Analysis of Rainfall DataAnalysis of Rainfall DataYearYear Rainfall Rainfall

IntensityIntensity

19181918 43.3043.30 19281928 54.4954.49 19381938 58.7158.71

19191919 53.0253.02 19291929 47.3847.38 19391939 42.9642.96

19201920 63.5263.52 19301930 40.7840.78 19401940 55.7755.77

19211921 45.9345.93 19311931 45.0545.05 19411941 41.3141.31

19221922 48.2648.26 19321932 50.3750.37 19421942 58.8358.83

19231923 50.5150.51 19331933 54.9154.91 19431943 48.2148.21

19241924 49.5749.57 19341934 51.2851.28 19441944 44.6744.67

19251925 43.9343.93 19351935 39.9139.91 19451945 67.7267.72

19261926 46.7746.77 19361936 53.2953.29 19461946 43.1143.11

19271927 59.1259.12 19371937 67.5967.59

Sample mean =Sample mean =

Sample variance = SSample variance = S2 2 ==

Approximately, Approximately, 68%68% within within 50.750.7 +/- +/- 11 xx 7.717.71 or or 43.0 to 58.443.0 to 58.4

Approximately, Approximately, 95%95% within within 50.750.7 +/- +/- 22 x 7.71 x 7.71 or or 35.3 to 66.135.3 to 66.1

n

xx i 50.7

1

)( 2

n

xxi 59.4

S = 7.71

Construction of HistogramConstruction of Histogram

1.1. Rearrange data in increasing orderRearrange data in increasing order

2.2. Note the range and divide into Note the range and divide into suitablesuitable

intervals (say at 4 inches in this example)intervals (say at 4 inches in this example)

3.3. Count number of occurrence in each Count number of occurrence in each

intervalinterval

4.4. Plot HistogramPlot Histogram

HISTOGRAM

FREQUENCY DIAGRAM

Total Area = 116

Total Area = 1.0

3/116 = 0.026

or 2.6%

Frequency DiagramFrequency Diagram

1.1. Determine total area of histogram, say ADetermine total area of histogram, say A

2.2. Modify the vertical scale of histogram by Modify the vertical scale of histogram by

dividing the value by A, dividing the value by A,

For the rainfall example, A= 116, For the rainfall example, A= 116,

ordinate of first strip = 3/116 = 0.026 or ordinate of first strip = 3/116 = 0.026 or

2.6%2.6%

Model

Area = 0.152

FREQUENCY DIAGRAM

Statistics of Sustained Live Statistics of Sustained Live LoadLoad

Floor Load Intensity (lb/ftFloor Load Intensity (lb/ft22) – ) –

National Bureau of Standard Report National Bureau of Standard Report

19521952

Data on First Floor, Bay Size Data on First Floor, Bay Size 400ft400ft22

7.87.8 72.672.6 42.542.5 55.955.9 26.026.0 66.466.4

73.473.4 106.5106.5 30.230.2 37.037.0 24.124.1 23.423.4

49.849.8 106.9106.9 48.448.4 55.055.0 54.854.8 65.765.7

62.562.5 68.768.7 118.2118.2 55.655.6

Xj, j= 1,2,3…….N N = 22

P(L.L.>56.88 lb/ft2) = ?

= 9/22

HistogramHistogram

1.1. Select interval, ∆X (e.g. ∆X=25 lb/ftSelect interval, ∆X (e.g. ∆X=25 lb/ft22))

2.2. Count no. observations within each iCount no. observations within each interval according to nterval according to

a < Xa < Xjj ≤ b ≤ b say nsay nii

HistogramHistogram3.3. Plot the resultsPlot the results

ScattergramScattergram