Describing Data

Question 1

Qualitative description properties - 3

Answer 1

• Shape
• Location
• Dispersion

Question 2

Shape - 5 (DEF + LIST)

Answer 2

• Make a smooth approximation of the histogram
• Shape of smooth curve can give idea of data distribution
• • Symmetrical
• • Right/Left Skewed
• • Uniform

Question 3

Location - 1

Answer 3

• The position of the peak on the x axis

Question 4

Dispersion - 1

Answer 4

• How much the data spreads on the x axis

Question 5

Numerical summeries - 1

Answer 5

• Describe the data distribution with numerical values

Question 6

Measures of center - 4 (DEF + LIST)

Answer 6

• Value which stands at the center or middle of the data set
• • Mean
• • Median
• • Mode

Question 7

Mean - 4

Answer 7

• Mean is average, computed by sum of all elements divided by number of elements.
• Mean is not robust, it is affected from outliers
• Sample mean is x bar
• Population mean is μ (Mu)

Question 8

Median - 2

Answer 8

• Middle value of the data set after sorting

- Is robust, not affected from outliers

Question 9

Mode - 4

Answer 9

• Value that occurs with highest frequency
• Mostly used for nominal data, not as much for numerical
• The number of modes defines how modal a data set is:
• • 1 = Unimodal
• • 2 = Bimodal
• • 3 + = Multimodal
• When a graph has multiple peaks it follows the same logic

Question 10

Measures of variation - 3

Answer 10

• Standard deviation
• Variance
• Range

Question 11

Variance - 3

Answer 11

• Is the average quadratic deviation from the average
• The sample variance is s^2
• The population variance is σ^2 (Sigma squared)

Question 12

Standard deviation - 4

Answer 12

• Measures how much the values deviate from the sample mean.
• It is the square root of the variance
• The sample standard deviation is s
• The population standard deviation is σ (Sigma)

Question 13

Range - 2

Answer 13

• Maximum - minimum

- It is very sensitive to extreme values because it uses only two values

Question 14

Percentiles and Quartiles - 5 (DEF + LIST)

Answer 14

• Percentile Pi indicates that i% of data is smaller than Pi and (100 - i)% is larger than Pi
• Quartiles divide data set in four groups, which approximately have 25% of values
• • Q1 = P25
• • Q2 = P50 = Median
• • Q3 = P75

Question 15

5 Number Summary - 6 (DEF + LIST)

Answer 15

• Graphical representation is boxplot
• • Minimum
• • First Quartile
• • Median
• • Third Quartile
• • Maximum

Question 16

Interquartile range - 1

Answer 16

• IQR is the difference between the third and first quartile

Question 17

Boxplot - 2

Answer 17

• Is graphical representation of 5 num summary
• Provides information on distribution (If median is not center of box and/or outliers than distribution is asymmetrical)

Question 18

Whiskers Boxplot - 2

Answer 18

• Lines extending from the box

- Are defined as a value which exceeds x * IQR

Question 19

Outliers - 1

Answer 19

• Points which are not included between the whiskers