Question

3. For the given data 10, 8, 3, 2, 3, 10, find
(a) Median
(b) Mean
(c) Mode
(d) Standard deviation
(e) Range
(f) Interquartile range, IQR

4. For the date 4, 16, 20, 24, 38, 57, 59, 60, 60, 74, compute the 10% trimmed mean.

5. Let ? and ? be any two events with their probabilities as ?(?) = 0.42 and ?(?)= 0.24.
(a) Find ? (??? ?)

(b) If the two given events are mutually exclusive, find ?(? ?? ?).
(c) If the two given events are not mutually exclusive and ?(? & ?)= 0.16, find ?(? ∪ ?).

Please answer this asap with solution steps. Thanks

Answer 1

3. (a) The data after arranging in ascending order is 2,3,3,8,10,10.
Median is the (n +1)/2 th number = 3.5th number = (3+8)/2 = 5.5
(b) Mean = (Sum of all the numbers)/6 = 36/6 = 6
(c) There are two modes 3 and 10.
(d) Standard deviation is

(e) Range = max - min = 8
(f) First quartile Q1 is (n + 1)/4 th term = 2.75 and the third quartile Q3 = 3*(n + 1)/4 th term = 10
Interquartile range = 10 - 2.75 = 7.25

4. 10% trimmed mean = mean of the numbers leaving bottom and top 10% of the data. Here a total of 10 terms are there, leaving first and last term, the mean of the remaining is
(16 + 20 + 24 + 38 + 57 + 59 + 60 + 60)/8 = 41.75

5. (a) P(not F) = 1 - P(F) = 1 - 0.24 = 0.76
(b) P(E or F) = P(E) + P(F) as E and F are mutually exclusive events
P(E or F) = 0.42 + 0.24 = 0.66
(c) If E and F are not mutually exclusive events, then
P(E∪F) = P(E) +P(F) - P(E&F)
or P(E∪F) = 0.42 + 0.24 - 0.16 = 0.50