Data-based and statistical reasoning

Question 1

Measures if central tendency

Answer 1

provide a single value representation for the middle of a group data

Question 2

arithmetic mean or average

Answer 2

measure of central tendency that equally weighs all values; it is most affected by outliers

Question 3

median

Answer 3

the value that lies in the middle of the data set. Fifty percent of data points are above and below the median

Question 4

mode

Answer 4

the data point that appears most often; there may be multiple (or zero) modes in a data set

Question 5

Normal distribution

Answer 5

is symmetrical. The mean, median, and mode are all the same in the normal distribution.

Question 6

standard distribution

Answer 6

is normal distribution with a mean of zero and a standard deviation of one; it is used for most calculations. 68% of data points occur within one standard deviation of the mean, 95 % within tow, and 99% within three.

Question 7

Skewed distribution

Answer 7

have differences in their mean, median, and mode; the skew direction is the direction of the tail of the distribution.

Question 8

Bimodal distributions

Answer 8

have multiple peaks, although not necessarily multiple modes, strictly speaking. It may be useful to preform data analysis on the two groups separately.

Question 9

Range

Answer 9

is the difference between the largest and smallest values in a data set.

Question 10

Interquartile range

Answer 10

the difference between the value of the third quartile and first quartile; interquartile range can be used to determine outliers.

Question 11

Standard deviation

Answer 11

a measurement of variability about the mean; standard deviation can also be used to determine outlier

Question 12

outliers

Answer 12

may be a result of true population variability, measurement error, or a non-normal distribution

Question 13

independent events

Answer 13

the probability does not change based on outcomes of other events

Question 14

dependent events

Answer 14

changes depending on the outcomes of other evens

Question 15

mutually exclusive outcomes

Answer 15

cannot occur simultaneously

Question 16

exhaustive

Answer 16

there are no other possible outcomes

Question 17

hypothesis test

Answer 17

use a known distribution to determine wether a hypothesis of no difference (the null hypothesis) can be rejected

Question 18

statistical significance

Answer 18

comparison of p-value and selected significance level

Question 19

Confidence intervals

Answer 19

are a range of values about a sample mean that are used to estimate the population mean. A wider interval is associated with a higher confidence level.

Question 20

Graphs for categorical comparison

Answer 20

pie charts and bar charts

Question 21

graphs for numerical data

Answer 21

histograms and box plots (box and whisker plots)

Question 22

Linear, semilog, and log log plots

Answer 22

can be distinguished by their axes

Δy/Δx

Question 23

slope

Answer 23

can be calculated most easily form linear plots

Question 24

tables

Answer 24

contains related or unrelated categorical data.

Question 25

arithmetic mean

Answer 25

sum of x/n

Question 26

median position

Answer 26

(n=1)/2

Question 27

range

Answer 27

xmax - xmin

Question 28

interquartile range

Answer 28

IQR (Q3 - Q1)

Question 29

standard deviation

Answer 29

sqrt ( (xi - x)^2 / (n - 1) ) . x is the mean .

Question 30

probability of two independent events

Answer 30

P(A and B) = P(A) x P(B)

Question 31

probability of at least one event occurring

Answer 31

P(A or B) = P(A) + P(B) - P(A and B)