Statistics Test

Result

Statistics Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

The mean of six numbers is 23. If one of the numbers is excluded, the mean of the remaining numbers becomes 20. The excluded number is

A
37

B
39

C
38

D
36

Solution

The mean of six numbers is 23

so sum of six numbers is 23×6 = 138

after excluding one number, the mean of the remaining numbers is 20

so sum of five numbers is 20×5 = 100

the difference between them is

138 − 100 = 38
Question 2
1 / -0

The mean of five observations is 15. If the mean of first three observations is 14 and that of last three is 17, then the third observation is

A
29

B
31

C
32

D
18

Solution

The mean of five observations is 15

so sum of these five observation is 15×5 = 75

the mean of first three observations is 14

so sum of first three observations is 14×3 = 42

so the sum of last two numbers is 75-42 = 33

the mean oflast three observations is 17

so sum of last three observations is 17×3 = 51

so the middle number is 51-33 = 18
Question 3
1 / -0

The mean of 50 observations is 39. If one of the observations which was 23 was replaced by 43, the resulting mean will be

A
38.4

B
39.4

C
39

D
40.3

Solution

The mean of 50 observations is 39.

so sum of these 50 observations is 50×39 = 1950

after replacing the observation value 23 by 43,

sum becomes 1970

so the mean is1970 / 50 = 39.4
Question 4
1 / -0

There are 50 numbers. Each number is subtracted from 53 and the difference between the mean of the numbers so obtained is found to be 3.5. The mean of the given number is

A
56.5

B
47.5

C
49.5

D
52.5

Solution

Let the mean of the initial sequence is x.

Given that, after subtracting 53 from each number, the difference between the means is 3.5

So, x−53 = 3.5

mean of the number is x = 53+3.5 = 56.5
Question 5
1 / -0

The traffic police recorded the speed (in km/h) of 10 motorists as 48, 52, 57, 55, 42, 39, 60, 49, 53 and 47. Later an error in recording instrument was found. If the instrument has recorded the speed 5 km/h less in each case, then the correct average speed of the motorists is

A
54.5 km/h

B
52.5 km/h

C
50.2 km/h

D
55.2 km/h

Solution

sum of all the recorded speeds is

48 + 52 + 57 + 55 + 42 + 39 + 60 + 49 + 53 + 47 = 502

because of the error, 5 km/h in each case

the sum increases by 50 i.e 552

so the average speed of 10 vehicle is 55.2 km/h