Week 1-Topic 2 Central Tendency And Measure Of Dispersion

Question 1

Measures of central tendency

Answer 1

Mean median mode

Question 2

Measures of dispersion

Answer 2

Range
Variance and standard deviation

Question 3

Weighted population mean

Answer 3

Frequency x Value
/
N

Question 4

3 shapes of data

Answer 4

Symmetrical
Positive skew
Negative skew

Question 5

Symmetrical distribution

Answer 5

Mean=mode=median

Question 6

Positive skew vs negative skew

Answer 6

Mean>median>mode

Mode>median>mean

(Visually, mean is always halfway)

Question 7

What does Geometric mean do and formula

Answer 7

Finds average change in rates overtime

N to the root of the value

Question 8

Geometric mean to find average percentage overtime. (WHEN ONLY HAVE INITIAL AND FINAL VALUES)

Answer 8

N to the root (VALUE AT END/VALUE AT START) -1

Question 9

Percentile formula

Answer 9

Lp= (n+1) x p/100

P is the percentile wanted

Question 10

Mean absolute deviation

Answer 10

Σxi−x bar
/
N

Question 11

Population variance

Answer 11

σ²=Σ(xi-μ)² / n

Question 12

Sample variance

Answer 12

s²=Σ(xi−x bar)²/n-1

Question 13

Standard deviation for population and sample variance

Answer 13

The root of the variance

Question 14

Coefficient of variation function and formula

Answer 14

σ/μ or s/x bar

Used to measure variation relative to size of observations.

Question 15

Chebyshev’s theorem

Answer 15

The proportion of value that lie within k standard deviations of the mean (for k>1) is at least 1-1/k squared.

E.g if k=2 at least 75% fall within +-2 population variance from mean.

Question 16

Empirical/Normal rule

Answer 16

68% lies within +-curly A from mean
95% lies within +-2 curly A from mean
99.7% lies within +-3 curly A from mean

Question 17

Bimodal distinction

Answer 17

2 or more peaks

Question 18

Skewness measurement

Answer 18

Skewness (Sk)=3(mean-median)/s

S is sample standard deviation.

Sk is from -3 to 3
+-1 is moderate skewness
0 symmetric

Question 19

Software coefficient of skewness

Answer 19

N/(n-1)(n-2) x (Σ(x-x bar)/s)

N is sample size
S is sample standard deviation

Question 20

Correlation coefficient formula and function.

Answer 20

Shows strength of relationship.

Formula Best to remember by write down

R= sum of (X-mean of X)(Y-mean of Y) / (n-1) SxSy

Sx and Sy are standard deviations of x and y

Question 21

Correlation coefficient range

Answer 21

-1 to 1

-1=perfect negative correlation
1=perfect positive correlation
Close to 0=no relationship.