lecture 4

what are the two types of descriptive

descriptive and inferential

types of descriptive statistics

measures of central tendency and measures of variation

types of central tendency

mean, median, mode

types of variation

range, variance, standard deviation

measure of variation

is as set if observation refers to how spread out the observation are from each other

the range

max-min

advantages of range

1. easy to calculate

2. gives quick idea about the nature of data

3. often uses only two entries from the data set

disadvantages of range

1. uses only two entries

2. affected by extreme values

3. approximate measure

deviation

the difference between the entry and the mean of the data set

the variation of ungrouped data

σ²=∑(x-µ)²/N

the population standard deviation

σ=the root of σ²

the sum of squares

SSx=∑(x-µ)²

Sample Variance

s²=1/n-1*∑(xi-x⁻)²

sample standard deviation

s=the root of s²

interpreting standard deviation

the more the entries are spread out, the standard deviation

the variance of grouped data

s²*f

skewness

is a measure of the asymmetry of the probability distribution of a random variable

types of skewness

1. symmetric

2. negatively skewness ( has a longer left tail)

3. positive skewness (has a longer raight tail)

calculating skewness

∑(x-⁻x)³/ (n-1).s³

interpretation of skewness

1. skewness close to 0 = symmetric

2. skewness close to 1 = positive

3. skewness close to -1 = negaitive

kurtosis

a measure of the peakedness of the probability distribution of a random variable

three main type of kurtosis

1. Mesokurtic

2. Leptokurtic

3. platykurtic

Mesokurtic

Normal distribution has a kurtosis of 3

Leptokurtic

distribution has a sharper peak and fatter tails than a normal distribution. Kurtosis greater than 3

platykurtic

Distribution has a flatter peak and thinner tails . kurtosis is less than than 3

calculating kurtosis

=∑(x-x⁻)^4/(n-1).s^4

population coefficient of variation

CV=σ/µ

sample coefficient of variation

CV=s/⁻x