Statistics Mean Median Mode Range Competitive Exams
50 questions · Mathematics
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Question 1 of 50
Marks of 80 and 90 carry weights 2 and 3 respectively. The weighted mean is
Explanation(160 + 270)/5 = 86.
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Question 2 of 50
The mode of 12, 15, 12, 18 and 12 is
Explanation12 occurs three times.
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Question 3 of 50
The median of 12, 7, 3, 9, 15 and 6 is
ExplanationOrdered: 3, 6, 7, 9, 12, 15. Average of 7 and 9 is 8.
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Question 4 of 50
The geometric mean of 4 and 9 is
ExplanationGM = square root of (4 x 9) = 6.
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Question 5 of 50
The mode of the ages 18, 19, 18, 20, 21, 18, 19 is
Explanation18 occurs three times.
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Question 6 of 50
For x = 1, 2, 3, 4, 5 with frequencies 2, 3, 5, 4, 1, the median is
ExplanationTotal = 15, so the median is the 8th value. Cumulative frequencies are 2, 5, 10, so the 8th value is 3.
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Question 7 of 50
A data set has mean 12. If 5 is added to each value, the new mean is
ExplanationAdding a constant to every value adds the same constant to the mean.
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Question 8 of 50
The mean of 10 numbers is 25. One number, 35, was wrongly read as 53. The correct mean is
ExplanationCorrect sum = 250 - 53 + 35 = 232, so the mean is 23.2.
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Question 9 of 50
The mean of 3, 5, 7, 9 and 100 is
ExplanationSum = 124 and 124 / 5 = 24.8; the outlier 100 pulls the mean upward.
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Question 10 of 50
A data set has range 15. If 10 is added to each value, the new range is
ExplanationAdding a constant shifts all values equally, so the range does not change.
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Question 11 of 50
Which measure of central tendency is most affected by extreme values?
ExplanationEvery value is used in the mean, so extreme values pull it strongly. The median and mode are not much affected.
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Question 12 of 50
The median of 3, 5, 7, 9 and 100 is
ExplanationThe median is the middle value, 7, and is not affected by the extreme value 100.
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Question 13 of 50
The mean of four numbers is 15. A fifth number, 25, is added. The new mean is
ExplanationNew sum = 60 + 25 = 85 and 85 / 5 = 17.
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Question 14 of 50
If the mean of 5 numbers is 12, their sum is
ExplanationSum = mean x number of values = 12 x 5 = 60.
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Question 15 of 50
The mean of 6, 8, x and 12 is 9. The value of x is
ExplanationTotal needed = 36. 6 + 8 + 12 = 26, so x = 10.
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Question 16 of 50
In a frequency table, x = 2, 4, 6 with frequencies 3, 4, 3. The mean is
ExplanationSum of fx = 6 + 16 + 18 = 40; sum of f = 10; mean = 4.
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Question 17 of 50
The mean of 4, 6, 8, 10 and 12 is
ExplanationSum = 40 and 40 / 5 = 8.
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Question 18 of 50
The mean of 50 students is 62. The first 30 have mean 60. The mean of the remaining 20 is
ExplanationTotal = 3,100; first 30 total 1,800; remaining total 1,300; 1,300 / 20 = 65.
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Question 19 of 50
The mean of 10, 20 and 30 is
ExplanationSum = 60 and 60 / 3 = 20.
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Question 20 of 50
The median of 3, 7, 5, 9 and 1 is
ExplanationArrange in order: 1, 3, 5, 7, 9. The middle value is 5.
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Question 21 of 50
A data set has mean 8. If every value is multiplied by 3, the new mean is
ExplanationMultiplying all values by a constant multiplies the mean by that constant.
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Question 22 of 50
The median of 4, 8, 6 and 10 is
ExplanationOrdered: 4, 6, 8, 10. For an even number of values, take the average of the two middle values: (6 + 8)/2 = 7.
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Question 23 of 50
The mean of five numbers is 20. When one number, 28, is removed, the mean of the remaining numbers is
ExplanationSum = 100; remaining sum = 72; 72 / 4 = 18.
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Question 24 of 50
In a perfectly symmetric distribution, the mean, median and mode are
ExplanationIn a symmetric distribution all three measures coincide.
