Practice
Mean, Median, Mode, and Range Practice
Fifty original questions on data summaries, missing values, frequency tables, weighted groups, transformations, and symbolic reasoning.
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Question 1
Explanation
The values total \(40\). Divide by \(4\): the mean is \(10\).
Question 2
Explanation
The values total \(55\). Divide by \(5\): the mean is \(11\).
Question 3
Explanation
The values total \(63\). Divide by \(3\): the mean is \(21\).
Question 4
Explanation
The values total \(35\). Divide by \(5\): the mean is \(7\).
Question 5
Explanation
The values total \(72\). Divide by \(4\): the mean is \(18\).
Question 6
Explanation
Order the values as \(3,6,9,12,15\). The middle value to \(9\).
Question 7
Explanation
Order the values as \(4,7,11,18\). The middle pair averages to \(9\).
Question 8
Explanation
Order the values as \(5,8,11,13,17,20\). The middle pair averages to \(12\).
Question 9
Explanation
Order the values as \(2,2,6,9,14\). The middle value to \(6\).
Question 10
Explanation
Order the values as \(12,18,25,31\). The middle pair averages to \(21.5\).
Question 11
Explanation
Compare frequencies. The correct response is \(4\) because it has the greatest frequency.
Question 12
Explanation
Subtract the minimum from the maximum: \(21-7=14\).
Question 13
Explanation
Compare frequencies. The correct response is \(2\) and \(5\) because both tie for greatest frequency.
Question 14
Explanation
Subtract the minimum from the maximum: \(31-14=17\).
Question 15
Explanation
Compare frequencies. The correct response is no mode because each value occurs once.
Question 16
Explanation
Use \(\text{sum}=n\bar{x}\): \(8(14)=112\).
Question 17
Explanation
Use \(\text{sum}=n\bar{x}\): \(12(7.5)=90\).
Question 18
Explanation
Use \(\text{sum}=n\bar{x}\): \(25(16)=400\).
Question 19
Explanation
Use \(\text{sum}=n\bar{x}\): \(6(21)=126\).
Question 20
Explanation
Use \(\text{sum}=n\bar{x}\): \(15(9.2)=138\).
Question 21
Explanation
The required total is \(5(11)=55\). The known values total \(36\), so \(x=55-36=19\).
Question 22
Explanation
The required total is \(4(16)=64\). The known values total \(45\), so \(x=64-45=19\).
Question 23
Explanation
The required total is \(6(13)=78\). The known values total \(66\), so \(x=78-66=12\).
Question 24
Explanation
The required total is \(4(28)=112\). The known values total \(80\), so \(x=112-80=32\).
Question 25
Explanation
The required total is \(5(9)=45\). The known values total \(33\), so \(x=45-33=12\).
Question 26
Explanation
The weighted total is \(33\), and the total frequency is \(6\). Therefore the mean is \(33/6=5.5\).
Question 27
Explanation
The weighted total is \(45\), and the total frequency is \(6\). Therefore the mean is \(45/6=7\).
Question 28
Explanation
The weighted total is \(34\), and the total frequency is \(8\). Therefore the mean is \(34/8=4.25\).
Question 29
Explanation
The weighted total is \(24\), and the total frequency is \(4\). Therefore the mean is \(24/4=6\).
Question 30
Explanation
The weighted total is \(150\), and the total frequency is \(10\). Therefore the mean is \(150/10=15\).
Question 31
Explanation
The combined total is \(10(70)+15(80)=1900\), and the combined count is \(25\). Their quotient is \(76\).
Question 32
Explanation
The combined total is \(8(12)+12(18)=312\), and the combined count is \(20\). Their quotient is \(15.6\).
Question 33
Explanation
The combined total is \(20(64)+30(74)=3500\), and the combined count is \(50\). Their quotient is \(70\).
Question 34
Explanation
The combined total is \(9(25)+6(40)=465\), and the combined count is \(15\). Their quotient is \(31\).
Question 35
Explanation
The combined total is \(14(88)+21(78)=2870\), and the combined count is \(35\). Their quotient is \(82\).
Question 36
Explanation
The original total is \(5(18)=90\). The new mean is \((90+30)/6=20\).
Question 37
Explanation
The original total is \(9(12)=108\). The new mean is \((108+22)/10=13\).
Question 38
Explanation
The original total is \(7(25)=175\). The new mean is \((175+15)/8=23.75\).
Question 39
Explanation
The original total is \(4(16)=64\). The new mean is \((64+26)/5=18\).
Question 40
Explanation
The original total is \(11(40)=440\). The new mean is \((440+20)/12=38.333\).
Question 41
Explanation
A common shift moves measures of center by the shift but preserves endpoint distance.
Question 42
Explanation
The median depends on ordered position rather than the outlier's magnitude.
Question 43
Explanation
Both endpoints scale by positive \(k\), so their difference also scales by \(k\).
Question 44
Explanation
All values tied at the greatest frequency are modes.
Question 45
Explanation
Range depends only on the maximum and minimum, not on order.
Question 46
Explanation
Three values with mean \(m\) have total \(3m\).
Question 47
Explanation
The original total is \(nm\); remove \(x\), then divide by the remaining count \(n-1\).
Question 48
Explanation
Each total equals its count times the common mean, so the combined quotient remains that mean.
Question 49
Explanation
With five ordered values, the third value is the median, so \(x=9\).
Question 50
Explanation
The required total is \(5(24)=120\), so the missing value is \(120-91=29\).
Keyboard: use Tab to move, arrow keys to change answer choices, and Enter to check an answer.
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Questions to review
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- Question 1Arithmetic meanEasy
- Question 2Arithmetic meanEasy
- Question 3Arithmetic meanEasy
- Question 4Arithmetic meanEasy
- Question 5Arithmetic meanEasy
- Question 6MedianEasy
- Question 7MedianEasy
- Question 8MedianEasy
- Question 9MedianEasy
- Question 10MedianEasy
- Question 11ModeEasy
- Question 12RangeEasy
- Question 13ModeEasy
- Question 14RangeEasy
- Question 15ModeEasy
- Question 16Mean-to-total conversionMedium
- Question 17Mean-to-total conversionMedium
- Question 18Mean-to-total conversionMedium
- Question 19Mean-to-total conversionMedium
- Question 20Mean-to-total conversionMedium
- Question 21Missing value from a meanMedium
- Question 22Missing value from a meanMedium
- Question 23Missing value from a meanMedium
- Question 24Missing value from a meanMedium
- Question 25Missing value from a meanMedium
- Question 26Frequency-table meanMedium
- Question 27Frequency-table meanMedium
- Question 28Frequency-table meanMedium
- Question 29Frequency-table meanMedium
- Question 30Frequency-table meanMedium
- Question 31Combined weighted meanMedium
- Question 32Combined weighted meanMedium
- Question 33Combined weighted meanMedium
- Question 34Combined weighted meanMedium
- Question 35Combined weighted meanMedium
- Question 36Updating a meanMedium
- Question 37Updating a meanMedium
- Question 38Updating a meanMedium
- Question 39Updating a meanMedium
- Question 40Updating a meanMedium
- Question 41Effects on summary statisticsHard
- Question 42Effects on summary statisticsHard
- Question 43Effects on summary statisticsHard
- Question 44Effects on summary statisticsHard
- Question 45Effects on summary statisticsHard
- Question 46Symbolic statistics reasoningHard
- Question 47Symbolic statistics reasoningHard
- Question 48Symbolic statistics reasoningHard
- Question 49Symbolic statistics reasoningHard
- Question 50Symbolic statistics reasoningHard