CBSE Class 9 Mathematics Statistics Assignment Set A

1 Which of the following is t he number of times a part icular item occurs in a class interval?
(A) Mean
(B) Frequency
(C) Cumulative frequency
(D) Median
Answer : B

2 What are the groups into which large data is condensed called?
(A) Class limits
(C) Class size
(B) Classes
(D) Class width
Answer : B

3 Find t he mean of first 5 whole numbers.
(A) 2.5
(B) 3
(C) 1.5
(D) 2
Answer : D

4 The relative humidity (in o/o) of a city for 10 days is given in the box.
92 .1 97 .1 95 .7 93 .3 89
96.2 94.9 97.3 92.1 98.3
Determine its range.
(A) 9.3
(B) 9.6
(C) 9.5
(D) 9.8
Answer : A

5 The demand for different shirt sizes, as obt ained from a survey, is given in the table.

Find the modal shirt size.
(A) 39
(B) 40
(C) 44
(D) 42
Answer : A

6 The class marks of a frequency distribution are given as 15, 20,25, ...........
Find the class corresponding to the class mark 20.
(A) 12.5 - 17.5
(B) 17.5 - 22.5
(C) 18.5 - 21.5
(D) 19.5 - 20.5
Answer : B

(7-10): The bar graph given shows the months of birthdays of 40 students of a class.

Answer the following questions based on the graph.

7 How many students were born in August?
(A) 6
(B) 4
(C) 5
(D) 3
Answer : A

8 In which mont h were the minimum number of students born?
(A) February
(B) June
(C) December
(D) May
Answer : B

9 In which mont hs were at least 5 students born?
(A) June and October
(B) March and November
(C) February and September
(D) May and August
Answer : D

10 In which months was the difference in the number of st udents born t he same as that in October and November?
(A) February and January
(B) May and July
(C) March and April
(D) August and September
Answer : C

11 Find the median of the first ten prime numbers.
(A) 24
(B) 14
(C) 12
(D) 22
Answer : C

12 In a school 90 boys and 30 girls appeared for a public examination.The mean marks of boys was found to be 45o/o whereas the mean marks of girls was 70%. What is the average marks o/o of the school?
(A) 61.50%
(B) 51.25%
(C) 40.50%
(D) 51.52%
Answer : B

13 What is a graph drawn with the midpoints of the t op sides of t he rectangles forming the histogram of a frequency distribution called?
(A) Bar graph
(B) Ogive
(C) Frequency polygon
(D) Frequency curve
Answer : C

14 What do yo u call t he value in a data around which the values of all the other observat ions t end to concentrate?
(A) Common value
(B) Range
(C) Measure of central t endency
(D) Midvalue
Answer : C

15 Of the class int ervals 10 - 20 and 20 - 30, the number 20 is included in which of the  following?
(A) 10-20
(B) 20-30
(C) 15-20
(D) Both (A) and (B)
Answer : B

16 Find the arithmetic mean of 30,36,39,23 and 27.
(A) 28
(B) 20
(C) 31
(D) 35
Answer : C

17 The median of given observations arranged in ascending order is 25.
11, 13, 15, 19, p + 2, p + 4, 30, 35, 39, 46 .
Find p.
(A) 22
(B) 24
(C) 21
(D) 26
Answer : A

18 Which one of the following is not a measure of central tendency?
(A) Mean
(B) Range
(C) Median
(D) Mode
Answer : B

(19-22): The following is a chart showing the temperature of a patient recorded at different times.

Read the temperature chart and answer the given questions.

19 What is the temperature of the patient at 21 hrs?
(A) 100° F
(B) 101° F
(C) 102° F
(D) 103° F
Answer : A

20 What is the percent age increase in temperature between 9 hrs and 15 hrs?
(A) 4%
(B) 3%
(C) 2%
(D) 1%
Answer : A

21 What is the percentage decrease in temperature between 17 hrs and 19 hrs?
(A) 1.02%
(B) 1.03%
(C) 1.04%
(D) 1.01%
Answer : D

22 What is the average temperature of the patient between 13, 15 and 17 hrs?
(A) 103 °F
(B) 102 °F
(C) 101 °F
(D) 100 °F
Answer : B

23 The mean of first 8 observations is 18 and last 8 observations is 20.1f the mean of all 15 observations is 19, find the 8th observat ion.
(A) 18
(B) 12
(C) 19
(D) 20
Answer : C

