Practice
Standard Deviation Practice
Fifty original questions on spread, population standard deviation, transformations, visual comparison, and normal-distribution intervals.
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Question 1
Explanation
Standard deviation measures spread, not the size or sign of the center.
Question 2
Explanation
Standard deviation is zero only when every deviation from the mean is zero.
Question 3
Explanation
It is the principal square root of a nonnegative variance.
Question 4
Explanation
Standard deviation uses all squared deviations.
Question 5
Explanation
Tighter clustering means smaller typical distance from the mean.
Question 6
Explanation
The mean is \(4\). The population variance is \(0\), so the standard deviation is \(0\).
Question 7
Explanation
The mean is \(4\). The population variance is \(1\), so the standard deviation is \(1\).
Question 8
Explanation
The mean is \(4\). The population variance is \(2.667\), so the standard deviation is \(\sqrt{8/3}\).
Question 9
Explanation
The mean is \(4\). The population variance is \(5\), so the standard deviation is \(\sqrt{5}\).
Question 10
Explanation
The mean is \(8\). The population variance is \(2.667\), so the standard deviation is \(\sqrt{8/3}\).
Question 11
Explanation
Set B's values lie farther from its center overall, so it has greater spread and a larger standard deviation.
Question 12
Explanation
Set B's values lie farther from its center overall, so it has greater spread and a larger standard deviation.
Question 13
Explanation
Set B's values lie farther from its center overall, so it has greater spread and a larger standard deviation.
Question 14
Explanation
Set B's values lie farther from its center overall, so it has greater spread and a larger standard deviation.
Question 15
Explanation
Set B's values lie farther from its center overall, so it has greater spread and a larger standard deviation.
Question 16
Explanation
Distribution B extends farther from its center, so its observations have larger typical distances from the mean.
Question 17
Explanation
Distribution B extends farther from its center, so its observations have larger typical distances from the mean.
Question 18
Explanation
Distribution B extends farther from its center, so its observations have larger typical distances from the mean.
Question 19
Explanation
Distribution B extends farther from its center, so its observations have larger typical distances from the mean.
Question 20
Explanation
Distribution B extends farther from its center, so its observations have larger typical distances from the mean.
Question 21
Explanation
Adding the same constant shifts every value and the mean equally, so every deviation and the standard deviation remain \(3\).
Question 22
Explanation
Adding the same constant shifts every value and the mean equally, so every deviation and the standard deviation remain \(2\).
Question 23
Explanation
Adding the same constant shifts every value and the mean equally, so every deviation and the standard deviation remain \(6\).
Question 24
Explanation
Adding the same constant shifts every value and the mean equally, so every deviation and the standard deviation remain \(4\).
Question 25
Explanation
Adding the same constant shifts every value and the mean equally, so every deviation and the standard deviation remain \(1.5\).
Question 26
Explanation
Multiplication by positive \(2\) scales every distance from the mean, so the new standard deviation is \(2(3)=6\).
Question 27
Explanation
Multiplication by positive \(4\) scales every distance from the mean, so the new standard deviation is \(4(5)=20\).
Question 28
Explanation
Multiplication by positive \(6\) scales every distance from the mean, so the new standard deviation is \(6(1.5)=9\).
Question 29
Explanation
Multiplication by positive \(0.5\) scales every distance from the mean, so the new standard deviation is \(0.5(8)=4\).
Question 30
Explanation
Multiplication by positive \(3\) scales every distance from the mean, so the new standard deviation is \(3(2.4)=7.199999999999999\).
Question 31
Explanation
The scale factor \(3\) multiplies standard deviation; the shift \(5\) does not. Thus the new standard deviation is \(11\).
Question 32
Explanation
The scale factor \(2\) multiplies standard deviation; the shift \(-7\) does not. Thus the new standard deviation is \(1\).
Question 33
Explanation
The scale factor \(4\) multiplies standard deviation; the shift \(6\) does not. Thus the new standard deviation is \(6\).
