IPMPrepThe mean of 28, 33, 8, 7 and x is 29. Find x.
Solution
Total of all 5 values = 5 × 29 = 145.
x = 145 − 76 = 69.
Answer: 69
Quantitative Ability · Counting and Data
Statistics: IPMAT practice questions
24 questions, 10 of them short answer (type the number, as in IPMAT Indore). Each is marked with the exam level it suits. Answer, then open the step-by-step solution.
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For the data 16, 25, 7, 25, 1, 20, 10, find mode + range.
Solution
Mode = 25 (appears 2 times).
Range = 25 − 1 = 24.
Sum = 49.
Answer: 49
The mean of 1, 55, 41, 17, 15, 23, 42 and x is 28. Find x.
Solution
Total of all 8 values = 8 × 28 = 224.
x = 224 − 194 = 30.
Answer: 30
The mean of 7, 23, 21, 59 and x is 26. Find x.
Solution
Total of all 5 values = 5 × 26 = 130.
x = 130 − 110 = 20.
Answer: 20
Find the variance of 8, 14, 12, 18 (divide by the number of values).
Solution
Mean = 13.
Squared deviations: 25, 1, 1, 25.
Variance = 524 = 13.
Answer: (B) 13
The mean of 14, 10, 3, 3 and x is 10. Find x.
Solution
Total of all 5 values = 5 × 10 = 50.
x = 50 − 30 = 20.
Answer: 20
A data set has mean 49 and standard deviation 5. Each value x is changed to 2x − 3. Find the new standard deviation.
Solution
Adding a constant does not change the spread; multiplying by a scales the SD by |a|.
New SD = |2| × 5 = 10.
Answer: (D) 10
Section A has 10 students with an average score of 59; section B has 22 students averaging 59. Find the average of all the students.
Solution
Total = 10 × 59 + 22 × 59 = 1888.
Average = 188832 = 59.
Answer: (A) 59
The mean of 20 observations was 46. Later it was found that one value, 95, had been recorded as 55. Find the correct mean.
Solution
Wrong total = 20 × 46 = 920.
Correct total = 920 − 55 + 95 = 960.
Correct mean = 48.
Answer: (B) 48
Section A has 25 students with an average score of 70; section B has 22 students averaging 70. Find the average of all the students.
Solution
Total = 25 × 70 + 22 × 70 = 3290.
Average = 329047 = 70.
Answer: (A) 70
For the data 21, 7, 29, 18, 21, 26, 10, find mode + range.
Solution
Mode = 21 (appears 2 times).
Range = 29 − 7 = 22.
Sum = 43.
Answer: 43
A data set has mean 51 and standard deviation 8. Each value x is changed to 1/2x + 9. Find the new standard deviation.
Solution
Adding a constant does not change the spread; multiplying by a scales the SD by |a|.
New SD = |12| × 8 = 4.
Answer: (B) 4
The mean of 28 observations was 80. Later it was found that one value, 53, had been recorded as 39. Find the correct mean.
Solution
Wrong total = 28 × 80 = 2240.
Correct total = 2240 − 39 + 53 = 2254.
Correct mean = 80.5.
Answer: (B) 80.5
Find the variance of 7, 1, 13, 11 (divide by the number of values).
Solution
Mean = 8.
Squared deviations: 1, 49, 25, 9.
Variance = 844 = 21.
Answer: 21
A data set has mean 12 and standard deviation 5. Each value x is changed to 5x + 0. Find the new mean.
Solution
Under y = ax + b, the mean becomes a × mean + b.
New mean = 5 × 12 + 0 = 60.
Answer: (B) 60
Find the variance of 6, 6, 18, 18 (divide by the number of values).
Solution
Mean = 12.
Squared deviations: 36, 36, 36, 36.
Variance = 1444 = 36.
Answer: 36
The mean of 54 observations was 50. Later it was found that one value, 40, had been recorded as 76. Find the correct mean.
Solution
Wrong total = 54 × 50 = 2700.
Correct total = 2700 − 76 + 40 = 2664.
Correct mean = 49 13.
Answer: (D) 49 13
A data set has mean 18 and standard deviation 6. Each value x is changed to 3x + 8. Find the new mean.
Solution
Under y = ax + b, the mean becomes a × mean + b.
New mean = 3 × 18 + 8 = 62.
Answer: (C) 62
The mean of 20 observations was 45. Later it was found that one value, 47, had been recorded as 37. Find the correct mean.
Solution
Wrong total = 20 × 45 = 900.
Correct total = 900 − 37 + 47 = 910.
Correct mean = 45.5.
Answer: (D) 45.5
Find the median of 28, 14, 22, 25, 8, 28, 27, 13, 22.
Solution
Sorted: 8, 13, 14, 22, 22, 25, 27, 28, 28.
Median = 22 (the middle value).
Answer: 22
Find the median of 27, 28, 21, 13, 27, 2, 1, 25.
Solution
Sorted: 1, 2, 13, 21, 25, 27, 27, 28.
Median = 23 (average of the two middle values).
Answer: 23
Section A has 34 students with an average score of 49; section B has 34 students averaging 71. Find the average of all the students.
Solution
Total = 34 × 49 + 34 × 71 = 4080.
Average = 408068 = 60.
Answer: (D) 60
Find the variance of 1, 13, 13, 4, 7, 16 (divide by the number of values).
Solution
Mean = 9.
Squared deviations: 64, 16, 16, 25, 4, 49.
Variance = 1746 = 29.
Answer: (B) 29
Section A has 19 students with an average score of 50; section B has 24 students averaging 50. Find the average of all the students.
Solution
Total = 19 × 50 + 24 × 50 = 2150.
Average = 215043 = 50.
Answer: (B) 50
These are original practice questions written by Target Campus in the pattern, syllabus and difficulty of IPMAT Indore, IPMAT Rohtak, JIPMAT, NPAT and SET. They are not previous-year papers.