24 A grouped frequency distribution table with classes of equal sizes using 63 - 72 (72 included) as one of the classes is constructed for the following data.
30,32,45, 54, 74, 78,108,112, 66, 76,88, 40, 14,20, 15,35,44, 66, 75,84,96, 102, 110, 88, 74, 112, 14, 34, 44
Find the number of classes in the distribution.
(A) 9
(B) 11
(C) 10
(D) 12
Answer : B

25 The mid-point of a class is m and l is the upper class limit in a continuous frequency distribution. Which of the following would be the lower class limit of the class?
(A) 2m + l
(B) 2m - l
(C) m - l
(D) m - 2l
Answer : B

26 The width of each of nine classes in a frequency distribution is 2.5 and the lower class boundary of the lowest class is 1 0.6. What is the upper class boundary of the highest class?
(A) 35.6
(B) 33.1
(C) 30.3
(D) 28.1
Answer : B

27 In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. What is the lower limit of the class?
(A) 6
(B) 7
(C) 8
(D) 12
Answer : B

28 In afrequency distribution, ogives are graphical representation of which of the following?
(A) Fr equency
(B) Relative frequency
(C) Cumulative frequency
(D) Raw data
Answer : C

29 Apart from plotting frequencies of the class intervals, which of the following are used to construct a frequency polygon?
(A) Upper limits of the classes
(B) Lower limits of the classes
(C) Any values of the classes
(D) Mid values of the classes
Answer : D

30 The mean wage of 150 labourers working in a factory running three shifts with 60,
40 and 50 labourers is ₹ 114. The mean wage of 60 labourers working in the first shift is ₹ 121.50 and that of 40 labourers working the second shift is ₹ 107.75. Find the mean wage of those who are working in the third shift.
(A) ₹ 110
(B) ₹ 100
(C) ₹ 120
(D) ₹ 115.75
Answer : A

31 The mean of n observations is X¯. If each observation is multiplied by k, what is the mean of new observations?
(A) kX¯
(B) x¯/k
(C) X¯ + k
(D) X¯ - k
Answer : A

32 The mean of 75 numbers is 25. If each number is divided by 5, find the new mean.
(A) 5
(B) 20
(C) 8
(D) 15
Answer : A

33 For which set of numbers do the mean, median and mode have the same value?
(A) 2,2, 2,4
(B) 1, 3, 3, 3, 5
(C) 1, 1, 2, 5, 6
(D) 1, 1, 1,2,5
Answer : B

34 Find the difference between arithmetic means of all even and odd numbers between 50 and 60.
(A) 2
(B) 0
(C) 1
(D) 3
Answer : B

35 For the set of numbers 2, 2, 4, 5 and 12 which of the following statements is true?
(A) Mean = Median
(B) Mean > Mode
(C) Mean < Mode
(D) Mode = Median
Answer : B

36 A cricketer has a mean score of 60 runs in ten innings. Find the number of runs that are to be scored in the eleventh inning to raise the mean score to 62.
(A) 62
(B) 78
(C) 58
(D) 82
Answer : D

37 Which of the following is the empirical relation between mean, mode and median?
(A) Mode= 3 Median - 2 Mean
(B) Mode= 2 Median - 3 Mean
(C) Median= 3 Mode - 2 Mean
(D) Mean = 3 Median - 2 Mode
Answer : A

38 Find the median of the data given.
(0, 2 , 2, 2, -3, 5, - 1, 5, 5, -3, 6, 6, 5, 6)
(A) 0
(B) - 1.5
(C) 2
(D) 3.5
Answer : D

39 The mean of 20 n umbers is 40. If 5 is subtracted f rom every number, what w ill be the new mean?
(A) 45
(B) 40
(C) 20
(D) 35
Answer : D

40 The mean of a, b, c, d and e is 28. If the mean of a, c, and e is 24, what is the mean of band d?
(A) 31
(B) 32
(C) 33
(D) 34
Answer : D

41 What is the algebraic sum of the deviations of a set of n values from their mean?
(A) 0
(B) n - 1
(C) n
(D) n + 1
Answer : A

42 The mean of 50 observations was 250. It was detected on checking that the value of 165 was wrongly copied as 115 for computation of mean. Find the correct mean.
(A) 215
(B) 151
(C) 156
(D) 251
Answer : D

