Quantitative Aptitude

Statistics — Tier II: Practice Questions with Answers

14 practice questions on Statistics — Tier II, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   Find the median of 9, 3, 7, 5, 11. Then a sixth value, 15, is added to the data set — find the new median.

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   Answer: Original median = 7, new median = 8

   Solution:

   1. Original data sorted: 3, 5, 7, 9, 11 — 5 values (odd), so the median is the 3rd value: 7.
   2. With 15 added, sorted data becomes: 3, 5, 7, 9, 11, 15 — now 6 values (even), so the median is the average of the 3rd and 4th: (7 + 9)/2 = 8.

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2. Q.2

   Find the mode of: 4, 8, 4, 6, 8, 4, 9

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   Answer: 4

   Solution:

   1. Counting occurrences: 4 appears 3 times, 8 appears 2 times, 6 and 9 appear once each.
   2. The most frequent value is 4.

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3. Q.3

   Find the mean, median and mode of: 5, −2, 5, 8, −2, 5, 10

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   Answer: Mean ≈ 4.14, Median = 5, Mode = 5

   Solution:

   1. Mean: sum = 5 + (−2) + 5 + 8 + (−2) + 5 + 10 = 29, and 29/7 ≈ 4.14.
   2. Median: sorted data is −2, −2, 5, 5, 5, 8, 10 — the 4th (middle) value is 5.
   3. Mode: 5 appears 3 times, more than any other value, so the mode is 5.

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4. Q.4

   The marks of 6 students are: 45, 60, 55, 70, 65, 50. Find the median.

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   Answer: 57.5

   Solution:

   1. Sort the data: 45, 50, 55, 60, 65, 70 — 6 values (even), so the median is the average of the 3rd and 4th values.
   2. Median = (55 + 60) / 2 = 57.5.

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5. Q.5

   Find the mean, median and mode of the data set: 10, 15, 10, 20, 15, 10, 25

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   Answer: Mean = 15, Median = 15, Mode = 10

   Solution:

   1. Mean: sum = 10+15+10+20+15+10+25 = 105, and 105 / 7 = 15.
   2. Median: sorted data is 10, 10, 10, 15, 15, 20, 25 — the 4th (middle) value is 15.
   3. Mode: 10 appears 3 times, more than any other value, so the mode is 10.

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6. Q.6

   Find the median of: 12, 7, 15, 9, 21, 7, 18

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   Answer: 12

   Solution:

   1. Sort the data: 7, 7, 9, 12, 15, 18, 21 — 7 values, so the median is the 4th value.
   2. The 4th value is 12.

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7. Q.7

   Find the mean and median of: 2, 3, 4, 5, 46. What does the gap between them tell you?

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   Answer: Mean = 12, Median = 4 (the outlier skews the mean, not the median)

   Solution:

   1. Mean = (2 + 3 + 4 + 5 + 46) / 5 = 60 / 5 = 12.
   2. Sorted data: 2, 3, 4, 5, 46 — median (3rd value) = 4.
   3. The mean (12) is far above the median (4) because the single large value, 46, is an outlier pulling the mean upward — the median is a better description of where most of this data actually sits.

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8. Q.8

   Find the mean, median and mode of: 12, 18, 12, 24, 18, 12, 30

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   Answer: Mean = 18, Median = 18, Mode = 12

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9. Q.9

   Find the mean and median of: 1, 2, 3, 4, 40. Which better represents a "typical" value here?

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   Answer: Mean = 10, Median = 3. The median better represents a typical value — the mean is pulled up by the outlier, 40.

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10. Q.10

    Find the mean, median and mode of: 7, −3, 7, 2, −3, 7, 9

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    Answer: Mean ≈ 3.71 (26/7), Median = 7, Mode = 7.

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11. Q.11

    Find the median of: 15, 22, 18, 30, 25, 19

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    Answer: 20.5. Sorted: 15,18,19,22,25,30; average of 19 and 22.

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12. Q.12

    Find the median of 4, 10, 6, 8. Then a fifth value, 20, is added — find the new median.

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    Answer: Original median = 7 (average of 6, 8); new median = 8 (middle of 4,6,8,10,20).

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13. Q.13

    Find the median of: 8, 3, 11, 5, 14, 3, 9

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    Answer: 8

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14. Q.14

    Find the mode of: 6, 9, 6, 7, 9, 6, 11

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    Answer: 6

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