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Question 25 of 50
For a moderately skewed distribution, the median is 12 and the mean is 11. The mode is
ExplanationEmpirical relation: Mode = 3 Median - 2 Mean = 36 - 22 = 14.
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Question 26 of 50
Deviations of five values from an assumed mean of 50 are -2, 3, 5, -1 and 0. The actual mean is
ExplanationMean = assumed mean + average deviation = 50 + 5/5 = 51.
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Question 27 of 50
The median of the first nine natural numbers is
ExplanationThe middle (5th) value of 1 to 9 is 5.
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Question 28 of 50
The variance of 3, 3 and 3 is
ExplanationAll values equal the mean, so every deviation is 0.
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Question 29 of 50
The median of 2, 4, 6, 8 and 10 is
ExplanationThe data is already ordered; the middle value is 6.
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Question 30 of 50
The value that occurs most often in a data set is the
ExplanationA data set may have more than one mode.
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Question 31 of 50
The middle value of a set of data arranged in order is the
ExplanationThe median divides ordered data into two equal halves.
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Question 32 of 50
The harmonic mean of 2 and 6 is
ExplanationHM = 2ab/(a + b) = 24/8 = 3.
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Question 33 of 50
The mean of 7 numbers is 8. Each is increased by 2 and then multiplied by 3. The new mean is
Explanation(8 + 2) x 3 = 30.
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Question 34 of 50
For 1, 2, 3, 4, 5, 6, 7, 8, the interquartile range (using the median-of-halves method) is
ExplanationLower half 1 to 4 gives Q1 = 2.5; upper half 5 to 8 gives Q3 = 6.5; IQR = 4.
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Question 35 of 50
The mean of 3, 5, 7, 9, 11, 13 and 15 is
ExplanationSum = 63 and 63 / 7 = 9, which equals the middle value for an evenly spaced set.
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Question 36 of 50
The coefficient of range for data with maximum 80 and minimum 20 is
Explanation(Max - Min)/(Max + Min) = 60/100 = 0.6.
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Question 37 of 50
The mean of the first five natural numbers is
ExplanationSum = 15 and 15 / 5 = 3.
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Question 38 of 50
The data 2, 3, 3, 5, 5, 7 has mode
ExplanationBoth 3 and 5 occur twice, so the data is bimodal.
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Question 39 of 50
The range of 3, 3, 3 and 3 is
ExplanationHighest and lowest are equal, so the range is 0.
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Question 40 of 50
The mean of the first 20 natural numbers is
ExplanationMean = (n + 1)/2 = 21/2 = 10.5.
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Question 41 of 50
The range of the temperatures -4, 3, 10, -8 and 6 is
ExplanationRange = 10 - (-8) = 18.
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Question 42 of 50
The mean of the first ten even numbers is
ExplanationSum = 110 and 110 / 10 = 11.
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Question 43 of 50
The median of 11, 3 and 8 is
ExplanationOrdered: 3, 8, 11. The middle value is 8.
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Question 44 of 50
The mode of 2, 3, 3, 4, 5, 3, 6 is
Explanation3 occurs three times, more than any other value.
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Question 45 of 50
The mean of 7, 9, 11 and 13 is
ExplanationSum = 40 and 40 / 4 = 10.
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Question 46 of 50
The range of 45, 60, 52, 38 and 70 is
Explanation70 - 38 = 32.
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Question 47 of 50
The mean of 8 numbers is 15. When 20 and 30 are added, the new mean is
ExplanationNew sum = 120 + 50 = 170 and 170 / 10 = 17.
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Question 48 of 50
The range of 12, 5, 20, 8 and 15 is
ExplanationRange = highest - lowest = 20 - 5 = 15.
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Question 49 of 50
The standard deviation of 2, 4, 4, 4, 5, 5, 7, 9 is
ExplanationMean = 5; the variance is (9 + 1 + 1 + 1 + 0 + 0 + 4 + 16)/8 = 4; SD = 2.
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Question 50 of 50
Class A has 20 students with mean 50 and class B has 30 students with mean 60. The combined mean is
ExplanationTotal marks = 1,000 + 1,800 = 2,800; 2,800 / 50 = 56.
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