Statistics Quiz: Mean, Median and Mode Practice

Spoilers! These are the Starter quiz’s answers. Easy, Medium, Hard and Mixed rounds show their own answers when you finish.

1. What is the mean of the first 10 natural numbers?

   • 5
   • 5.5
   • 6
   • 10

   Answer: 5.5. Mean of the first n natural numbers = (n + 1)/2 = 11/2 = 5.5.

2. What is the median of 7, 3, 9, 4, 12, 8?

   • 7
   • 8
   • 7.5
   • 8.5

   Answer: 7.5. Sort first: 3, 4, 7, 8, 9, 12. With 6 values, the median is the average of the 3rd and 4th: (7 + 8)/2 = 7.5.

3. What is the mode of 2, 3, 5, 3, 7, 5, 3, 8?

   • 3
   • 5
   • 2
   • 8

   Answer: 3. The mode is the most frequent value: 3 appears three times, 5 only twice.

4. The mean of 5 numbers is 18. When one number is removed, the mean of the rest becomes 16. Which number was removed?

   • 24
   • 28
   • 20
   • 26

   Answer: 26. Total before = 5 × 18 = 90; total after = 4 × 16 = 64. Removed number = 90 − 64 = 26.

5. In a moderately skewed distribution, the mean is 30 and the median is 28. Using the empirical relation, what is the mode?

   • 24
   • 26
   • 32
   • 22

   Answer: 24. Mode = 3 Median − 2 Mean = 84 − 60 = 24.

6. What is the range of the data 15, 8, 22, 31, 12?

   • 16
   • 19
   • 31
   • 23

   Answer: 23. Range = highest − lowest = 31 − 8 = 23.

7. Class A has 30 students with an average score of 60, and class B has 20 students with an average of 70. What is the average score of all 50 students?

   • 65
   • 64
   • 66
   • 62

   Answer: 64. Combined mean = (30 × 60 + 20 × 70)/50 = 3,200/50 = 64. It leans towards the bigger class, so it is not 65.

8. The mean of 20 observations was found to be 40. Later it was found that one observation, 52, had been copied as 25. What is the correct mean?

   • 40.85
   • 41.35
   • 41.25
   • 42.35

   Answer: 41.35. The total was short by 52 − 25 = 27. Correct mean = 40 + 27/20 = 41.35.

9. Marks of 10 students: 10 marks (2 students), 20 marks (3 students), 30 marks (4 students), 40 marks (1 student). What is the mean mark?

   • 25
   • 22
   • 26
   • 24

   Answer: 24. Mean = sum of (f × x)/sum of f = (20 + 60 + 120 + 40)/10 = 240/10 = 24.

10. If 4 is added to every observation in a data set, which of these does NOT change?

    • Mean
    • Median
    • Range
    • Mode

    Answer: Range. Adding a constant shifts every value, so mean, median and mode all rise by 4; the gap between the highest and lowest stays the same.