Lecture 2- Summarizing data: Descriptive statistics

Question 1

What are the three order of measurement of average?

Answer 1

First order: Measures of central tendency

• Second Order: Measures of dispersion
• Third order: Measures of skewness and kurtosis

Question 2

What are measures of central tendency?

Answer 2

-yield information about

“particular places or locations in a group of numbers.”

Question 3

What are the different types of central tendency?

Answer 3

• Mean
• Mode
• Median
• Percentiles
• Quartitles

Question 4

What is the arithmetic mean?

Answer 4

• Mean is the average of a group of numbers
• Applicable for interval and ratio data only
• Affected by extreme outliers which reduce its reliability

Question 5

What is the mode and the different types of mode?

Answer 5

• Most frequently occurring dataset
• Applicable for all levels of data

-Bimodal:– In a tie for the most frequently occurring value, two
modes are listed

-Multimodal: Data sets that contain more than two modes

Question 6

What is the median and how to work it out?

Answer 6

• Middle number in an order array of numbers
• If N is odd (N+1)/2
• If even so they have the same amount of number each side of the dataset

Question 7

What are quartiles and examples of them

Answer 7

• Quartile - measures of central tendency that divide a group of data into four
subgroups

• Q1: 25% of the data set is below the first quartile
• Q2: 50% of the data set is below the second quartile
• Q3: 75% of the data set is below the third quartile

Question 8

How to work out quartiles?

Answer 8

• Find a quarter of the number in the dataset for the 1st
• FInd half of the number for Q2
• Find 3/4 of the number for Q3

Question 9

What is the measures of dispersion?

Answer 9

-tools that describe the
spread or the dispersion of a set of data.

–Range 
– Inter-quartile Range 
–Variance 
– Standard Deviation
–Coefficient of Variation

Question 10

What is the range?

Answer 10

-The difference between the largest and the smallest
values in a set of data

Advantage:– easy to compute (ignore how the data
is distributed)

Disadvantage:is affected by extreme values

Question 11

What is the Inter-quartile range?

Answer 11

• range of values between the first and third quartiles

- Q3-Q1 to find the IQR

Question 12

How to work out deviation?

Answer 12

-Subtracting the mean from each data value gives the
deviation from the mean (X - µ)

• An examination of deviation from the mean can reveal
information about the variability of the data

-The Sum of Deviation from the arithmetic mean is always zero: Sum (X - µ) = 0

Question 13

What is the standard deviation and the variance?

Answer 13

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Question 14

formula for variance and standard deviation

Answer 14

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Question 15

What does the standard deviation show?

Answer 15

-A low standard deviation means that most of the numbers are very close to the average.

• A high standard deviation means that the numbers are spread out.

• A standard deviation closer to zero, indicates that the points are
closer to the mean.

Question 16

What is the empirical rule?

Answer 16

-68% of the population members lie within one standard deviation of the
mean

-approximately 95% lie within two standard deviations
of the mean

-approximately 99.7% lie within three standard deviations of the mean.

+ and - the mean

Question 17

What is the coefficient of variation (CV)?

Answer 17

Ratio of the standard deviation to the mean, expressed as a percentage

-useful when comparing Std Dev computed
from data with different means

• Measurement of relative dispersion

Question 18

What is the formula for coefficient of variation?

Answer 18

CV=standard deviation/mean x 100

Question 19

Measures of shape

Answer 19

Symmetrical – the right half is a mirror image of the
left half

• Skewness – shows that the distribution lacks
symmetry; used to denote the data is sparse at one
end, and piled at the other end
– Absence of symmetry
– Extreme values in one side of a distribution

Question 20

Coefficient of skewness

Answer 20

formulas for skewness

Question 21

When do you know if something is positive, negative or not skewed?

Answer 21

If Sk < 0, the distribution is negatively skewed (skewed to the left).

• If Sk = 0, the distribution is symmetric (not skewed).
• If Sk > 0, the distribution is positively skewed (skewed to the right).

Question 22

Mean, median mode of skewness

Answer 22

• If the mean is greater than the mode, the distribution is positively skewed.
• If the mean is less than the mode, the distribution is negatively skewed.
• If the mean is greater than the median, the distribution is positively skewed.
• If the mean is less than the median, the distribution is negatively skewed.

Question 23

What are the different types of kurtosis?

Answer 23

Peakedness of a distribution
• Leptokurtic: high and thin
• Mesokurtic: normal in shape
• Platykurtic: flat and spread out

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