Ncert exemplar solutions mathematics class 9 Solutions for Chapter 14 statistics and probability

The class mark of the class 90-120 is:

(A) 90

(B) 105

(C) 115

(D) 120

The range of the data:

25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20 is

(A) 10

(B) 15

(C) 18

(D) 26

In a frequency distribution, the mid value of a class is 10 and the width of the class is 6. The lower limit of the class is:

(A) 6

(B) 7

(C) 8

(D) 12

The width of each of five continuous classes in a frequency distribution is 5 and the lower classlimit of the lowest class is 10. The upper class-limit of the highest class is:

(A) 15

(B) 25

(C) 35

(D) 40

Let m be the mid-point and l be the upper-class limit of a class in a continuous frequency distribution. The lower class limit of the class is:

(A) 2m + l

(B) 2m – l

(C) m – l

(D) m – 2l

The class marks of a frequency distribution are given as follows:

15, 20, 25, …

The class corresponding to the class mark 20 is:

(A) 12.5 – 17.5

(B) 17.5 – 22.5

(C) 18.5 – 21.5

(D) 19.5 – 20.5

In the class intervals 10-20, 20-30, the number 20 is included in:

(A) 10-20

(B) 20-30

(C) both the intervals

(D) none of these intervals

A grouped frequency table with class intervals of equal sizes using 250-270 (270 not included in this interval) as one of the class interval is constructed for the following data :

268, 220, 368, 258, 242, 310, 272, 342,

310, 290, 300, 320, 319, 304, 402, 318,

406, 292, 354, 278, 210, 240, 330, 316,

406, 215, 258, 236.

The frequency of the class 310-330 is:

(A) 4

(B) 5

(C) 6

(D) 7

A grouped frequency distribution table with classes of equal sizes using 63-72 (72 included) as one of the class 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, 95, 96,

102, 110, 88, 74, 112, 14, 34, 44.

The number of classes in the distribution will be :

(A) 9

(B) 10

(C) 11

(D) 12

To draw a histogram to represent the following frequency distribution:

the adjusted frequency for the class 25-45 is :

(A) 6

(B) 5

(C) 3

(D) 2

The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is:

(A) 28

(B) 30

(C) 35

(D) 38

If the mean of the observations:

x, x + 3, x + 5, x + 7, x + 10

is 9, the mean of the last three observations is

The frequency distribution:

has been represented graphically as follows :

Do you think this representation is correct? Why?

In a diagnostic test in mathematics given to students, the following marks (out of 100) are recorded:

46, 52, 48, 11, 41, 62, 54, 53, 96, 40, 98, 44

Which ‘average’ will be a good representative of the above data and why?

A child says that the median of 3, 14, 18, 20, 5 is 18. What doesn’t the child understand about finding the median?

A football player scored the following number of goals in the 10 matches:

1, 3, 2, 5, 8, 6, 1, 4, 7, 9

Since the number of matches is 10 (an even number), therefore, the median

= (5th observation + 6th observation)/2 = (8+6)/2 = 7

Is it the correct answer and why?

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? If not, correct the statement.

The blood groups of 30 students are recorded as follows:

A, B, O, A, AB, O, A, O, B, A, O, B, A, AB, B, A, AB, B,

A, A, O, A, AB, B, A, O, B, A, B, A

Prepare a frequency distribution table for the data.

The value of π upto 35 decimal places is given below:

3. 14159265358979323846264338327950288

Make a frequency distribution of the digits 0 to 9 after the decimal point.

The scores (out of 100) obtained by 33 students in a mathematics test are as follows:

69, 48, 84, 58, 48, 73, 83, 48, 66, 58, 84 000

66, 64, 71, 64, 66, 69, 66, 83, 66, 69, 71

81, 71, 73, 69, 66, 66, 64, 58, 64, 69, 69

Represent this data in the form of a frequency distribution.

Prepare a continuous grouped frequency distribution from the following data:

Also find the size of class intervals.

Convert the given frequency distribution into a continuous grouped frequency distribution:

In which intervals would 153.5 and 157.5 be included?

The expenditure of a family on different heads in a month is given below:

Draw a bar graph to represent the data above.

Expenditure on Education of a country during a five year period (2002-2006), in crores of rupees, is given below:

Represent the information above by a bar graph.

Solution:

The following table gives the frequencies of most commonly used letters a, e, i, o, r, t, u from a page of a book:

Represent the information above by a bar graph.

If the mean of the following data is 20.2, find the value of p:

Obtain the mean of the following distribution:

The following are the marks (out of 100) of 60 students in mathematics.

16, 13, 5, 80, 86, 7, 51, 48, 24, 56, 70, 19, 61, 17, 16, 36, 34, 42, 34, 35, 72, 55, 75, 31, 52, 28,72, 97, 74, 45, 62, 68, 86, 35, 85, 36, 81, 75, 55, 26, 95, 31, 7, 78, 92, 62, 52, 56, 15, 63,25, 36, 54, 44, 47, 27, 72, 17, 4, 30.

Construct a grouped frequency distribution table with width 10 of each class starting from 0 – 9.

Refer to Q1 above. Construct a grouped frequency distribution table with width 10 of each class, in such a way that one of the classes is 10 – 20 (20 not included).

Draw a histogram of the following distribution:

Draw a histogram to represent the following grouped frequency distribution:

The lengths of 62 leaves of a plant are measured in millimetres and the data is represented in the following table:

Draw a histogram to represent the data above.