Descriptive Stats

Question 1

What are measures of central tendency

Answer 1

Methods employed to determine central point in a given distribution

Question 2

Mode

Answer 2

• Corresponds to score that has highest frequency in a frequency distribution (visually its the
  highest value)
• For grouped distribution (histogram) its defined as the most frequently occurring interval (or
  the mid-point of that interval).
• It is applicable to almost all kinds of data-sets.

Question 3

Disadvantages of mode

Answer 3

• Lack of reliability
• Lack of precision in some cases

Question 4

Unimodal distribution

Answer 4

Distributions with single highest values

Question 5

Bimodal distribution

Answer 5

Distributions with two highest values

Question 6

Properties of mean

Answer 6

• If a constant is added (or subtracted) to every score in a distribution, the mean is increased
  (or decreased) by that constant.
• If every score is multiplied (or divided) by same constant, the mean will be multiplied (or
  divided) by the same constant.
• The sum of deviations from the mean will be equal to zero.
• The sum of squared deviations from the mean will be less than the sum of squared
  deviation around any other point in the distribution.

Question 7

Median

Answer 7

• Corresponds to determining middle score of a distribution, after arranging the data in ascending order.
• Corresponds to 50th percentile of a distribution.
• If a distribution has odd number of scores then median is literally the middle value in a distribution
  (provided the data is arranged in ascending order).
• If a distribution has even number of scores then median corresponds to average of two middle scores.
• In principle it divides a distribution into two equal halves.

Question 8

Disadvantages of median

Answer 8

• Its not applicable to all kinds of data-sets.
  (e.g., The median cannot be identified for categorical nominal data, as it cannot be
  logically ordered).
• Median is more informative if there are not many ties, and the distribution is skewed.

Question 9

Whathappens if there is a great deal of variability

Answer 9

No measure of central tendency is very representative of the scores, if the
distribution contains a great deal of variability.

Question 10

Different measures of variability

Answer 10

• Range
• Semi-Interquartile range
• Mean deviation
• Variance
• Standard deviation.

Question 11

Range

Answer 11

• Evaluates width of a distribution by subtracting lowest (lowest real limits) from highest
  score (highest real limits).
• The advantage is that it captures whole distribution.

Question 12

Disadvantages of range

Answer 12

• The major disadvantage of range is that, just like mode, it’s unreliable.
• The range can be changed drastically by removing or adding just one score in the
  distribution.

Question 13

Semi interquartile range

Answer 13

• This type of measure of variability can be used for open-ended distribution.
• The interquartile range is obtained by subtracting the 25th percentile from the 75th
  percentile. The semi-interquartile range is half the interquartile range.
• It does not get affected much by addition or subtraction of extreme scores from a
  distribution.

Question 14

Mean deviation

Answer 14

• It evaluates distance of every score from the mid point of the distribution and averages it

Question 15

Deviation score = ?

Answer 15

Mean - Individual score

Question 16

Mean deviation calculation

Answer 16

• Deviation score
• Mean of al deviation scores (take absolute deviation scores

Question 17

What is variance also referred to as

Answer 17

Mean square

Question 18

SS = ?

Answer 18

summation of (individual score - mean)^2

Question 19

Variance = ?

Answer 19

SS / N

Question 20

Standard deviation

Answer 20

• calculated by taking the root of teh variance
• also called the root mean square
• affected by scores having large deviations in distribution

Question 21

Properties of standard deviation

Answer 21

• If a constant is added (or subtracted) to every score in a distribution, the standard deviation
  is not affected.
• If every score is multiplied (or divided) by same constant, the standard deviation will be
  multiplied (or divided) by the same constant.
• The standard deviation from the mean will be smaller than the standard deviation from any
  other point in the distribution.

Question 22

What is positive skewness

Answer 22

A positive skewness represents asymmetrical
distribution with long right tail.

Question 23

What is negative skewness

Answer 23

A negative skewness represents
asymmetrical distribution with long left tail.

Question 24

Skewness = ?

Answer 24

Summation of (individual score - mean)^3 / N

Question 25

Central tendencies of a skewed distribution

Answer 25

- When the distribution is negatively skewed, the mean will be to the left of the median - When the distribution is positively skewed, the mean will be to the right of the median

Question 26

Important distinction

Answer 26

two distributions can both be symmetric (i.e., skewness equals zero), unimodal, and bell-shaped and yet not be identical in shape.

Question 27

How can kurtosis be measured

Answer 27

by raising deviations from the mean to the fourth power, taking their average, and then dividing by the square of the population variance.

Question 28

What does negative kurtosis indicate?

Answer 28

relatively thin tails and a lesser peakedness in the middle (a platykurtic distribution).

Question 29

What does positive kurtosis indicate

Answer 29

relatively fat tails and more peakedness in the middle of the distribution (a leptokurtic distribution),

Question 30

What is mesokurtic distribution?

Answer 30

If the kurtosis measure is set to zero for the normal (mesokurtic) distribution (by subtracting 3 in the above formula),

Question 31

What is kurtosis measured relative to?

Answer 31

relative to the kurtosis of a normal distribution, which is 3. Therefore, we are always interested in the “excess“ kurtosis,

Question 32

Excess kurtosis= ?

Answer 32

Excess kurtosis = sample kurtosis – 3

Question 33

What is kurtosis used for quantifying?

Answer 33

non-normality—the deviation from a normal distribution—of a distribution.

Question 34

What does a value of 3 or more indicate?

Answer 34

large departure from normality.

Question 35

What does a very small value of kurtosis indicate?

Answer 35

a deviation from normality, but it is considered as benign deviations.

Question 36

What is population analysis?

Answer 36

statistics applied to the whole data set

Question 37

What is ample analysis

Answer 37

Statistics applied ot a sub set of teh whole data

Question 38

Sample variance can be

Answer 38

Larger or smaller than population variance

Question 39

What equals to the population variance

Answer 39

If infinitely many sample variances are calculated and their average is taken

Question 40

What is degree of freedom

Answer 40

The number of deviations that are free to vary

Question 41

df = ?

Answer 41

N-1

Question 42

What is confidence interval?

Answer 42

the range of likely values of the parameter

Question 43

What is teh standard error of mean

Answer 43

the standard deviation divided by the square root of the number of samples.

Question 44

What is the variance

Answer 44

the average of the squared deviations from the mean across the number of samples.

Question 45

What are outliers

Answer 45

those observations that differ strongly (different properties) from the other data points in the sample of a population.

Question 46

Sources of outliers

Answer 46

Human errors (wrong data entry), Measurement errors (faulty system/ tool), Data manipulation error (Faulty data pre-processing), Sampling errors (creating samples from heterogeneous sources),

Question 47

Methods for indicating outliers

Answer 47

1. Tukey’s Fences (or Quartile method) 2. Z – Score 3. Local Outlier Function 4. Angle based Outlier Detection (AbOD) 5. Silhouette (K-Means Clustering) 6. Confidence Interval (CI) of fit

Question 48

What is H-spread

Answer 48

The length of the box and is equal to teh interquartile range, not teh semi-interquartile range

Question 49

What are the inner fences

Answer 49

The outermost limits of teh plot

Question 50

Inner fence is equal to

Answer 50

1.5 times the H spread

Question 50

The whiskers do not generally extend to the

Answer 50

inner fences

Question 51

End of upper and lower inner fences are known as

Answer 51

upper adjacent value and lower adjacent value