Question 34
Explanation
The scale factor \(0.5\) multiplies standard deviation; the shift \(12\) does not. Thus the new standard deviation is \(2.5\).
Question 35
Explanation
The scale factor \(6\) multiplies standard deviation; the shift \(-2\) does not. Thus the new standard deviation is \(18\).
Question 36
Explanation
The interval is \(50\pm1(5)\), so the chapter-level normal approximation gives \(68\%\).
Question 37
Explanation
The interval is \(60\pm2(8)\), so the chapter-level normal approximation gives \(95\%\).
Question 38
Explanation
The interval is \(100\pm3(12)\), so the chapter-level normal approximation gives \(99\%\).
Question 39
Explanation
The interval is \(72\pm1(4)\), so the chapter-level normal approximation gives \(68\%\).
Question 40
Explanation
The interval is \(30\pm2(3)\), so the chapter-level normal approximation gives \(95\%\).
Question 41
Explanation
Use symmetry and the \(68\%\), \(95\%\), and \(99\%\) approximations. The requested region corresponds to approximately \(34\%\).
Question 42
Explanation
Use symmetry and the \(68\%\), \(95\%\), and \(99\%\) approximations. The requested region corresponds to approximately \(16\%\).
Question 43
Explanation
Use symmetry and the \(68\%\), \(95\%\), and \(99\%\) approximations. The requested region corresponds to approximately \(16\%\).
Question 44
Explanation
Use symmetry and the \(68\%\), \(95\%\), and \(99\%\) approximations. The requested region corresponds to approximately \(13.5\%\).
Question 45
Explanation
Use symmetry and the \(68\%\), \(95\%\), and \(99\%\) approximations. The requested region corresponds to approximately \(5\%\).
Question 46
Explanation
The factor \(4\) scales deviations; the shift \(-9\) does not.
Question 47
Explanation
Equal shifts preserve every distance from the corresponding mean.
Question 48
Explanation
The chapter-level normal approximation places about \(95\%\) within two standard deviations.
Question 49
Explanation
Set A lies four units from the mean, whereas Set B lies only one unit away.
Question 50
Explanation
Signed deviations sum to zero; squaring retains their magnitudes.
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- Question 10Calculate standard deviationEasy
- Question 11Compare standard deviationsEasy
- Question 12Compare standard deviationsEasy
- Question 13Compare standard deviationsEasy
- Question 14Compare standard deviationsEasy
- Question 15Compare standard deviationsEasy
- Question 16Visual spread comparisonMedium
- Question 17Visual spread comparisonMedium
- Question 18Visual spread comparisonMedium
- Question 19Visual spread comparisonMedium
- Question 20Visual spread comparisonMedium
- Question 21Standard deviation under shiftsMedium
- Question 22Standard deviation under shiftsMedium
- Question 23Standard deviation under shiftsMedium
- Question 24Standard deviation under shiftsMedium
- Question 25Standard deviation under shiftsMedium
- Question 26Standard deviation under scalingMedium
- Question 27Standard deviation under scalingMedium
- Question 28Standard deviation under scalingMedium
- Question 29Standard deviation under scalingMedium
- Question 30Standard deviation under scalingMedium
- Question 31Affine transformationsMedium
- Question 32Affine transformationsMedium
- Question 33Affine transformationsMedium
- Question 34Affine transformationsMedium
- Question 35Affine transformationsMedium
- Question 36Normal central intervalsMedium
- Question 37Normal central intervalsMedium
- Question 38Normal central intervalsMedium
- Question 39Normal central intervalsMedium
- Question 40Normal central intervalsMedium
- Question 41Normal one-sided regionsHard
- Question 42Normal one-sided regionsHard
- Question 43Normal one-sided regionsHard
- Question 44Normal one-sided regionsHard
- Question 45Normal one-sided regionsHard
- Question 46Advanced standard-deviation reasoningHard
- Question 47Advanced standard-deviation reasoningHard
- Question 48Advanced standard-deviation reasoningHard
- Question 49Advanced standard-deviation reasoningHard
- Question 50Advanced standard-deviation reasoningHard