Chpt 3- Numerically Summarizing Data

Question 1

arithmetic mean

Answer 1

adding all the values of a variable in a data set, then dividing by the number of observations.
(average)

Question 2

median

Answer 2

The value that lies in the middle of the data when arranged in ascending order. (M)

If the number of observation is even, then the median is the data set value that falls at the mean of the observations between n/2 and n/2 +1 positions. (The average of the two middle values on the ascending list)

If the number of observations is odd, then the median is the data set value that falls at (n+1)/2. (The middle value on the ascending list)

Question 3

resistant statistic

Answer 3

a numerical data summary is described as resistant if extreme values do not affect its value substantially.

In a given data set, the mean may be resistant but not the median, or visa versa.

Question 4

mode

Answer 4

the mode of a variable is the most frequent observation(s) that occurs in the data set.

Question 5

Pareto chart

Answer 5

bar graph that organizes data by frequency, or relative frequency.

Either ascending or descending.

Question 6

Pareto chart

Answer 6

bar graph that organizes data by ascending or descending frequency, or relative frequency.

Question 7

Side-by-side bar graph

Answer 7

compares data for more than one variable.

Question 8

Ogive graph

Answer 8

a graph representing cumulative frequency or relative frequency of the data.

Question 9

frequency polygon

Answer 9

connects data points with a line.

Question 10

Range

Answer 10

The range (R) of a variable is the difference between the largest and smallest data values.

R = largest data value (minus) smallest data value

Question 11

dispersion

Answer 11

the degree to which the data are spread out

Question 12

population standard deviation around a variable

Answer 12

square root of the sum of squared deviations about the population mean, divided by

Question 13

The Empirical Rule

Answer 13

If a distribution is roughly bell-shaped, then…
99.7% fall within 3 standard deviations of the mean.
95% fall within 2 standard deviations of the mean.
68% fall within 1 standard deviation of the mean.

Question 14

modal class

Answer 14

The class of data that has the highest frequency

Question 15

z-score

Answer 15

the distance that a data value is from the mean in terms of the number of standard deviations (the number of standard deviations from the mean).

Unitless
Has a mean (center) of 0 and a standard deviation (spread) of 1.

Question 16

kth percentile

Answer 16

Pk of a set of data is a value such that k percent of the observations are less than or equal to the value.

Question 17

quartiles

Answer 17

divide data sets into fourths.

To find quartiles…
- Arrange data in ascending order
- Determine the median, M, or Q2
- Divide the data set into halves (below M and above M)
Q1 is the median of the bottom half. Q3 is the median of the top half.

Question 18

Interquartile range IQR

Answer 18

the range of the middle 50% of the observations.

IQR = Q3 - Q1

Question 19

outliers

Answer 19

extreme observations in the data set.

(Median and IQR are resistant to outliers. Mean and Standard Deviation are NOT resistant to outliers.)

Question 20

Fences

Answer 20

Fences are a way to check for outliers using quartiles.

Lower fence = Q1 - 1.5(IQR)
Upper fence= Q3 + 1.5(IQR)

Outside either fence indicates an outlier.

Question 21

Five-Number Summary

Answer 21

Minimum, Q1, Q2 (median M), Q3, Maximum