Mathematics Class IX Questions Bank

Question 1 of 51

1. Question
1 point(s)
Is it correct to say that in a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval ? Justify your answer.
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Hint

It is not correct because in a histogram, the area of each rectangle is proportional to the corresponding frequency of its class
Question 2 of 51

2. Question
1 point(s)
The mean of a data is $\bar x $. What will be the new mean if each value of the data is increased by a ?
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Hint

Mean $=\bar x=\dfrac{\sum x_i}{n}$
$\dfrac{x_1+a+x_2+a+…+x_n+a}{n}\\ \\ =\dfrac{(x_1+x_2+…+x_n)+n_a}{n}\\ \\ =\dfrac{\sum x_i}{n}+\dfrac{na}{n}=\bar x+a$
Question 3 of 51

3. Question
1 point(s)
Observe the data : 16, 9, 3, 9, 9, 3, 2. Since, 16 is the highest value in the observation, so the mode of the data is 16. Is it correct ?
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Hint

No mode is the number that occur most times. Here mode is 9
Question 4 of 51

4. Question
1 point(s)
What is the median of first 19 natural numbers ?
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Hint

First 19 natural numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 19
Median is 10
Question 5 of 51

5. Question
1 point(s)
The mean of 5 numbers is 27. If one of the numbers is excluded, the mean of remaining numbers is 25. Find the excluded number.
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Hint

Excluded number $=(27\times5)-(25\times4)$
$135-100=35$
So the excluded number is 35
Question 6 of 51

6. Question
1 point(s)
Find the median of first ten prime numbers.
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Hint

First ten prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Median $=\dfrac{11+13}{2}=\dfrac{24}{2}=12$
Question 7 of 51

7. Question
1 point(s)
The weights, in grams of 30 oranges picked at random from a basket are given below:
70, 110, 119, 81, 158, 144, 125, 120, 155, 90, 102, 62, 98, 156, 145, 150, 135. 140, 82, 125, 61, 85, 117, 121, 121, 130, 65, 69, 92, 100.
Construct the continunous grouped frequency distribution table, width of each class being 20 grams and first class being 60–80 (80 not included).
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Question 8 of 51

8. Question
1 point(s)
Average monthly consumption of petrol for first 3 months is 86 litres and for next 9 months is 152 litres. Find the average consumption for the whole year.
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Hint

Average consumption $=\dfrac{3\times86+9\times152}{12}$
$=\dfrac{258+1368}{12}\\ \\ =\dfrac{1626}{12}=135.5$
Question 9 of 51

9. Question
1 point(s)
The mean marks scored by 100 students was 40 Later on, it was discovered that a score of 53 was misread as 83. Find the correct mean marks.
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Hint

Correct mean $=\dfrac{100\times40+53-83}{100}$
$=\dfrac{4000+53-83}{100}\\ \\ =\dfrac{3970}{100}=39.70$
Question 10 of 51

10. Question
1 point(s)
Find the mean of 3, 4, 6, 7, 8, 14. If 5 is added to each observation, what will be the new mean ?
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Hint

Mean $=\dfrac{37+4+6+7+8+14}{6}=\dfrac{42}{6}=7$
If 5 is added then new mean $=7+5=12$
Question 11 of 51

11. Question
1 point(s)
Find the median of data : 26, 56, 32, 33, 60, 17, 34, 29 and 45. If 26 is replaced by 62, find the new median.
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Hint

$17,26,29,32,33,34,45,56,60$
Median $=33$
Now
$17, 29, 32, 33, 34, 45, 56, 60,62$
New median $=34$
Question 12 of 51

12. Question
1 point(s)
Find the median of the following data : 23, 31, 47, 24, 46, 27, 37, 30.
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Hint

$23,24,27,30,31,37,46,47$
Median $=\dfrac{30+31}{2}=\dfrac{61}{2}=30.5$
Question 13 of 51

13. Question
1 point(s)
The median of the observations $26, 29, 42, 53, x, x + 2, 70, 75, 82, 93$ arranged in ascending order is $65$. Find the value of $x $ :
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Hint

$26,29,42,53,x,x+2,70,75,82,93$
A/Q $\dfrac{x+x+2}{2}=65$
$2x+2=130\Rightarrow 2x=128\\ \\ \Rightarrow x=64$
Question 14 of 51

14. Question
1 point(s)
The following data represents height (in cm) of 20 students of a class : 132, 130, 134, 135, 130, 131, 134, 135, 133, 133, 130, 131, 133, 136, 135, 134, 130, 133, 129, 136.
Make a frequency table for the above information
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Question 15 of 51

15. Question
1 point(s)
The mean of 70 observations was found to be 150. While checking, it was detected that one value 210 was wrongly copied as 140, while calculating the mean. Find the correct mean.
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Hint

Correct mean $=\dfrac{70\times150+210-140}{70}$
$=\dfrac{10500+210-140}{70}\\ \\ =\dfrac{10570}{70}=151$
Question 16 of 51

16. Question
1 point(s)
The class marks of a distribution are 6, 10, 14, 18, 22, 26, 30. Find the class size and the class intervals.
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Hint

