Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of a value 40?
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Solution
Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1.
Correct Answer: C — 2
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Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of the value 40?
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Solution
Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1
Correct Answer: C — 2
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Q. If the data set has a mean of 30 and a variance of 16, what is the standard deviation?
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Solution
Standard Deviation = √Variance = √16 = 4.
Correct Answer: A — 4
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Q. If the data set has a mean of 50 and a median of 45, what can be said about the data distribution?
A.
Symmetric
B.
Positively skewed
C.
Negatively skewed
D.
Uniform
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Solution
Since the mean is greater than the median, the distribution is positively skewed.
Correct Answer: B — Positively skewed
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Q. If the data set has a mean of 50 and a standard deviation of 10, what is the z-score of the value 70?
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Solution
Z-score = (X - Mean) / Standard Deviation = (70 - 50) / 10 = 2.
Correct Answer: B — 2
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Q. If the data set has a mean of 50 and a variance of 16, what is the standard deviation?
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Solution
Standard Deviation = √Variance = √16 = 4.
Correct Answer: B — 4
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Q. If the data set is 1, 2, 2, 3, 4, 4, 4, 5, what is the mode?
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Solution
Mode = 4 (most frequent value).
Correct Answer: C — 4
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Q. If the data set is 4, 4, 4, 5, 5, 6, what is the mode?
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Solution
Mode = 4 (most frequent value).
Correct Answer: A — 4
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Q. If the data set is {5, 7, 7, 8, 10}, what is the mode?
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Solution
Mode = 7 (most frequently occurring value).
Correct Answer: B — 7
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Q. If the data set is {5, 7, 8, 9, 10}, what is the interquartile range?
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Solution
Q1 = 7, Q3 = 9; Interquartile Range = Q3 - Q1 = 9 - 7 = 2.
Correct Answer: B — 3
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Q. If the data set is {5, 7, 8, 9, 10}, what is the standard deviation?
A.
1.58
B.
2.58
C.
3.58
D.
4.58
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Solution
Mean = 7.8. Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²]/5 = 2.5. Standard Deviation = √2.5 ≈ 1.58.
Correct Answer: A — 1.58
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Q. If the data set is: 3, 7, 7, 19, what is the median?
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Solution
Median = (7 + 7) / 2 = 7.
Correct Answer: A — 7
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Q. If the data set is: 5, 7, 8, 9, 10, what is the median?
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Solution
Median is the middle value. Here, the middle values are 7 and 8, so Median = (7+8)/2 = 7.5.
Correct Answer: B — 8
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Q. If the data set {1, 2, 3, 4, 5} is transformed to {2, 3, 4, 5, 6}, what happens to the standard deviation?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Cannot be determined
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Solution
The standard deviation remains the same because the transformation is a shift.
Correct Answer: C — Remains the same
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Q. If the data set {10, 20, 30, 40, 50} is transformed to {x + 5}, what happens to the standard deviation?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Cannot be determined
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Solution
Standard deviation remains the same as adding a constant does not affect dispersion.
Correct Answer: C — Remains the same
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Q. If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?
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Solution
Q1 is the median of the first half of the data set {3, 7}, which is 7.
Correct Answer: B — 7
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Q. If the data set {3, 7, 8, 12, 14} is given, what is the median?
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Solution
Median is the middle value, which is 8.
Correct Answer: A — 8
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Q. If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the deviations from the mean?
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Solution
The sum of deviations from the mean is always 0.
Correct Answer: A — 0
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Q. If the density of a substance is calculated as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the relative uncertainty?
A.
0.025
B.
0.02
C.
0.005
D.
0.01
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Solution
Relative uncertainty = (absolute uncertainty / density) = 0.2 / 8.0 = 0.025.
Correct Answer: B — 0.02
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.5 g/cm³, what is the range of possible values for the density?
A.
7.5 to 8.5 g/cm³
B.
8.0 to 8.5 g/cm³
C.
8.0 to 9.0 g/cm³
D.
7.0 to 9.0 g/cm³
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Solution
Range = (8.0 - 0.5) to (8.0 + 0.5) = 7.5 to 8.5 g/cm³.
Correct Answer: A — 7.5 to 8.5 g/cm³
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the absolute error in the density?
A.
0.1 g/cm³
B.
0.01 g/cm³
C.
0.5 g/cm³
D.
0.2 g/cm³
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Solution
The absolute error is given directly as ±0.1 g/cm³.
Correct Answer: A — 0.1 g/cm³
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the absolute error in the volume calculated from this density?
A.
0.025 cm³
B.
0.1 cm³
C.
0.2 cm³
D.
0.5 cm³
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Solution
Volume = mass/density; if mass is constant, the absolute error in volume = (mass * absolute error in density) / (density²).
Correct Answer: A — 0.025 cm³
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the relative uncertainty in the density?
A.
0.025
B.
0.02
C.
0.005
D.
0.1
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Solution
Relative uncertainty = (absolute uncertainty / measured value) = 0.2 / 8.0 = 0.025.
Correct Answer: B — 0.02
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the fractional error in the density?
A.
0.0125
B.
0.01
C.
0.005
D.
0.02
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Solution
Fractional error = (absolute error / measured value) = 0.1 / 8.0 = 0.0125.
Correct Answer: B — 0.01
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.2 g/cm³, what is the range of possible densities?
A.
7.8 to 8.2 g/cm³
B.
7.5 to 8.5 g/cm³
C.
8.0 to 8.4 g/cm³
D.
8.0 to 8.2 g/cm³
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Solution
Range = 8.0 ± 0.2 gives 7.8 to 8.2 g/cm³.
Correct Answer: A — 7.8 to 8.2 g/cm³
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Q. If the density of a substance is measured as 8.0 g/cm³ with an uncertainty of ±0.1 g/cm³, what is the relative uncertainty in the density?
A.
0.0125
B.
0.01
C.
0.005
D.
0.02
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Solution
Relative uncertainty = (absolute uncertainty / measured value) = 0.1 / 8.0 = 0.0125.
Correct Answer: B — 0.01
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Q. If the determinant | x 2 | | 3 4 | = 0, find x.
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Solution
Setting the determinant to zero gives x*4 - 2*3 = 0, thus x = 1.5.
Correct Answer: B — 2
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Q. If the directrix of a parabola is given by the equation y = -p, what is the equation of the parabola?
A.
y^2 = 4px
B.
x^2 = 4py
C.
y^2 = -4px
D.
x^2 = -4py
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Solution
The equation of a parabola with directrix y = -p is y^2 = -4px.
Correct Answer: C — y^2 = -4px
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Q. If the distance between the object and the image formed by a lens is 70 cm, and the object distance is 30 cm, what is the image distance?
A.
40 cm
B.
50 cm
C.
60 cm
D.
70 cm
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Solution
Image distance (v) = Object distance (u) + Distance between object and image = 30 cm + 70 cm = 40 cm.
Correct Answer: A — 40 cm
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Q. If the distance between the plates of a capacitor is doubled, what happens to its capacitance?
A.
It doubles
B.
It halves
C.
It remains the same
D.
It quadruples
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Solution
Capacitance is inversely proportional to the distance between the plates. If the distance d is doubled, the capacitance C becomes C/2.
Correct Answer: B — It halves
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