43 The mean of the data x₁, x₂' x₃, ..... , x_n is 'a:
Find the mean of the data X₁ + a ,x₂ + a, X₃ + a_{1 '"I} X_n + a
(A) a+ a
(B) a a
(C) a+ a
(D) a - a
Answer : C

44 If the mean of 9 observations p, p + 2, p + 4, p + 6, p + 8, p- 2, p - 4, p - 6 and p - 8 is 10. Find the mean of the least 5 observations.
(A) 6
(B) 25
(C) 10
(D) 9
Answer : A

45 The median of the data 26, 56, 32, 33, 60, 17, 34, 29, 45, is 33. If 26 is replaced with 62, what is the new median?
(A) 34
(B) 29
(C) 32
(D) 33
Answer : A

46 The mean of 6 numbers is 20. If one number is deleted, their mean is 15. Find the deleted number.
(A) 45
(B) 52
(C) 20
(D) 36
Answer : A

47 The number of children in 10 families of a locality are 1, 4, 3, 3, 4, 2, 2, 3, 3 and 5.
Find the mean number of children per family.
(A) 3
(B) 4
(C) 1
(D) 2
Answer : A

Here, all the rectangle bars are of the same length and have equal spacing in between them.

(ii) It can be observed that maximum number of girls per thousand boys (i.e., 970) is for ST and minimum number of girls per thousand boys (i.e., 910) is for urban. Also, the number of girls per thousand boys is greater in rural areas than that

in urban areas, backward districts than that in non-backward districts, SC and ST than that in non SC/ST.

 

Question : Given below are the seats won by different political parties in the polling outcome of a state assembly elections:

 

(i) Draw a bar graph to represent the polling results.

(ii) Which political party won the maximum number of seats?

Answer:  (i) By taking polling results on x-axis and seats won as y-axis and choosing an appropriate scale (1 unit = 10 seats for y-axis), the required graph of the above information can be constructed as follows.

 

(i) Represent the given information with the help of a histogram.

(ii) How many lamps have a lifetime of more than 700 hours?

Answer: (i) By taking life time (in hours) of neon lamps on x-axis and the number of lamps on y-axis, the histogram of the given information can be drawn as follows.

 

Here, 1 unit on y-axis represents 10 lamps.

(ii) It can be concluded that the number of neon lamps having their lifetime more than 700 is the sum of the number of neon lamps having their lifetime as 700 − 800, 800 − 900, and 900 − 1000. 

Therefore, the number of neon lamps having their lifetime more than 700 hours is 184. (74 + 62 + 48 = 184) 

 

Question :  The following table gives the distribution of students of two sections according to the mark 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.

Answer:  We can find the class marks of the given class intervals by using the following formula.

Taking class marks on x-axis and frequency on y-axis and choosing an appropriate scale (1 unit = 3 for y-axis), the frequency polygon can be drawn as follows.

 

 

It can be observed that the performance of students of section ‘A’ is better than the students of section ‘B’ in terms of good marks.

 

Question : The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:

 

Represent the data of both the teams on the same graph by frequency polygons.

[Hint: First make the class intervals continuous.]

Answer:  It can be observed that the class intervals of the given data are not continuous.

There is a gap of 1 in between them. Therefore, 1/2 = 0.5 has to be added to the upper class limits and 0.5 has to be subtracted from the lower class limits.

Also, class mark of each interval can be found by using the following formula.

 

Class mark = Upper Class Limit + Lower Class Limit / 2

Continuous data with class mark of each class interval can be represented as follows.

Question :  A random survey of the number of children of various age groups playing in park was found as follows:

Draw a histogram to represent the data above.

Answer:  Here, it can be observed that the data has class intervals of varying width. The proportion of children per 1 year interval can be calculated as follows.

Taking the age of children on x-axis and proportion of children per 1 year interval on y-axis, the histogram can be drawn as follows.

Question : Define array or arrayed data.

Question : Define frequency.

Question : Write the relation between class mark, lower limit and upper limit of a class interval.

Question : Define primary data.

Question : Define secondary data. How it is differ from the primary data?

Question : Find the mode of the following data :

How many students are there whose marks are less than the modal value?

Question : Following data represents the favourite fruit liked by 20 children.

Make a frequency table to find how many more children chose apple as their favourite fruit than pomegranate.

Question : Make a bar graph of the given data

Question : Following frequency table represents the number of students in each section of class 9th of ABC school. Find the mean number of students per sections.

Click on link below to download CBSE Class 9 Mathematics Statistics Assignment Set A