$10-6=4,14-10=4$
class size $=4$
We subtract $\dfrac{4}{2}=2$ from each class mark to get lower limit and add 5 to each class to get the upper limit
$(4-8),(8-12),(12-16),(16-20),(20-24),(24-28),(28-32)$
Question 17 of 51

17. Question
1 point(s)
The points scored by a basket ball team in a series of matches are as follows :17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28.
Find the median and the mode for the data.
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Hint

$2,5,7,7,8,10,10,10,14,17,18,24,25,27,28,48$
Median $=\dfrac{10+14}{2}=\dfrac{24}{2}=12$
As 10 occurs most frequently so the mode is 10
Question 18 of 51

18. Question
1 point(s)
Find the mean of the following data :
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Hint

$\bar x=\dfrac{322}{40}=8.05$
Question 19 of 51

19. Question
1 point(s)
The mean of 15 numbers is 9. If each observation is multipled by 4, what will be the new mean?Give reason for your answer.
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Hint

Mean of 15 numbers = 9
when each observations is multiplied with 4 then new mean $=9\times4=36$
Question 20 of 51

20. Question
1 point(s)
The mean of 13 observations is 14. If the mean of the first 7 observations is 12, and that of the last 7 observations is 16, find the seventh observation.
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Hint

seventh sum of 130 observation $=14\times13=182$
seventh sum of 7 observation $=7\times12=84$
seventh sum of last 7 observation $=7\times16=112$
$=(112+84)-182$
seventh observation $=196-182=14$
Question 21 of 51

21. Question
1 point(s)
Observe the following table :
If the mean of the data is 25.75, find the value of p.
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Hint

$\dfrac{895+15p}{31+p}=25.75\\ \\ \Rightarrow 895+15p=798.25+25.75p\\ \\ \Rightarrow p=9$
Question 22 of 51

22. Question
1 point(s)
If the mean of five observations $x, x + 2, x + 4, x + 6, x + 8$ is $11$, find the mean of first three observations.
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Hint

$\dfrac{x+x+2+x+4+x+6+x+8}{5}=11\\ \\ \Rightarrow 5x+20=55\Rightarrow\ 5x=35\Rightarrow x=7$
Three observation are $7,9,11$
Mean $=\dfrac{7+9+11}{3}=\dfrac{27}{3}=9$
Question 23 of 51

23. Question
1 point(s)
The following observations have been arranged in ascending order where median of the data is $63 : 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95$. Find the mean of the data.
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Hint

A/Q $\dfrac{x+x+2}{2}=63$
$\Rightarrow 2x+2=126\\ \\ \Rightarrow 2x=124\Rightarrow x=62$
observation are $29,32,48,50,62,64,72,78,84,95$
Mean $=\dfrac{29+32+48+50+62+64+72+78+84+95}{10}=\dfrac{614}{10}=61.4$
Question 24 of 51

24. Question
1 point(s)
Find the arithmetic mean of the following table
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Hint

$\bar x=\dfrac{1848}{30}=61.6$
Question 25 of 51

25. Question
1 point(s)
Calculate the ariithmetic mean of the following data :
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Hint

$\bar x=\dfrac{1902}{30}=63.4$
Question 26 of 51

26. Question
1 point(s)
The mean of 14 values of a data is 23. If one more vlaue is introduced in the data, the mean of 15 values becomes 25. Find the fifteenth value.
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Hint

Fifteenth value $=(15\times25)-(14\times23)$
$=375-322=53$
Question 27 of 51

27. Question
1 point(s)
The mean of 50 observations of a data was 70. At later stage, it was noted that a value of 85 was wrongly read as 60. Find the value of the correct mean.
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Hint

Correct mean $=\dfrac{70\times50+85-60}{50}$
$=\dfrac{3500+85-60}{50}\\ \\ =\dfrac{3525}{50}=70.5$
Question 28 of 51

28. Question
1 point(s)
Find the average daily income of the employees of the company.
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Hint

$\bar x=\dfrac{27220}{50}=544.4$
Question 29 of 51

29. Question
1 point(s)
Find the mean salary of 50 workers of a factory from the following data.
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Hint

$\bar x=\dfrac{291500}{60}=4858.33$
Question 30 of 51

30. Question
1 point(s)
The mean weight per student in a group of 7 students is 55 kg. The individual weights of 6 of them in kg are 52, 54, 55, 53, 56, 54. Find the weight of the seventh student.
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Hint

Weight of 6 students $=52+54+55+53+56+54=324$
weight of 7 students $=7\times55=385$
weight of 7th student $=385-324=61\ kg$
Question 31 of 51

31. Question
1 point(s)
The mean of 25 observations is 36. If the mean of the first 13 observation is 32 and that of last 13 observations is 39, find the 13th observation.
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Hint

$13^{th}$ observation $=[(13\times32)+(13\times39)]-(25\times36)$
$=(416+507)-900\\ \\ =923-900=23$
Question 32 of 51

32. Question
1 point(s)
In a city, the weekly observation made in a study on the cost of living index are given in the following table :
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Hint

