Mean, Median & Mode (Railway Maths) (Part – II)

Total Questions: 50

31. Find the mode for the following data of student ages: 16, 17, 15, 17, 16, 15, 14, 14, 13, 17, 13, 12, 12, 16, 10, 14, 17, 10, 11. [Group D 11/10/2022 (Evening) ]

Correct Answer: (c) 17
Solution:

16, 17, 15, 17, 16, 15, 14, 14, 13, 17, 13, 12, 12, 16, 10, 14, 17, 10, 11.
On arranging the numbers, 10, 10, 11, 12, 12, 13, 13, 14, 14, 14, 15, 15, 16, 16, 16, 17, 17, 17, 17,
So, mode = 17

32. The mean of the observations 29, 36, 21, 18, 7, 19, k, k is 21.25 and mode of the observations 29, 22, 15, 22, 18, 21, p, p is 29. Find the value of (p - k). [Level 6 (09/05/2022) Shift 1]

Correct Answer: (d) 9
Solution:

33. The mean of a certain number of observations is 12. If one observation is removed and the mean remains unaltered, then the removed observation is: [Level 6 (09/05/2022) Shift 2]

Correct Answer: (a) 12
Solution:

The mean remains unaltered only if the observations having mean equal to original mean is removed. Clearly, here 12 is removed.

34. If the median of a, a/2, 2a/3, a/4, 3a/6 is 6, then what is the value of a where a is natural number? [Level 6 (09/05/2022) Shift 2]

Correct Answer: (b) 10
Solution:

35. The mode and the mean of a grouped data are 27.5 and 28.5 respectively. Find the median, correct to two places of decimal, using empirical relation. [Level 4 (10/05/2022) Shift 1]

Correct Answer: (c) 28.17
Solution:

36. In the data set given below, what is the difference between the Median and the Mode? {2.1, 5, 6, 7, 8, 9.3, 11, 15, 17, 19, 21, 27, 31, 31, 33, 16.5, 14, 10} [Level 5 (12/06/2022) Shift 1]

Correct Answer: (b) 17
Solution:

On arranging lowest to highest, 2.1, 5, 6, 7, 8, 9.3, 10, 11, 14, 15, 16.5, 17, 19.21, 27, 31, 31, 33 Mode = 31 (Most repeated)
Median = 14 , Difference = 31 - 14 = 17

37. If assumed mean, a = 142.5, dᵢ = xᵢ − a, fᵢ = frequency of xᵢ, the i-th value Σfᵢdᵢ = 130.5 and Σfᵢ = 90 then find the arithmetic mean of all the values of xᵢ. [Level 2 (13/06/2022) Shift 1]

Correct Answer: (d) 143.95
Solution:

38. If 12 is subtracted from each of n values x₁, x₂, ……, xₙ, then the sum of the resulting numbers is 92. If 8 is subtracted from each of the n values, then the sum of the numbers is 208. What is the mean of the given n values? (Give your answer correct to one decimal place.) [Level 2 (13/06/2022) Shift 1]

Correct Answer: (c) 15.2
Solution:

39. If the ratio of the mode and median is 13 : 9, then find the ratio of the mean and mode using empirical relation. [Level 3 (14/06/2022) Shift 2]

Correct Answer: (d) 7 : 13
Solution:

40. What is the Median of 5, 2, 7, 8, 1 and 4 ? [Level 5 (15/06/2022) Shift 1 ]

Correct Answer: (a) 4.5
Solution:

On arranging,
1, 2, 4, 5, 7, 8 , Median = 4 + 5/2 = 4.5