Practice Problems: Descriptive Statistics

Question 1:
A civil engineer is analyzing the compressive strength of concrete cylinders from a batch used in a bridge construction project. The compressive strengths (in psi) of 10 cylinders are: 3500, 3650, 3720, 3580, 3690, 3710, 3620, 3670, 3590, 3740. What is the mean compressive strength of the concrete cylinders?

(a) 3620 psi
(b) 3647 psi
(c) 3670 psi
(d) 3695 psi

Question 2:
A mechanical engineer is testing the tensile strength of steel specimens. The following tensile strengths (in MPa) were recorded: 450, 470, 460, 480, 465, 475, 455, 490, 485, 470. What is the median tensile strength?

(a) 470 MPa
(b) 472.5 MPa
(c) 467.5 MPa
(d) 465 MPa

Question 3:
An environmental engineer measured pH levels at 8 different locations in a lake: 7.2, 7.5, 7.3, 7.2, 7.8, 7.2, 7.6, 7.4. What is the mode of the pH measurements?

(a) 7.3
(b) 7.4
(c) 7.2
(d) 7.5

Question 4:
A transportation engineer collected travel time data (in minutes) for a commuter route over 12 days: 25, 28, 30, 27, 26, 29, 31, 25, 28, 30, 27, 32. Calculate the range of the travel times.

(a) 5 minutes
(b) 6 minutes
(c) 7 minutes
(d) 8 minutes

Question 5:
A structural engineer measured the deflections (in mm) of a beam at midspan under load testing: 12.5, 13.2, 12.8, 13.5, 12.6, 13.0, 12.9, 13.3. Calculate the population variance of these deflection measurements.

(a) 0.095 mm²
(b) 0.102 mm²
(c) 0.110 mm²
(d) 0.118 mm²

Question 6:
A quality control engineer is monitoring the diameter of machined shafts (in inches): 1.250, 1.248, 1.252, 1.251, 1.249, 1.253, 1.250, 1.247. Calculate the sample standard deviation of the shaft diameters.

(a) 0.00182 in
(b) 0.00196 in
(c) 0.00208 in
(d) 0.00215 in

Question 7:
An electrical engineer measured voltage drops (in volts) across resistors in a circuit: 4.8, 5.2, 4.9, 5.0, 5.1, 4.7, 5.3, 5.0. What is the first quartile (Q₁) of the voltage drop data?

(a) 4.85 V
(b) 4.875 V
(c) 4.90 V
(d) 4.95 V

Question 8:
A geotechnical engineer conducted standard penetration tests at a construction site. The N-values obtained were: 15, 18, 22, 20, 16, 19, 21, 17, 23, 20. Calculate the third quartile (Q₃) of the N-values.

(a) 20.5
(b) 21.0
(c) 21.25
(d) 21.5

Question 9:
A water resources engineer measured daily streamflow rates (in ft³/s) over a week: 125, 142, 138, 156, 148, 135, 162. Calculate the interquartile range (IQR) of the streamflow data.

(a) 15.5 ft³/s
(b) 17.0 ft³/s
(c) 18.5 ft³/s
(d) 20.0 ft³/s

Question 10:
A materials engineer tested the hardness of aluminum alloy samples using the Brinell method. The hardness values were: 85, 88, 92, 87, 90, 89, 91, 86, 88, 90. Calculate the coefficient of variation (CV) for this dataset.

(a) 2.18%
(b) 2.35%
(c) 2.52%
(d) 2.68%

Question 11:
A construction manager tracked the daily productivity (in cubic yards of concrete poured) over 9 days: 45, 52, 48, 50, 47, 51, 49, 46, 53. What percentile does the value 49 cubic yards represent?

(a) 50th percentile
(b) 55th percentile
(c) 60th percentile
(d) 66th percentile

Question 12:
An HVAC engineer measured indoor temperatures (°F) in 10 different office spaces: 68, 70, 72, 69, 71, 73, 70, 68, 72, 71. Calculate the mean absolute deviation (MAD) of the temperature data.

(a) 1.24°F
(b) 1.44°F
(c) 1.64°F
(d) 1.84°F

Question 13:
A chemical engineer monitored the reaction temperature (°C) in a batch reactor over 8 cycles: 155, 158, 162, 157, 160, 159, 161, 156. Calculate the population standard deviation of the reaction temperatures.

(a) 2.12°C
(b) 2.27°C
(c) 2.42°C
(d) 2.56°C

Question 14:
A traffic engineer collected speed data (mph) from 15 vehicles on a highway: 62, 65, 68, 64, 66, 70, 63, 67, 69, 65, 71, 64, 66, 68, 67. What is the 80th percentile speed?

(a) 68 mph
(b) 68.5 mph
(c) 69 mph
(d) 69.5 mph

Question 15:
An industrial engineer collected cycle time data (in seconds) for an assembly process: 45.2, 46.8, 44.5, 47.3, 45.9, 46.2, 44.8, 47.0, 45.5, 46.5. One measurement of 55.0 seconds was also recorded. Is this measurement an outlier based on the IQR method (using 1.5×IQR rule)?

(a) Yes, it is an outlier
(b) No, it is not an outlier
(c) Cannot be determined
(d) It is a borderline case

Question 16:
A petroleum engineer measured the viscosity (in cP) of crude oil samples at different temperatures. The viscosities were: 28, 32, 30, 35, 29, 31, 33, 30. Calculate the sample variance.

(a) 4.57 cP²
(b) 5.14 cP²
(c) 5.71 cP²
(d) 6.28 cP²

Question 17:
A manufacturing engineer measured the thickness (in mm) of sheet metal samples: 2.45, 2.48, 2.46, 2.50, 2.47, 2.49, 2.46, 2.48, 2.47, 2.49. What is the relative frequency of measurements that are 2.48 mm or greater?

(a) 0.30
(b) 0.40
(c) 0.50
(d) 0.60

Question 18:
A nuclear engineer measured radiation levels (in mR/hr) at 7 monitoring stations: 0.12, 0.15, 0.13, 0.14, 0.16, 0.13, 0.17. Calculate the z-score for the measurement of 0.17 mR/hr.

(a) 1.43
(b) 1.58
(c) 1.73
(d) 1.88

Question 19:
A coastal engineer measured wave heights (in meters) during a storm: 2.5, 3.1, 2.8, 3.4, 2.9, 3.2, 3.0, 2.7, 3.3, 2.6. What is the weighted mean if the first five measurements have a weight of 1 and the last five measurements have a weight of 2?

(a) 2.91 m
(b) 2.97 m
(c) 3.03 m
(d) 3.09 m

Question 20:
An aerospace engineer measured the thrust force (in kN) of a jet engine during 12 test runs: 245, 252, 248, 255, 250, 247, 253, 249, 251, 246, 254, 250. Calculate the skewness coefficient using the formula: Skewness = 3(Mean - Median)/Standard Deviation.

(a) -0.12
(b) 0.00
(c) 0.12
(d) 0.24