Download presentation

Presentation is loading. Please wait.

Published byChristian Sparks Modified over 3 years ago

1
**CS1512 Foundations of Computing Science 2 Lecture 20 Probability and statistics (2)**

© J R W Hunter, 2006

2
**Ordinal data a1 ≤ a2 ≤ a3 ≤ ... ≤ ak ≤ ... ≤ aK**

X is an ordinal variable with values: a1, a2, a3, ... ak, aK ‘ordinal’ means that: a1 ≤ a2 ≤ a3 ≤ ≤ ak ≤ ≤ aK cumulative frequency at level k: ck = sum of frequencies of values less than or equal to ak ck = f1 + f2 + f fk = (f1 + f2 + f fk-1 ) + fk = ck fk also (%) cumulative relative frequency

3
**CAS marks % relative frequencies % cumulative relative frequencies**

4
**Enzyme concentrations**

Concentration Freq Rel.Freq % Cum. Rel. Freq. ≤ c < % ≤ c < % ≤ c < % ≤ c < % ≤ c < % ≤ c < % ≤ c < % ≤ c < % ≤ c < % ≤ c < % Totals

5
Cumulative histogram

6
**Discrete two variable data**

7
**Continuous two variable data**

X Y

8
**Time Series Time and space are fundamental (especially time)**

Time series: variation of a particular variable with time

9
**Summarising data by numerical means**

Further summarisation (beyond frequencies) Measures of location (Where is the middle?) Mean Median Mode

10
**Mean = n _ sum of observed values of X Sample Mean (X) =**

number of observed values x = n use only for quantitative data

11
**Sigma xi = x1 + x2 + ... + xi + ... + xn-1 + xn**

Sum of n observations n xi = x1 + x xi xn xn i = 1 If it is clear that the sum is from 1 to n then: x = x1 + x xi xn xn Sum of squares x2 = x x xi xn xn2

12
x from frequencies If X is a categorical variable with values: a1, a2, a3, ... ak, aK x = x1 + x xi xn xn (order of summation isn’t important) (e.g. piglets: ) Group together those x’s which have value a1, those with value a2, ... x = x x x x’s which have value a1 - there are f1 of them x x x’s which have value a2 - there are f2 of them x x x’s which have value aK - there are fK of them = f1 * a f2 * a fk * ak fK * aK K = fk * ak k = 1

13
Mean Litter size Frequency Cum. Freq ak fk Total K x = fk * ak k = 1 = 1* * *7 + 3* * *10 + 8* *12 + 3*13 + 2*14 = 375 _ X = 375 / 36 = 10.42

14
**Median Sample median of X = middle value when n sample observations**

are ranked in increasing order = the ((n + 1)/2)th value n odd: values: , 163, 152, 157 and 157 rank order: 152, 157, 157, 163, 183 median: n even: values: , 173, 180, 164 rank order: 164, 165, 173, 180 median: ( )/2 = 169

15
**Median Median = 10.5 Litter size Frequency Cum. Freq 5 1 1 6 0 1 7 2 3**

Total Median = 10.5

16
**Median from cumulative distribution**

cumulative % frequency polygon

17
**Mode Sample mode = value with highest frequency (may not be unique)**

Litter size Frequency Cum. Freq Mode = 10

18
**Skew left skewed symmetric right skewed**

mean < mode mean mode mean > mode

19
**Variance Measure of spread: variance**

20
**Variance sample variance = s2**

sample standard deviation = s = √ variance

21
**Variance and standard deviation**

K x2 = fk * ak2 k = 1 = 1* * * * * * * * *196 = 4145 x = 375 (x)2 / n = 375*375 / 36 = 3906 s2 = ( ) / (36-1) = 6.83 s = 2.6 Litter size Frequency Cum. Freq ak fk Total

22
**Piglets Mean = 10.42 Median = 10.5 Mode = 10 Std. devn. = 2.6**

23
Quartiles and Range Lower quartile: value such that 25% of observations are below it (Q1). Median: value such that 50% of observations are below (above) it (Q2). Upper quartile: value such that 25% of observations are above it (Q3). Range: the minimum (m) and maximum (M) observations. Box and Whisker plot: m Q1 Q Q M

24
Estimating quartiles

25
**Linear Regression y y = mc + c x**

Calculate m and c so that (distance of point from line)2 is minimised y y = mc + c x

26
**Time Series - Moving Average**

Time Y point MA * * smoothing function can compute median, max, min, std. devn, etc. in window

Similar presentations

OK

Copyright © Action Works 2008 All Rights Reserved - Photos by David D

Copyright © Action Works 2008 All Rights Reserved - Photos by David D

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on precautions of tsunami wave Ppt on principles of peace building review Ppt on personal swot analysis Ppt on rational numbers for class 8 Ppt on medical tourism in dubai Ppt on hdfc bank Download ppt on verb in hindi Download ppt on children's day Ppt on applied operational research course Ppt on 5g wireless system