QU1 chapter 3 notes

Question 1

What are the measures of central tendency

Answer 1

1. Arithmetic mean
2. median
3. mode
4. geometric mean

Question 2

describe arithmetic mean

Answer 2

• most commonly used measure of central tendency
• affected by extreme values
• do not use when data has extreme values

Question 3

how do you calculate arithmetic mean

Answer 3

sum of all numerical values then divide them by total number of observations

Question 4

describe median and calculate

Answer 4

• the middle value in an ordered array of data
• not affected by extreme values (outliers)
• if N is odd, then median is the middle number
• if N is even, then median is the average of the two middle numbers

Question 5

describe mode

Answer 5

the value in a set of data that appears most frequently

• not affected by extreme value
• used for descriptive purposes only (because it is more variable from sample to sample than other measures of central tendency)

Question 6

Describe geometric mean

Answer 6

help measure the status of an investment over time

- useful measure of the rate of change or a variable over time

Question 7

how do you calculate the geometric mean

Answer 7

multiply all the numbers together then to the exponent of 1/number of variables

Question 8

What is a quartiles

Answer 8

• most widely used measure of noncentral location
• used to describe properties of large sets of numerical data
• whereas the median is the value that splits the ordered array in half (50% of the observations are smaller and 50% are larger), quartiles are descriptive measures that split the ordered data into 4 quarters

Question 9

how do you compute quartiles
Computer the quartiles of the 3 year annualized returns after removing CI signature Select Canadian Seg I. The ordered array is:

5.34 6.15 6.85 7.11 9.05 10.16 10.79 11.35 13.43 13.43 13.93 17.1

Answer 9

Solution:
Q1 = (n+1)/4 ordered observation
= 13 + 1 / 4 = 3.5 ordered observation

Step 2: Q1 is approximated by using the arithmetic mean of the third and fourth ordered observations

Q1 = 6.85 + 7.11 / 2 = 6.98

In addition:
Q3 = 3(n+1)/4 ordered observation
3(13+1) /4 = 10.5 ordered observation

Therefore, using rule 2, Q3 is approximated by the arithmetic mean of the 10th and the 11 ordered observation

Q3 = 13.43 + 13.43 /2 
	= 13.43

Question 10

What are the measures of variation

Answer 10

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

Question 11

describe range

Answer 11

difference between the largest and the smallest observation

- ignores the way in which data are distributed

Question 12

what is interquartile range

Answer 12

• measure of variation
• also called mid-spread (spread in the middle 50%)
• not affected by extreme values

Question 13

How do you calculate interquartile range

Answer 13

difference between the first and third quartiles

Question 14

what is variance

Answer 14

• important measure of variation

- shows variation about the mean

Question 15

how do you calculate the sample variance

Answer 15

sum of the squared differences around the arithmetic mean divided by the sample size minus 1

Question 16

what is standard deviation

Answer 16

• most important measure of variation
• shows variation about the mean
• has the same units s the original data
• most practical and most commonly used measure of variation

Question 17

which measure of variation is most important

Answer 17

standard deviation

Question 18

how do you calculate standard deviation

Answer 18

square root of the sum of the squared differences around the arithmetic mean divided by the sample size minus

Question 19

What is coefficient of variation (CV)

Answer 19

• measures relative variation
• expressed as %
• higher value indicates greater variability relative to the mean
• used to compare two or more sets of data measures in different units
• measures the scatter in the data relative to the mean

Question 20

what is the calculation for coefficient of variation

Answer 20

CV = (standard deviation/mean) 100%

Question 21

What is shape of a distribution

Answer 21

• describes how data is distributed
• measures shape
• can be symmetric or skewed

Question 22

If the mean and median are equal the shape will be

Answer 22

symmetric (or zero skewed)

Question 23

if the mean exceeds the median, the shape is

Answer 23

Right Skewed

- the variable is called positive or right skewed

Question 24

if the median exceeds the mean the shape is

Answer 24

called left-skewed

- also called negative

Question 25

how does positive skews happen

Answer 25

when the mean is increased by some unusually high values

Question 26

how does negative skews happen

Answer 26

when the mean is reduced by some extremely low values

Question 27

How is that variables are symmetrical (shapes)

Answer 27

when there are no really extreme values (low and high values balance each other)

Question 28

What is the 5 number summary used for

Answer 28

to determine the shape of a distribution

Question 29

what does the 5 number summary include

Answer 29

1. smallest value 2. first quartile (Q1) 3. the second quartile (Q2) 4. the third quartile (Q3) 5. the largest number

Question 30

what is used to display data using 5-number summary

Answer 30

box-and-whisker plot

Question 31

using the 5 number summary to recognize symmetry in data

Answer 31

1. the distance from x smallest to the median = the distance form the median to x largest 2. the distance form x smallest to Q1 equals the distances form Q3 to x largest

Question 32

5-number summary what dos the right-skewed distribution mean

Answer 32

the distance from the median to x largest is greater than the distance form the x smallest to the median also the distance form Q3 to x largest is greater than the distance form x smallest to Q1

Question 33

5 -number summary what does the left skewed distribution

Answer 33

the distance from x smallest to the median is greater than the distance form the median to x largest also the distance form the x smallest to Q1 is greater than the distance form Q3 to x largest

Question 34

what does the coefficient of correlation measure

Answer 34

measures the strength of the linear relationship between two quantitative variables

Question 35

how do you calculate coefficient of correclation

Answer 35

??

Question 36

what are the features of correlation coefficient

Answer 36

1. unit free 2. ranges between -1 and 1 3. the closer to -1, the stronger the negative linear relationship 4. the closer to 1, the stronger the positive linear relationship 5. the closer to 0 the weaker any positive or negative linear relationship

Question 37

what is the data analysis objective

Answer 37

should report the summary measures that best meet the assumptions about the data set

Question 38

what are the pitfalls in numerical descriptive measures

Answer 38

1. data analysis is objective | 2. data interpretation is subjective (should be done in fair, neutral and clear manner)

Question 39

What are some ethical considerations for numerical descriptive measures

Answer 39

1. should document both good and bad results 2. should be presented in fair, objective and neutral manner 3. should not use inappropriate summary measures to distort facts

Question 40

what is central tendency

Answer 40

??