Statistical Analysis on Pile Length Data
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Calculating range, variation, standard deviation, mean deviation, and skewness measure from a table showing pile lengths and frequencies. The process involves finding the range, variation, mean, mean deviation, and skewness using mathematical formulas. The step-by-step analysis includes determining the arithmetic mean and applying the relevant statistical calculations.
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Presentation Transcript
Example: for the following table find rang, variation, standard deviation, mean deviation, and skewness measure Pile length Frequency Solution 3 2 7 3 1) Range 8 1 R = Xmax- Xmin 12 5 19 4 R = 74- 3 21 2 R = 71 25 1 2) Variation 31 4 38 To find variation we must find first the arithmetic mean 6 45 1 ? ?= ?=1 ???? ?? 52 5 ? ?=1 60 6 68 3 74 4
Example: for the following table find rang, variation, standard deviation, mean deviation, and skewness measure Xi(fi) 3(2)=6 Pile length Frequency ? 3 2 ???? = 6 + 21 + 8 + 60 + 76 + 42 + 25 + ?=1 7 3 7(3)=21 124 + 228 + 45 + 260 + 360 +204+296 8 1 8(1)=8 =1755 12 5 12(5)=60 ? ??= 2 + 3 + 1 + 5 + 4 + 2 + 1 + 4 + 6 + 1 +5 + 6 + 3 + 4 = 47 19 4 19(4)=76 ?=1 21 2 21(2)=42 25 1 25(1)=25 ?=1755 47=37.34 31 4 31(4)=124 38 6 38(6)=228 45 1 45(1)=45 ? 2.?? ? ?= ?=1 ?? (? 1) 52 5 52(5)=260 60 6 60(6)=360 68 3 68(3)=204 74 4 74(4)=296
(Xi - ?)2.fi (Xi - ?)2 (Xi - ?) Pile length (Xi) Frequency ? ? 2.?? = 23797.46 ?? 3 1179.2 -34.34 2 2358.4 7 920.5 -30.34 3 2761.5 ?=1 8 860.8 -29.34 1 860.8 ? = 47 12 642.1 -25.34 5 3210.5 ? 2.?? ? 19 336.6 -18.34 ?= ?=1 4 1346.4 ?? (? 1) 21 267 -16.34 2 534 25 152.3 -12.34 1 152.3 ?=23797.46 (47 1) 31 40.2 -6.34 4 160.8 38 0.44 0.66 6 2.64 45 58.68 7.66 1 58.68 ?=517.334 52 214.92 14.66 5 1074.6 60 513.48 22.66 6 3080.88 68 940.04 30.66 3 2820.12 74 1343.96 36.66 4 5375.84
3) Standard deviation |Xi - ?|.fi |Xi - ?| (Xi - ?) Pile length (Xi) Frequency ? = ?= 517.334 = 22.745 68.68 34.34 3 -34.34 2 91.02 30.34 7 -30.34 3 4) Mean deviation 29.34 29.34 8 -29.34 1 ? ?? ? .?? ? ?.? = ?=1 126.7 25.34 12 -25.34 5 73.36 18.34 19 -18.34 4 32.68 16.34 21 -16.34 2 ? ?? ? .?? = 918.98 12.34 12.34 25 -12.34 1 ?=1 25.36 6.34 31 -6.34 4 ? = 47 3.96 0.66 38 0.66 6 7.66 7.66 45 7.66 1 ?.? =918.98 73.3 14.66 52 14.66 5 47 135.96 22.66 60 22.66 6 ?.? = 19.553 91.98 30.66 68 30.66 3 146.64 36.66 74 36.66 4
5a) Skewness measure by first theorem Pile length (Xi) Cumulative Frequency Frequency ?1=3 ? ? ? 3 2 2 ? = 37.34 7 5 3 8 6 1 ? = 22.745 12 11 5 ? = 47 19 15 4 21 ? 2= 23.5 17 2 25 18 1 31 22 4 ? = 38 38 28 6 ?1=3 37.34 38 22.745 45 29 1 52 34 5 60 40 6 ?1= 0.087 68 43 3 74 47 4
5b) Skewness measure by second theorem (Xi - ?)2.fi (Xi - ?)3.fi (Xi - ?) ?2=?3 ?3 -34.34 2358.4 -80987.5 -30.34 2761.5 -83783.9 ? ?.?? ? ??= ?=1 ?? -29.34 860.8 -25255.9 ? -25.34 3210.5 -81354.1 ? = 22.745 -18.34 1346.4 -24693 ?3= 11766.8 -16.34 534 -8725.6 -12.34 152.3 -1879.4 ? 3.?? ? ?3= ?=1 ?3= 61861.8 ?2= 1316.2 11766.8 ?? -6.34 160.8 -1019.5 ? 0.66 2.64 1.7 ,?3= 1316.2 7.66 58.68 449.5 47 14.66 1074.6 15753.6 ,?2= 0.11 22.66 3080.88 69812.7 30.66 2820.12 86464.9 36.66 5375.84 197078.3
