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(a) 1000 (b) Marathi,Bengali (c) 800

There are five sectors. Three sectors are green out of five sectors. Therefore, probability of getting a green sector = 3/5

There is one blue sector out of five sectors. Non-blue sectors = 5 – 1 = 4 sectors Therefore, probability of getting a non-blue sector = 4/5

raw

Data available in an unorganised form is called raw data.

upper class limit

In class interval 26-33, 33 is known as upper class limit.

random

An experiment whose outcomes cannot be predicted exactly in advance, is called a random experiment.

(d) Upper limit of class interval 75-85 is 85.

Note The upper value of class interval is called its upper class limit and lower value of a class interval is called lower class limit

size

The difference between the upper and lower limits of a class interval is called the size of the class interval.

20

In the class interval 20-30, the lower class limit is 20.

i) Angle of sector on Rent = 90° 

Angle of sector on Savings = 90° 

Angle of sectors are equal. 

So, their amounts are also equal. 

Expenditure on rent is ₹3000.

ii) Smallest angle of sector on Education is the item of expenditure is minimum

So, expenditure on education is minimum.

iii) Largest angle of sector on Food is the item of expenditure is maximum. So, expenditure on food is maximum.

The mode of observation 4, 6, 6, 6, 8, 8, 8, 8, 9 is 8.

Mean of 2, 4, 6 and 8 is 5.

Solution of this questions will have to be done by the student rather than an other example is giving here for the convenience ot the students.

My family members height are as follows in cm 70, 85, 110, 150, 170

Airthmetic mean = \(\frac{70+85+110+150+170}{5}\) = \(\frac{858}{5}\) = 117 cm

Solution of this questions will have to be done by the student rather than an other example is giving here for the convenience ot the students.

My family members ages are as follows 7, 9.5, 10, 25.5, 28

Mean = \(\frac{7+9.5+10+25.5+28}{5}\) = \(\frac{80}{5}\) = 16 years

Solution of this questions will have to be done by the student rather than an other example is giving here for the convenience to the students.

Weight of students are as follows :

23, 18, 22, 25, 24. 28, 30, 27, 32, 25

Table:

Arranging the observations in ascending order

18, 22, 23, 24, 25, 25, 27, 28, 30, 32

(1) Subhash has more weight.

(2) Four students weight is more than 25 kg.

(3) Eight students weight is in between 20 to 30 kg.

Arranging these observations in ascending orders.

3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4,
4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7

In the given observations 4 occurs more times, therefore mode is 4.

(i) As per the given graph in session 2015 – 16 the number of girls are more than the number of boys students.

(ii) In the session 2014 – 15 the number of boys and girls students are equal.

(iii) In session 2015 – 16 the total number of students.
= Boys students + Girls students
= 250 + 300
= 550.

(i) True,

(ii) False,

(iii) True,

(iv) False.

Median of 24, 36, 46, 17, 18, 25, 35 is 25.

The median of observation 2,3, 4,7,5 and 1 Median is 3.5.

Arranging these observations in ascending orders

21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 23, 24. 24, 24, 24, 24, 24, 25, 25, 25

by observing the number 24 is repeated more so mode of this is 24.

Jyoti has not done correct because we have to take all observations.

Arranging the marks in ascending order

5, 9, 10, 12, 15, 16, 19, 20, 20, 20,20, 23, 24, 25, 25

It is clear that 20 occurs more times

∴ Mode = 20

Here N = 15 which is odd

∴ Median = (n+1)/2  term

= (15+1)/2= 8^th term = 20

Yes, mode and median are same,

The range of observation 2, 15, 16, 26, 28 range will be 26.

Mean = Sum of all observations/ Number of observations 

or, 27 = (26 + 28 + 25 + x + 24)/ 5 

or, 27 = (103 + x)/5 

or, 135 = 103 + x 

or, x = 135 – 103 

So, x = 32

Correct option is A) 2

sum = (2 - a) + 2 + (2 + a) = 6

Number of observations = 3

\(\therefore\) Mean = \(\frac{sum\,of\,observations}{number\,of\,observations}=\frac63=2\)

(a) There are 11 outcomes namely M, M, A, A, T, T, H, E, I, C, S. 

(b) (i) Probability of getting ‘M’ = 2/11 

(ii) Probability of getting a vowel = 4/11 

(iii) Probability of getting a consonant = 7/11 

(iv) Probability of getting X = 0 = 0/11

Correct option is C) 2.5

Ascending order of given observations is 0, 1, 2, 2.5, 3, 5 and 7.

Number of observations is n = 7

Median = \((\frac{n+1}2)^{th}\) or \((\frac{7+1}2)^{th}\)

 = 4^th term in ascending order of observations.

\(\therefore\) Median = 2.5

Correct option is D) 7

Ascending order of given observations is 2, 3, 5, 7, 11, 13, 17.

Number of observations is n = 7 = odd

Median = \((\frac{n+1}2)^{th}\) term in ascending order of observations

 = \((\frac{7+1}2)^{th}\) or 4th term in ascending order of observations.