First we obtain the class marks as given in the following table.
Then, The frequency polygon is as follows
Question 33 of 51

33. Question
1 point(s)
The distance (in km) covered by 20 cars in 2 hours are given below : 125, 120, 130, 134, 100, 90, 96, 100, 110, 120, 112, 116, 104, 96, 100, 98, 120, 122, 124, 92. Represent the data as a continuous frequency distribution table with equal class size, starting from 90 – 95.
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Question 34 of 51

34. Question
1 point(s)
The following table gives the distribution of students of two sections according to the marks obtained by them.
Represent the marks of the students of both the sections on the same graph by two frequency polygons.
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Question 35 of 51

35. Question
1 point(s)
Obtain the mean of the following data :
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Hint

$\bar x=\dfrac{322}{40}=8.05$
Question 36 of 51

36. Question
1 point(s)
If the mean of the following distribution is 6, find the value of p.
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Hint

$\dfrac{42+2P+10}{10}=6\\ \\ \Rightarrow 2P+52=60\\ \\ \Rightarrow 2P=8\Rightarrow P=4$
Question 37 of 51

37. Question
1 point(s)
Find the mean salary of 20 workers of a factory from the table.
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Hint

$\bar x=\dfrac{143000}{20}=7150$
Question 38 of 51

38. Question
1 point(s)
The weights (in grams) of 30 oranges, picked at random from a basket of oranges are given below 90, 30, 45, 55, 65, 60, 50, 75, 70, 60, 70, 70, 60, 95, 85, 80, 35, 45, 40, 45, 55, 30, 110, 75, 100, 40, 60, 85, 40, 100
Construct a grouped frequency distrubution table with equal class intervals, one of them being 30-40.
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Question 39 of 51

39. Question
1 point(s)
Draw a histogram and frequency polygon (in the same diagram) for the following data :
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Question 40 of 51

40. Question
1 point(s)
Draw a histogram and a frequency polygon from the following data :
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Hint

Calculate the difference between the upper limit of the class interval and the lower limit of the next class interval, i.e. 20 – 21 = 1.
Half of the difference value is added to the upper limit of the class interval and half of the difference value is deducted from the lower limit of the class interval.
Exclusive series of the given inclusive series as follows:
Class Intervals Frequency
15.5-20.5 – 4
20.5-25.5 – 12
25.5-30.5 – 18
30.5-35.5 – 26
35.5-40.5 – 14
40.5-45.5 – 10
45.5-50.5 – 6
To draw frequency polygon, basically, the histogram is constructed and then the mid-points of the tops of rectangles in the histogram are marked. The marked mid-points are joined by using a foot rule to obtain the frequency polygon curve.
Question 41 of 51

41. Question
1 point(s)
The weights (in kg) of 60 persons are given below. Find the mean weight of a person by (i) direct method (ii) deviation method.
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Hint

$\bar x=\dfrac{3759}{60}=62.65\\ \\ \bar x=a+\dfrac{\sum f_id_i}{n}=63+\left(\dfrac{-21}{62}\right) \\ \\ =63-\dfrac{7}{20}=62.65$
Question 42 of 51

42. Question
1 point(s)
Draw a frequency polygon for the following data :
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Question 43 of 51

43. Question
1 point(s)
Draw a frequency polygon for the following data:
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Question 44 of 51

44. Question
1 point(s)
Draw a histogram and frequency polygon for the following distribution :
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Question 45 of 51

45. Question
1 point(s)
The following table gives the distribution of students of two sections according to the marks obtained by them.
Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons, compare the performance of the two sections
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Hint

Performance of section A is better than section B
Question 46 of 51

46. Question
1 point(s)
The runs scored by two teams A and B in 7 overs in a cricket match are given.
Represent the data of both the teams on the same graph by frequency polygon.
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Question 47 of 51

47. Question
1 point(s)
Following table shows the frequency distribution for the speeds of cars passing through a particular point on a highway.
Draw a histogram and a frequency polygon to represent the above data.
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Hint

Along the horizontal axis, we represent the class intervals on some suitable scale. The corresponding frequencies are represented along the vertical axis on a suitable scale.
We construct rectangles with class intervals as the bases and the respective frequencies as the heights.
Let us draw a histogram for this data and mark the mid-points of the top of the rectangles as B, C, D, E, F, G and H, respectively. Here, the first class is 30-40 and the last class is 90-100.
Also, consider the imagined classes 20-30 and 100-110 each with frequency O. The class marks of these classes are 25 and 105 at the points A and I, respectively.
Join all these points by dotted line.
Question 48 of 51

48. Question
1 point(s)
Draw a histogram to represent the above data. Make a frequency polygon for given frequency table
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Question 49 of 51

49. Question
1 point(s)
Draw a histogram to represent the following distribution.
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Question 50 of 51

50. Question
1 point(s)
Following table gives the distribution of the marks obtained by the students of a class. Represent the data by frequency polygon.
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Question 51 of 51

51. Question
1 point(s)
Draw the frequency polygon without constructing the histogram of the following observations.
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