Probability and Statistics

1 )

The median of a set of 7 distinct observations is 10.5 If each of the last 3 observation of the set is increased by 3 then the median of the new set = _______

in decreased by 2

is two times the original median

remain the same as that of the original set

is increased by 2

View Solution

Answer :

Here median = M = [(n + 1) / 2] = 4^th observation (∵ n = odd)

∴ median remain same even if last 3 observation values are increased.

2 )

The value of the variable of the given data for which the number of observations with values less than it and greater than it are equal is _______

mean

median

mode

range

View Solution

Answer :

This is definition of median.

3 )

The daily pocket expanses of 8 students are 20, 17, 8, 15, 22, 9, 10, 14 the median of the data is ______

14.5

15.5

View Solution

Answer :

Here n = 8 i.e. even numbers.

∴ median = M = [{[(n/2)^th observation] + [(n/2) + 1]^th observation} / 2]

∴ M = [(4^th + 5^th observation) / 2] = [(15 + 14) / 2] = 14.5.

4 )

The median of first n + 3 natural number is _______

[(n + 4) / 2]

[(n – 4) / 2]

[(n – 1) / 2]

[(n + 3) / 4]

View Solution

Answer :

median = [(n + 1) / 2]th observation,

hence n = n + 3

∴ M = [(n + 4) / 2].

5 )

The marks for passing in the examination in a subject is 33.4 out of 9 students who appeared at the examination have failed and the marks of remaining student are 78, 40, 97, 65, 50. The median of the data is ________ marks.

View Solution

Answer :

out of 9, marks of 5 students are 40, 50, 65, 78, 97.

∵ 4 have failed ⇒ Their marks are less than 33.4.

∵ n = 5 ⇒ median = [(n + 1) / 2]th reading i.e. 5^th reading.

∴ data in ascending order: marks of 4 failed students 40, 50, 65, 78, 97

∴ 5^th reading = 40 i.e. median = 40.

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