 20 21 22 23. The average of an odd set of consecutive numbers is the middle number. So, the average is 20. 17 18 19 (20) 21 22 23

Question 11 - "bookend approach" The average (arithmetic mean) of 8 consecutive integers is 20.5. What is the average of the first 7 of these integers? 21 20 19 18 17

b see the next card for faster alternative approach Because we are dealing with consecutive integers, we can use the "bookend" approach to get the average. ⇒average = (smallest integer + largest integer)/2 The smallest integer equals "x" and the largest equals "x + 7," so we have ⇒20.5=x + (x + 7)/2 ⇒41=2x+7 →2x=34 ⇒x=17 Since we know x equals 17 (the first consecutive integer), we can calculate the average of the first seven numbers using the following average formula: ⇒average=sum/quantity ⇒average=(17+18+19+20+21+22+23)/7 ⇒average=140/7=20

in your own words, explain the "bookend approach" and the "balance point method" methods

bookend; use it when we have an evenly spaced set of numbers. they can be even, odd, consecutive or not. it says that the average = large number - small number /2 balance point; see picture use it to visualize the average and the other members of the set of odd or even number of set members.

Question 3 - "what does consecutive really means?" If x < y < z, what is the average of the integers x, y, and z? 1) x, y, and z are consecutive integers. 2) z = 2x

c Since we know from statement one that z = x + 2 and from statement two that z = 2x, we can let x + 2 = 2x and determine that x = 2. Therefore, x = 2, y = 3, and z = 4, all of which yields an average for the three integers of 3.

Question 10 - "all in the footnotes" What is the average of the average of the first 12 positive multiples of 8 and the average of the first 6 positive multiples of 20? 49 52 55 61 70

d NOTE: This question is not the same as asking for the average of the sum of the first 12 multiples of 8 and the sum of the first 6 multiples of 20. In this case, you would add the first 12 multiples of 8 and the first 6 multiples of 20 and then divide by 18 (the total number of numbers in the sum).

Question 15 - "study the scenarios" Three cars were purchased from Tom's car lot on a certain day. If the average (arithmetic mean) purchase price of a car was $20,000, what was the median purchase price of the three cars that were purchased? 1) The purchase price of one car was $20,000. 2) The sum of the purchase prices of two cars was $40,000.

d really think about it. study the scenarios in each option.