Descriptive statistics pt II Flashcards
Practice drawing frequency table questions.
get 80% score
Practice arithmetic mean questions.
Get 80% score
What does Σ stand for?
in statistical and calculus formulae
and what does the i at the bottom stand for?
The Greek letter capital sigma (Σ) indicates summation.
The “i = 1” at the bottom indicates that the summation is to start with X1
Geometric mean
Recall geometric mean
and its formula
(G.M) of a series containing n observations is the nth root of the product of all the values.
(x1x2 x3* x4* x5*…xn)^(1/n)
Example of geometric mean question and application. Let’s say you own a piece of art that increases in value by 50% the first year after you buy it, 20% the second year, and 90% the third year.
To answer, write equation you will use and answer
(1.5* 1.2* 1.9)(1/3) = 1.50663725458
Q2 of geometric mean. The average person’s monthly salary in a certain town jumped from $2,500 to $5,000 over the course of ten years. Using the geometric mean, what is the average yearly increase?
- Find the geometric mean. (2500*5000)^(1/2) = 3535.53390593.
- Divide by 10
since it asks 10 years
final ans: 353.53
What are the steps in obtaining harmonic mean?
e.g. 1, 5, 8, 10
https://www.statisticshowto.com/calculus-definitions/harmonic-mean/
- Get reciprocals of the data
- Add reciprocals
- get mean of reciprocals
- reciprocate answer
1/1 + 1/5 + 1/8 + 1/10 = 1.425 then (1.425/4)^-1
2.80702
Median
What are the steps to obtain median?
- Arrange in ascending order
- If even divide middle numbers by 2
Quartiles
How is data divided into quartiles?
- Data is arranged in ascending order or in graph
- divide total frequency by 4
- at n/4 is each quartile
Quartiles
How is data divided into quartiles?
- Data is arranged in ascending order or in graph
- obtain median which will be Q2 (2nd quartile line)
- then on the divided data obtain median of each to obain Q1 and Q3
Interquartile range
What is the interquartile range
It is the distance between the first and third quartile marks.
Q3-Q1
it tells us the range of the middle half of the data.
Outliers
When is a point considered an outlier
When it is substantially above Q3 or below Q1
How are outliers obtained?
- 1.5*IQR then
- add to Q3 or
- minus from Q1
Mode
What does mode refer to?
It refers to the value represented by the greatest number of individuals.
Where is mode on the frequency distribution graph?
It is the value at which the curve peaks
Distributions having two peaks (equal or unequal in height) are called?
Bimodal
Any more then they become multimodal
Range
Define range as used in statistics.
the difference between the largest and the smallest values in a sample.
What is one disadvantage if using range as a measure of dispersion?
it is extremely sensitive to outliers
Variability
Variability can be defined as
how close the scores in a distribution are to the centre/mean.
Thus, one can see on average how far each data point is from the centre
Measure of variability
One measure of variability is sum of squares. Write down the formula.
(SS) = ∑(X−μ)^2).
we square to get rid of negative values.
Note that as you calculate
Variance
Variance is defined as the average squared difference of the scores from the mean. True or false?
True
What is the symbol for variance
σ2 “sigma-squared”
What is the formula for obtaining variance?
σ2=∑(X−μ)2/N-1
Basically, SS/N-1
N-1: is the degrees of freedom
In general, as your sample size (N) gets bigger, the effect of subtracting 1 becomes less and less. What does this infer
larger sample sizes will bring the estimate of the sample variance closer to that of the population variance
Thus, larger sample sizes better reflect the population
Standard deviation. σ
Standard deviation is
square root of the variance
most commonly used measure of spread
The greater the standard deviation
in terms of distribution
the greater the distribution away from centre/mean.
