Practice Questions: Statistics | CSAT Preparation - UPSC PDF Download

Mean of 5 observations = 11
We know:

⇒ 5x + 20 = 55 ⇒ 5x = 35 ⇒ x = 7

⇒ 5x + 25 = 45 ⇒ 5x = 20 ⇒ x = 4Therefore, the l as t three obs erv ati ons are 4 + 5 , 4 + 7 and 4 + 10 , i . e. , 9, 11 and 1/3

If x is the mean of x₁, x₂, x₃, x₄,...x_n, then we have: 

Let the numbers be x₁, x₂, ...x_n.
Hence, mean = 
Now the new numbers after decreasing every number by 8 : (x₁ − 8), (x₂ − 8)...,(x_n − 8)

Hence, mean is decreased by 8.

Mean weight of six boys = 48 kg
Let the weight of the 6th boy be x kg.

⇒ 235 + x = 288 ⇒ x = 53
Hence, the weight of the 6th boy is 53 kg.

Mean of the marks scored by 50 students = 39
Sum of the marks scored by 50 students = (39 x 50) = 1950
Correct sum = (1950 + 43 -23) = 1970
Mean = 1970/50 = 39.4

Mean of 100 items = 64
Sum of 100 items = 64 x 100 = 6400
Correct sum = (6400 + 36 + 90 - 26 - 9) = 6491
Correct mean = 6491/100 = 64.91

Mean of 100 observations = 50
Sum of 100 observations = 100 x 50 = 5000
It is given that one of the observations, 50, is replaced by 150.
New sum = (5000 - 50 + 150) = 5100 And,
Resulting mean = 5100/100 = 51

⇒ 303 + 9p = 328 + 8p ⇒ p = 25

Arranging the weight of 10 students in ascending order, we have:
0, 13, 15, 20, 27, 29, 31,34, 43, 50, 56
Here, n is 11, which is an odd number.
Thus, we have:

= Value of 6th term
= 29

Arranging the numbers in ascending order, we have:
31,35, 36, 38, 40, 44, 45, 52, 55, 60
Here, n is 10, which is an even number.
Thus, we have:

= Mean of the weights of 5th student

We will arrange the given data in ascending order as:
3, 4, 4, 5, 6, 7, 7, 7, 12
Here, n is 9, which is an odd number.
Thus, we have:

We will arrange the data in ascending order as:
22, 34, 39, 45, 54, 54, 56, 68, 78, 84
Here, n is 10, which is an even number.
Thus, we have:

Here, 14 occurs 4 times, 15 occurs 5 times, 16 occurs 1 time, 18 occurs 1 time, 19 occurs 1 time and 20 occurs 1 time. Therefore, the mode, which is the most occurring item, is 15.

The given data is in ascending order.
Here, n is 10, which is an even number.
Thus, we have:



= 24
Also, x + 3 = 24 ⇒ x = 21