Mathematics Class X

Question 1 of 30

1. Question
1 point(s)
The weight (in kg) of 5 men are 62, 65, 69, 66 and 61. The median is
- 45 kg
- 66 kg
- 65 kg
- 55 kg
Correct

Incorrect

Hint

arrange in ascending order $=61, 62, 65, 66, 69$
Median $=\left(\dfrac{5+1}{2}\right)^{th}$ item
$=3^{rd}$ item
$\therefore65$ is the median
Question 2 of 30

2. Question
1 point(s)
The mean of $x, x + 3, x + 6, x + 9$ and $x + 12$ is
- $x + 6$
- $x + 3$
- $x + 9$
- $x + 12$
Correct

Incorrect

Hint

Mean $=\dfrac{x+x+3+x+6+x+9+x+12}{5}$
$=\dfrac{5x+30}{5}=x+6$
Question 3 of 30

3. Question
1 point(s)
The mean of a data is P. if each observation is multiplied by 3 and then 1 is added to each result then the mean of the new observation so obtained is
- P
- 3P
- P + 1
- 3P + 1
Correct

Incorrect

Hint

New mean $= 3p+1$
Question 4 of 30

4. Question
1 point(s)
The mean of 20 observations is 12.5. By error one observation was noted as – 15 instead of 15. Then the correct mean is
- 11.75
- 11
- 14
- None of these
Correct

Incorrect

Hint

New mean $=\dfrac{20\times12.5-(-15)+15}{20}$
$=\dfrac{280}{20}=14$
Question 5 of 30

5. Question
1 point(s)
The average age of 5 teachers is 28 years. If one teacher is excluded, the mean gets reduced by 2 years. The age of the excluded teacher is
- 26 years
- 33 years
- 36 years
- None of these
Correct

Incorrect

Hint

$26=\dfrac{140-x}{4}\Rightarrow x=36$ years
Question 6 of 30

6. Question
1 point(s)
Which of the following is not a measure of central tendency?
- Mean
- Median
- Mode
- Standard deviation
Correct

Incorrect

Hint

Standard deviation
Question 7 of 30

7. Question
1 point(s)
The true statement for the data:- 1, -1, 0, 2, 3, 5, 5, 6, 8, 10, 11, is
- Mean = mode = median
- Mode = median = 5
- Mean = median = 5
- Mean = mode = 5
Correct

Incorrect

Hint

Mode is 5
Median = 5
Mean $=\dfrac{sum}{11}=\dfrac{50}{11}\angle5$
Question 8 of 30

8. Question
1 point(s)
The mean weight of a class of 34 student is 46.5kg. If the weight of the teacher is included, the mean rises by 500 gm. Then the weight of the teacher is
- 175 kg
- 62 kg
- 64 kg
- 72 kg
Correct

Incorrect

Hint

Weight of teacher $=46.5+500g\times 35=64\ kg$
Question 9 of 30

9. Question
1 point(s)
If in a data, 10 numbers arranged in increasing order. If the 7th entry is increased by 4, then the median increases by
- zero
- 4
- 6
- 5
Correct

Incorrect

Hint

Median is $5^{th}$ and $6^{th}$ data hence it is not affected by $7^{th}$ entry
Question 10 of 30

10. Question
1 point(s)
20 years ago, when my parents married their average age was 23 years, now the average age of my family consisting of myself and my parents only is 35 years. My parent age is
- 34 years
- 42 years
- 24 years
- 19 years
Correct

Incorrect

Hint

Total age of parents $=23\times2+20\times2=86\$ years
$35=\dfrac{86+x}{3}\\ \\ \Rightarrow x=19$ years
Question 11 of 30

11. Question
1 point(s)
The mean of $x, x+3, x+6, x+9$ and $x+12$ is
- $x+6 $
- $x+3 $
- $ x+9 $
- $x+12$
Correct

Incorrect

Hint

$\bar =\dfrac{5x+30}{5}=x+6$
Question 12 of 30

12. Question
1 point(s)
The average income of Sambhu and Ganesh is Rs 3000 and that of Arun and Vinay is Rs 500. What is the average income of Sambhu, Ganesh, Arun, Vinay?
- 1750
- 1850
- 1000
- 2500
Correct

Incorrect

Hint

Sum of income of Sambhu and Ganesh $=2\times300=6000$
Sum of income of Arun and Vinay $=2\times500=1000$
Average income $=\dfrac{7000}{4}=1750$
Question 13 of 30

13. Question
1 point(s)
If the arithmetic mean of a number of series is $\bar x $ and the sum of $(n-1) $ numbers is $ k$, then the $n^{th} $ number is
- $n+k $
- $n+k $
- $n-k $
- $n-k $
Correct

Incorrect

Hint

Sum of the number $=n\bar X$
Sum of $(n-1)$ number $=k$
$n^{th}$ number $=n\bar X-k$
Question 14 of 30

14. Question
1 point(s)
The numbers $3, 5, 6, 4$ have frequencies $x, x+2, x-8, x+6$ respectively. If their mean is $4$ then $x=$
- 5
- 6
- 7
- 8
Correct

Incorrect

Hint

The sum $=3x+5x+10+6x-48+4x+24=18x-14$
No. of observation $=4x(\because x+x+2+x-8+x+6)$
Mean $=4=\dfrac{18x-14}{4x}\\ \\ \Rightarrow x=7$
Question 15 of 30

