Describing Data

Question 1

sample mean (3)

Answer 1

• sum of all observations in a sample divided by n, the number of observations
• varies, depending on the composition of the sample
• symbol: Y bar

Question 2

standard deviation (4)

Answer 2

• common measure of the spread of a distribution and indicates how far the different measurements typically are from the mean
• 67% of the data lies within Y bar +/- s and 95% of data lies within Y bar +/- 2s
• the square root of the variance
• symbol: s

Question 3

variance (2)

Answer 3

• a measure of spread of data from the mean
• symbol (sample): s^2
• symbol (population): σ (sigma)

Question 4

deviation (2)

Answer 4

• the difference between a measurement and the mean

- formula: Yi - Y bar

Question 5

sum of squares

Answer 5

• summation in the numerator of the variance formula

Question 6

what is the general rule for rounding answers?

Answer 6

• round descriptive statistics to one decimal place more than the measurements themselves

Question 7

coefficient of variation (4)

Answer 7

• standard deviation expressed as a percentage of the mean
• CV = (s/Y bar) x 100%
• higher CV means more variability and lower CV means individuals are more similar relative to the mean
• only applicable if all measurements are > or = to 0

Question 8

how do you calculate mean from a frequency table? (3)

Answer 8

1. calculate the sample size by adding all the frequencies
2. multiply each value by their frequency before adding them together
3. divide #2 by #1

Question 9

how do you calculate standard deviation from a frequency table?

Answer 9

• when subtracting the mean from each value, multiply it by its frequency

Question 10

median (2)

Answer 10

• middle measurement of a set of observations

- median = Y([n+1]/2)

Question 11

interquartile range (2)

Answer 11

• difference between the third and first quartiles of the data and spans the middle 50% of the data
• IQR = third quartile - first quartile

Question 12

first quartile

Answer 12

• middle value of the measurements lying below the median

Question 13

second quartile

Answer 13

• median

Question 14

third quartile

Answer 14

• middle value of the measurements larger than the median

Question 15

box plot (4)

Answer 15

• displays median and interquartile range
• lower and upper edges of the box are the first and third quartiles, thus the IQR is visualized by the span of the box
• lines extend vertically from the box to represent the “non-extreme” values in the data
• “extreme” values are represented as isolated dots

Question 16

“extreme” values

Answer 16

• values lying farther from the box edge than 1.5x the IQR

Question 17

mean vs median (2)

Answer 17

• median is the middle value of the data, less sensitive to extreme observations and is a more informative descriptor of the typical observation in those cases
• mean is the centre of gravity or balance, greatly affected by skewed distributions but better mathematical properties and is the more reliable measure to estimate

Question 18

SD vs IQR (2)

Answer 18

• SD reflects the variation among all of the data points, but is very sensitive to extreme observations
• IQR is a better indicator of spread of the main part of the distribution when data is strongly skewed to one side or there are extreme observations

Question 19

percentile of a measurement

Answer 19

• specifies the % of observations less than or equal to it, while other observations exceed it

Question 20

quantile of a measurement

Answer 20

• specifies the fraction of observations less than or equal to it

Question 21

cumulative relative frequency

Answer 21

• at a given measurement, is the fraction of observations less than or equal to that measurement

Question 22

what are the 2 common descriptions of data

Answer 22

1. location (or central tendency)

2. width (spread)

Question 23

what are the measures of location? (3)

Answer 23

• mean
• mode
• median

Question 24

population mean

Answer 24

• symbol: μ

- fixed value that we try to predict using the sample mean

Question 25

what are the measures of width? (4)

Answer 25

• range
• variance
• standard deviation
• coefficient of variation

Question 26

range (3)

Answer 26

• maximum minus the minimum
• poor measure of distribution width as small samples tend to give lower estimates of the range
• biased estimator of the the true range of the population (tends to be lower)

Question 27

skew

Answer 27

• measurement of asymmetry and refers to the pointy tail of skewed distributions

Question 28

adding/multiplying mean by constant, c

Answer 28

adding: Y + c
multiplying: Y * c

Question 29

adding/multiplying SD by constant, c

Answer 29

adding: s
multiplying: |c| * s

Question 30

adding/multiplying variance by constant, c

Answer 30

adding: s^2
multiplying: s^2 * c^2

Question 31

adding/multiplying median by constant, c

Answer 31

adding: M + c
multiplying: M * c

Question 32

adding/multiplying IQR by constant, c

Answer 32

adding: IQR
multiplying: |c| * IQR