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Statistics
Published in Surinder S. Virdi, Advanced Construction Mathematics, 2019
A cumulative frequency curve, also known as an ogive, may also be used to represent a frequency distribution. The cumulative frequency for each class is obtained by adding all frequencies up to that class and plotted against corresponding upper class boundaries. The points are joined by a smooth curve to get the cumulative frequency curve or ogive, as shown in example 17.5. Cumulative frequency curves may be used to determine the median and the dispersion of the data. The values, which divide the data into 4 equal parts, are called quartiles and denoted by Q1, Q2 and Q3. Q1 = the lower quartile or first quartileQ2 = the middle quartile or second quartileQ3 = the upper quartile or third quartile. The difference between the upper and lower quartiles is called the interquartile range:Interquartile range = Q3 − Q1
Billing Data Statistics and Applications
Published in J. Lawrence, P.E. Vogt, Electricity Pricing, 2017
An ogive is a graphical representation of a cumulative frequency distribution; thus, for example, a plot of the consolidated factor vs. some function of usage would result in an ogive graph. To forecast kWh sales by the price blocks of a rate, an ogive is developed from the historical relationship between the consolidated factor, as a percentage, and the associated ratio of “use to average use.” The use to average use is the ratio of the upper end kWh interval (corresponding to a given consolidated factor) to the monthly mean kWh usage per bill (which for the March data is 614,588,356 kWh ÷ 860,963 Bills = 713.838 kWh/Bill).
Probability and sampling
Published in H. G. Davies, G. A. Hicks, Mathematics for scientific and technical students, 2014
In Section 12.6(d) it was seen that plotting cumulative frequency against the variable x for a set of data which appears to be normally distributed produces an ogive. If the same data is plotted on normal probability paper the points will lie on, or close to, a straight line if the data has a normal distribution. This is achieved by creating a non-linear vertical scale (see Figure 13.8). In Figure 13.3(b) it was seen that the probability of a value x in between two values x1 and x2 is the shaded area under the curve.
Ballistic response and energy dissipation characteristic of single and double curvature shell against projectile impact: a comparative study
Published in Mechanics Based Design of Structures and Machines, 2022
Nikhil Khaire, G. Tiwari, M. A. Iqbal
Also, to observe the failure mode in detail, the permanent deformation of SHS and SCS was obtained in terms of the radius of dishing and transverse deformation through experimental and numerical simulation, see Figs. 17–20. It was found that irrespective of the shape of the target and projectiles, ascending the diameter of the target, radius of dishing and crown deformation increased. However, ascending the target thickness, both radius of dishing and crown deformation decreased. Similarly, against the hemispherical projectile, the target experienced more radius of dishing, while the crown deformation was less compared to the ogive nosed projectile (for total perforation cases). Moreover, SHS experienced a higher radius of dishing and crown deformation compared to SCS against both the projectiles. Against ogive projectile, for 150 mm diameter, the radius of dishing of SHS was 10.22 and 22.19%, and 9.09% and 19.7% higher deformation than the SCS for thickness 1 and 1.5 mm, experimentally and numerically, respectively. Similarly, for 200 mm diameter, the radius of dishing of SHS was 11.6% and 16.9%, and 12.7% and 20.2% than the SCS for thickness 1 and 1.5 mm, experimentally and numerically, respectively. Against hemispherical projectile, for 150 mm diameter, the radius of dishing of SHS was 31.71% and 36.67%, and 30.12% and 35.23% higher than the SCS for thickness 1 and 1.5 mm for experimentally and numerically, respectively. Similarly, for 200 mm diameter, the radius of dishing of SHS was 41.8% and 45.65%, and 40.3% and 44.3% higher than the SCS for thicknesses 1 and 1.5 mm experimental and numerical, respectively. A similar trend was observed for the crown transverse deformation. Against ogive projectile, numerical results for 150 mm and 200 mm diameter showed that the crown deformation of SHS was 12.03% and 13.2%, and 17.2% and 19.6% higher than the SCS for thickness 1 and 1.5 mm, respectively. Similarly for experimental results crown deformation of SHS was 13.2% and 14.6%, and 19.2% and 20.6% higher than the SCS for thickness 1 and 1.5 mm, respectively. Against hemispherical projectile, for 150 mm and 200 mm diameter, the crown deformation of SHS was 43.9% and 66.3%, and 63.2% and 65.18% higher than the SCS for 1.0 mm and 1.5 mm thickness, respectively. Similarly for experimental results crown deformation of SHS was 41.2% and 63.5%, and 59.3% and 63.2% higher than the SCS for thickness 1 and 1.5 mm, respectively.