15. Question
1 point(s)
The average value of the median of 2, 8, 3, 7, 4, 6, 7 and the mode of 2, 9, 3, 4, 9, 6, 9 is
- 9
- 8
- 7.5
- 6
Correct

Incorrect

Hint

Median of [2, 3, 4, 6, 7, 7, 8] is 6
Mode of [2, 9, 3, 4, 9, 6, 9] is 9
Average $=\dfrac{9+6}{2}=\dfrac{15}{2}=7.5$
Question 16 of 30

16. Question
1 point(s)
The median of the following incomplete frequency distribution is 4. The frequency of 8 is
- 1
- 2
- 3
- 4
Correct

Incorrect

Hint

As median is 4 so its CF = 10
$\dfrac{18+f+1}{2}=10\\ \\ 18+f+1=20\\ \\ 19+f=20\\ \\ F=1$
Question 17 of 30

17. Question
1 point(s)
The mode of a frequency distribution can be determined graphically from
- histogram
- polygon
- ogive
- frequency curve
Correct

Incorrect

Hint

Histogram
Question 18 of 30

18. Question
1 point(s)
The mode of a continous series is
- Mode $=1+\dfrac{f-f_1}{2f-f_1-f_2}\times h $
- Mode $=1-\dfrac{f_1+f_2}{2f-f_1-f_2}\times h $
- Mode $=1-\dfrac{f+f_2}{2f-f_1-f_2}\times h $
- None of these
Correct

Incorrect

Hint

$l+\dfrac{f_m-f_1}{2f_m-f_1-f_2}\times h$
Question 19 of 30

19. Question
1 point(s)
For a certain moderately skew distribution if mean is 24.6, median = 26.1 then its mode is
- 1.5
- 50.7
- 25.35
- 29.1
Correct

Incorrect

Hint

Mode = 3 median – 2 mean
$=3\times26.1-2\times24.6=29.1$
Question 20 of 30

20. Question
1 point(s)
Histogram is useful to determine graphically the value of
- arithmetic mean
- median
- mode
- none of these
Correct

Incorrect

Hint

Mean
Question 21 of 30

21. Question
1 point(s)
In an examination, 10 students scored the following marks 35, 19, 28, 32, 63, 02, 47, 31, 13, 98. Its range is
- 2
- 46
- 98
- 50
Correct

Incorrect

Hint

Range $= 98-2=96$
Question 22 of 30

22. Question
1 point(s)
Find the mean of $ x, x+8, x+11, x+1$
- $x+4 $
- $ x+5 $
- $2x+9 $
- $ x+6$
Correct

Incorrect

Hint

Mean $=\dfrac{(x+x+8+x+11+x+14)}{4}$
$=\dfrac{(4x+20)}{4}\\ \\ =\dfrac{4(x+20)}{4}\\ \\ =x+5$
Question 23 of 30

23. Question
1 point(s)
Find the average of first 40 natural number
- 21
- 20.5
- 21.5
- 19.5
Correct

Incorrect

Hint

Sum $=\dfrac{n(n+1)}{2}=\dfrac{40\times41}{2}=820$
Average $=\dfrac{820}{40}=20.5$
Question 24 of 30

24. Question
1 point(s)
The average of 11 result is 60. If average of first 6 result is 58 and that of last 6 is 63. Find the sixth result.
- 56
- 62
- 66
- 68
Correct

Incorrect

Hint

$6\times(63+58)-60\times11=66$
Question 25 of 30

25. Question
1 point(s)
A batsman makes a score of $87 $ runs in $\mathrm{17^{th}} $ inning and thus increases his average by 9. Find his average after $\mathrm{17^{th}} $ inning.
- 39
- 40
- 35
- 29
Correct

Incorrect

Hint

Let the average of $16$ is $x$
Sum of $16$ innning $=16x$
$\dfrac{16x+87}{17}=x+3\\ \\ \Rightarrow 16x+87=17x+51\\ \\ \Rightarrow x=36$
So average of $17$ inning $=36+3$
Question 26 of 30

26. Question
1 point(s)
Three years ago average age of A, B was with C joining then, the average age becomes 22 years. How old is C
- 24
- 27
- 28
- 30
Correct

Incorrect

Hint

Average age of $A+B=18 \times 2+2\times3=42$
Average age of $A+B+C=66$
C’S age $=66-42=24$
Question 27 of 30

27. Question
1 point(s)
Find the median of given data
- 38
- 35
- 19.5
- 35.58
Correct

Incorrect

Hint

$\dfrac{N}{2}=13.5$
Median class $=10-20$
Median $=l+\left[\dfrac{\dfrac{N}{2}-CF}{f}\right]\times h$
$=10+\dfrac{13.5-3}{11}\times10\\ \\ =10+\dfrac{105}{11}=19.5$
Question 28 of 30

28. Question
1 point(s)
Histogram is a
- one dimensional figure
- two dimensional figure
- three dimensional figure
- none of these
Correct

Incorrect

Hint

Two dimensional figure
Question 29 of 30

29. Question
1 point(s)
Which of the following central tendency cannot be find with any of the graph.
- mean
- median
- mode
- none
Correct

Incorrect

Hint

Mean
Question 30 of 30

30. Question
1 point(s)
By the cumulative frequency curve which of the central tendency can be find
- mean
- median
- mode
- none
Correct

Incorrect

Hint

Median

Mathematics Class X

Olympiad Questions-Statistics-Class X

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