Probability and Statistics

6 )

If the median of the observations x, (x/5), (x/2), (x/3), (x/7), (x/4), (x/8) (x > 0) is 10 value of x is ________

View Solution

Answer :

marks: (x/8), (x/7), (x/5), (x/4), (x/3), (x/2), x (ascending order)

median = [(n + 1) / 2]th as n = 7

∴ M = 4^th observation = (x/4) & M = 10 ⇒ x = 40.

7 )

For the data 3, 3, 3, 3, 3 which of the following is true ?

Select correct option from following options

(a) δM > δx (b) δM = δx

View Solution

Answer :

All observation are same

∴ x = M = 3 hence δM = δx.

8 )

The sum of 10 observations is 150 and the sum of their squares is 2700. The standard deviation is _______

3âˆš5

5âˆš3

View Solution

Answer :

Standard deviation = S = √[{(∑xi²) / n} – {(∑xi) / n}²]

given: n = 10

∑xi = 150

∑xi² = 2700

∴ S = √[{(2700) / 10} – {(150) / 10}²]

= √(45)

= 3√5.

9 )

The standard deviation and coefficient of variation of 7, 7, 7, 7, 7 is _______

0, 7

7, 0

7, 7

0, 0

View Solution

Answer :

all observation are same.

∴ standard deviation = 0

as coefficient of variation = [(standard deviation) / (mean)]

∴ it is also 0.

10 )

If n = 10, x = 12 and xi² = 1530 the value of coefficient of variation is _______

25%

20%

30%

35%

View Solution

Answer :

n = 10, x = 12 and xi² = 1530

standard deviation = S = √[{(∑xi²) / n} – {(∑xi) / n}²]

= √[{(1530) / 10} – 144]

= 3

coefficient of variation = [(standard deviation) / (mean)] = (3/12) = (1/4)

∴ % coefficient of variation = (1/4) × 100 = 25%.

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