Math Olympiad Test: Statistics- 4 - Class 10 MCQ

Let the excluded number be x and the sum of rest of numbers be y.

Then,  

⇒ 126 = x + y

Also, 19 = y/5

⇒ y = 95 

∴ From (i), x = 31.

Arithmetic mean =

= 

= 

= 6.27

The incorrect sum of observations = 12.5 x 20 = 250

Now, correct sum = 250 - (-15) + 15 = 280

∴ Correct mean = 280/20 = 14

Mean = 

⇒  20 (15 + 5 p) = 295 + 100 p + 5 p²

⇒  300 + 100 p = 295 + 100 p + 5 p²

⇒ 5p² = 5

⇒ p² = ±1 ⇒ p = 1 ( ∵p ≠ - 1)

⇒ 

= 25 + 2 = 27 

Average speed = Total distance covered/Total time taken

Let x be the distance between P and Q.

Thus, time taken by bus from P to Q (t₁) = x/60

Thus, time taken by bus from Q to P (t₂) = x/90

Total distance covered = 2x  and total time taken = t₁ + t₂

Average speed,  = 

= 

= 72 km/hr

Let the number of candidates that appeared from school III- be x.

Average score of the candidates of all the four schools

= 

⇒ 9768 + 66 x = 10340 + 55 x

⇒ 11x = 572

⇒ x = 52

(i) The intersection point of less than ogive and more than ogive, the x-coordinate is the median. Median is 18.

(ii) Less than ogive is drawn by taking the upper limit of class interval along x-axis and their corresponding less than cumulative frequencies along y-axis.

(iii) Sum of 50 numbers = 50 x 18 = 900 

If each number is increased by 4, then

new sum = 900 + 4 x 50 = 1100

∴ New Mean = 1100/50 = 22

(iv) Let seven consecutive numbers are x, x + 1, x + 2, ...., x + 6.

Mean = 

⇒ 

Smallest number x = 17 Largest number = x + 6 = 17 + 6 = 23.

To find the mean let us put the data in the table given below:


Thus, the mean of the given data is 62.4. 
Now, to find the median let us put the data in the table given below:

Now, N = 50 ⇒ N/2 = 25. 
The cumulative frequency just greater than 25 is 36 and the corresponding class is 60 – 80. 
Thus, the median class is 60 – 80. 
∴ l = 60, h = 20, N = 50, f = 12 and cf = 24. 
Now,

Hence, Mean = 62.4, Median = 61.67 and Mode = 60.21

Here,n = 275 ⇒ n/2 = 137.5 

Median class is 5 - 7

Median = 

= 

= 5 + 1.84 = 6.84