Part 4: Data Analysis Flashcards Preview

GRE Math > Part 4: Data Analysis > Flashcards

Flashcards in Part 4: Data Analysis Deck (42)
Loading flashcards...
1

Define central tendency.

Central tendency are the values in the center of data along a number line, which include the mean, the median, and the mode.

2

Define mean.

The arithmetic average.

3

Define median.

The value of the piece of data in the exact middle of a data series.

4

Define mode.

The value that occurs the most frequently in a list.

5

What is a measure of position?

It is the categorization of data in ordered groups, like percentiles and quartiles.

6

How do you determine a median in set containing an even number of values?

Average the two middle values.

7

What is a measure of dispersion?

It is the degree of spread in the data, including range, the interquartile range, and the standard deviation.

8

What is the range?

The difference between to two outliers in a set.

9

What is the interquartile range?

The difference between Q1 and Q3.

10

What is standard deviation?

It is the amount that each data differs from the mean. So, the greater the range, the greater the standard deviation.

11

How is standard deviation calculated?

1. Find the mean.
2. Find the difference between the mean and each value.
3. square each difference.
4. find the average of each squared difference.
5. Take the nonnegative square root of the average of the squared differences.

12

What is standardization?

It is the process where you subtract the mean then divide by the standard deviation to determine how many standard deviations away a piece of data is from the mean.

13

What are some characteristics of sets?

Non repeated and non ordered values.

14

If a set is represented by S, how do you represent the number of values in a set?

|S|

15

How is an empty set represented.

ø

16

What is the multiplication principle?

If there are k choices for the 1st object and m choice for the 2nd object, then there are km choices for their combination.

17

What is a permutation?

It is the number of ways n objects can be ordered, determined by multiplying n(n-1)(n-2)...1. Also representing as n!

18

How do you determine a permutation for a subset of objects? Where n is the number of objects in the set, and k is the number of items.

n!/(n - k!)

19

What is a combination?

It is selection of a set without worrying about ordering the items.

20

What is the formula for determining a combination?

n!/k!(n-k)!

21

What are the two different notations for selecting k objects from n?

nCk and (n k)

22

What is probability rule #1 for events E and F? (or)

P(E or F) = P(E) + P(F) - P (E and F)

23

What is probability rule #2 for events E and F? (mutually exclusive or)

If E and F are mutually exclusive, then the P(EorF) becomes P(E) + P(F)

24

Probability rule #3 for events E and F? (and)

If E and F are independent, then P(EandF) = P(E)P(F)

25

Exercise 1. The daily temperatures, in degrees Fahrenheit, for 10 days in May were 61, 62, 65, 65, 65, 68, 74, 74, 75, and 77.
(a) Find the mean, median, mode, and range of the temperatures.
(b) If each day had been 7 degrees warmer, what would have been the mean, median, mode, and range of those 10 temperatures?

Mean: 68.6 degrees
Median: 66.5 degrees
Mode: 65 degrees
Range: 16

b) 75.6, 73.5, 72, 16

26

Exercise 2. The numbers of passengers on 9 airline flights were 22, 33, 21, 28, 22, 31, 44, 50, and 19. The standard deviation of these 9 numbers is approximately equal to 10.22.
(a) Find the mean, median, mode, range, and interquartile range of the 9 numbers.
(b) If each flight had had 3 times as many passengers, what would have been the mean, median, mode, range, interquartile range, and standard deviation of the 9 numbers?
(c) If each flight had had 2 fewer passengers, what would have been the interquartile range and standard deviation of the 9 numbers?

19, 21, 22, 22, 28, 31, 33, 44, 50
Mean: 30
Median: 28
Mode: 22
Range: 31
Interquartile Range: 38.5 - 21.5 = 17
Difference from Mean:
8, 3, 9, 2, 8, 1, 14, 20, 11
Squares:
64, 9, 81, 4, 64, 1, 196, 400, 121
Average of the squares: 940/9 = 104.44444
Square root of the average:
10.22
Standard Deviation is 10.22


3x: 57, 63, 66, 66, 84, 93, 99, 132, 150
Mean: 90
Median: 84
Mode: 66
Range: 93
Interquartile Range: 115.5 - 64.5 = 51
Difference from the mean:
-24, 9, -27, -6, -24, 3, 42, 60, -33
Square of the differences:
576, 81, 729, 36, 576, 9, 1764, 3600, 1089
Average of the squares: 940
Square root of the average: 30.66
Standard Deviation: 30.66

Two Fewer: 20, 31, 19, 26, 20, 29, 42, 48, 17
Interquartile Range: 17
Standard Deviation: 10.22





27

Exercise 4. Find the mean and median of the values of the random variable X, whose relative frequency distribution is given in the following table.
0: 0.18
1: 0.33
2: 0.10
3: 0.06
4: 0.33

Mean: 2.03
Median: 1

28

Eight hundred insects were weighed, and the resulting measurements, in milligrams, are summarized in the following boxplot.
Data Analysis Figure 20
(a) What are the range, the three quartiles, and the interquartile range of the measurements?
(b) If the 80th percentile of the measurements is 130 milligrams, about how many measurements are between 126 milligrams and 130 milligrams?

Range: 146 - 105 = 41
Q1: 114
Q2: 118
Q3: 126
Interquartile Range: 126-114 = 12
b) 800 * 0.05 = 40

29

In how many different ways can the letters in the word STUDY be ordered?

5! = 5 * 4 * 3 * 2 * 1 = 120

30

Exercise 7. Martha invited 4 friends to go with her to the movies. There are 120 different ways in which they can sit together in a row of 5 seats, one person per seat. In how many of those ways is Martha sitting in the middle seat?

4! = 4 * 3 * 2 * 1 = 24