P2.2. Summary Measures

Question 1

compressing mass of data for better comprehension and description

Answer 1

Summary measures

Question 2

3 Category of Summary Measures:

Answer 2

• measures of central tendency
• measure of dispersion
• measures of location

Question 3

refers to “center” of the distribution of observations

three most common measures?

Answer 3

Measures of Central Tendency

1. mean
2. median
3. mode

Question 4

also known as average

Answer 4

(Arithmetic) MEAN

Question 5

• sensitive to extreme observations [outliers]
• involves all observation in its computation
• any change in the observation will change the mean value
• calculated for any quantitative variable
  * unit is the same as that of the original set of observations

Answer 5

(Arithmetic) MEAN

Question 6

• sum of the deviations of the observations from the mean is equal to zero
  [point of balance or center of gravity of the distribution]
• serves as basis for the computation of higher statistical methods

Answer 6

(Arithmetic) MEAN

Question 7

middle most value in a set of observations put in an array

Answer 7

MEDIAN

Question 8

• always exists and is unique
• not influence by outliers
• does not make use of all the observations in its computation
• can be calculated for any quantitative variable
• can be calculated for some qualitative variable

Answer 8

MEDIAN

Question 9

• most frequently occurring value in a set of observation
• no calculations needed
• determined for any type of variable

it is possible to have:
* no mode
* unimodal; bimodal; multimodal

Answer 9

MODE

Question 10

• gives information as to the tendency of values to clump together
• tools describing the variability of the observations: HOMOGENOUS & HETEROGENOUS
• may be used for quantitative variables only

four most common measures?

Answer 10

Measures of Dispersion

1. range
2. variance
3. standard deviation
4. coefficient variation

Question 11

• simplest measure of location
• highest observation – lowest observation
• does not tell anything about the observation between these two extreme observations
• may be used for quantitative variables

no observations given.

Answer 11

RANGE

Question 12

• measure of variability that takes the mean as the reference point
• involves all observations
• unit: squared unit of the original set of observations
• hard to interpret

no observations given.

Answer 12

VARIANCE

Question 13

• square root of variance
• unit is the same as that of the original set of observations

Answer 13

STANDARD DEVIATION

Question 14

* expresses the SD as percentage of mean

most appropriate when:
* unit of measurement of variables being compared are different
* *means being compared are markedly different *

Answer 14

COEFFICIENT VARIATION

Question 15

measure of dispersion is low or small

Answer 15

homogenous distribution of observation

Question 16

measure of dispersion is high or large

Answer 16

heterogenous distribution of observation

Question 17

• determines the location/ position of particular value in an array of distribution
• provide more details about a part of the entire distribution of observations in a given data
• used for both qualitative and quantitative data

three most common measures?

Answer 17

Measures of Location

1. quartiles
2. deciles
3. percentiles

Question 18

points of distribution that divides the observation into 4 equal parts

Answer 18

QUARTILES

Question 19

points of distribution that divides the observation into 10 equal parts

Answer 19

DECILES

Question 20

points of distribution that divides the observation into 100 equal parts

Answer 20

PERCENTILES

Question 21

• calculated by dividing the cumulative frequency by the total no. of observations (n)
• then multiply it by 100

Answer 21

CUMULATIVE PERCENTAGE

To find the value of particular percentile, refer to the cumulative percentage equal to or higher than the percentile in question