 = 7

Arranging in ascending order : 

6, 8, 9, 12, 13, 15, 18, 20, 21, 25 

Since number of observations is even, the median is given by finding the average or mean of the two middle most observations: 

So, median = (13+15)/2 = 28/2 = 14

Arranging in ascending order. 

2, 2, 3, 5, 7, 7, 9, 9, 10, 11, 15 

Since number of observations is odd, the middle most value is the median. The middle most value is 7, so median is 7.

Colour Y has more chance to show up with arrow than the others because Y has more region than both colours B and R.

(a) What is the class width?

The width of the class is 5.

(b) How many teachers are having the maximum teaching experience and how many have the least teaching experience?

Teachers having maximum teaching experience is 2 and Teachers having least teaching experience is 5.

(c) How many teachers have teaching experience of 10 to 20 years?

Teachers have teaching experience of 10 to 20 years is 7 + 2 = 9.

(i) The eldest (50−55 years) = 1 person

This is because the height of the rectangle with class interval 50−55 as base is 1 unit.

The youngest (20−25 years) = 2 persons

This is because the height of the rectangle with class interval 20−25 as base is 2 units.

(ii) The group containing the most number of teachers is 35−40 years. This is because the height of the rectangle with class interval 35−40 as base is the maximum.

The group containing the least number of teachers is 50−55 years. This is because the height of the rectangle with class interval 50−55 as base is the minimum.

(iii) Class size = The range between the upper and the lower boundaries of the class

For example, the size of the class 20−25 years is 5.

(iv) The class mark is the mid-point of the class interval.

i.e., Class mark = (upper limit + lower limit) / 2

Hence, the class mark of each class is as follows:

For Class 20 – 25:

Class mark = (20+25)/2 = 45/2 = 22.5

Similarly, the class marks of the other classes are 27.5, 32.5, 37.5, 42.5, 47.5, 52.5.

In a bar graph, bars can be drawn horizontally or vertically.

Correct option is  A) Data

A pictograph represents data through pictures of objects

C) P.C.Mahalanobis

C) Frequency

The correct answer is (C) M

The correct answer is (D) B and G

The correct answer is (D)

Correct option is  A) |||

The correct answer is (D)

Number of visitors on Monday, Tuesday, Wednesday, Thursday, Friday and Saturday were 550, 700, 1000, 900, 900, and 1250 respectively. (a) The total number of visitors from Monday to Saturday = 550 + 700 + 1000 + 900 + 900 + 1250 = 5300(b) The number of visitors was maximum on Saturday and the number was 1250. (c) The number of visitors was minimum on Monday and the number was 550. (d) The number of visitors on Saturday was 1250 which was equal to the total number of visitors on Monday (550) and Tuesday (700). 

Number of visitors on Monday, Tuesday, Wednesday, Thursday, Friday and Saturday were 550, 700, 1000, 900, 900, and 1250 respectively. 

(a) The total number of visitors from Monday to Saturday = 550 + 700 + 1000 + 900 + 900 + 1250 = 5300

(b) The number of visitors was maximum on Saturday and the number was 1250. 

(c) The number of visitors was minimum on Monday and the number was 550. 

(d) The number of visitors on Saturday was 1250 which was equal to the total number of visitors on Monday (550) and Tuesday (700).

(D) 17

First we have to arrange the marks (out of 10) obtained by 28 students in a Mathematics test.

0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5, 5, 5, 5, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10.

The number of students who obtained marks more than or equal to 5 is 17.

(D) B and G

From the question it is given that A, B, G, M and O stand for the fruits Apple, Banana, Grapes, Mango and Orange respectively.

So, by observing the choices of the fruits of 42 students in a class Banana (B) and Grapes(G) are liked by an equal number of students i.e. 8 students each.

The correct answer is (D) 17

(i) Ascending order of the numbers in groups:

(30-39): 37, 39

(40 – 49): 44, 48, 48

(50 – 59): 50, 52, 53, 55, 56, 58, 58, 59

(60 – 69): 60, 60, 60, 61, 62, 64, 67, 68

(70 – 79): 70, 75, 77, 78

(80 – 89): 84, 88

(90 – 99): 90, 98

(100-109): 100

(ii) The highest score is 100.

(iii) The lowest score is 37.

(iv) Range is = Maximum observation – Minimum observation.

= 100 – 37

= 63.

(v) If 40 is the pass mark, then only 2 students have failed.

(vi) 8 students have scored 75 or more.

(vii) 51, 54 and 57 are not there between 50 and 60.

(viii) 5 students scored less than 50.

The given raw data can be arranged in an ascending order.

The class intervals are 30 – 39, 40 – 49, …, 100 – 109.

Then, take the raw data and place it in the appropriate class intervals.

(i)  The marks can be arranged in an ascending order as shown below:

(ii) The Highest score is 100.

(iii) The Lowest score is 37.

(iv) The Range is 100 – 37 i.e., 63.

(v) If 40 is the passing mark, then the number of students who failed is 2 (i.e. 37, 39).

(vi) The number of students scoring 75 and above is 8 (i.e. 75, 77, 78, 84, 88, 90, 98, 100).

(vii) The marks 51, 54, and 57 do not actually appear between 50 and 60.

(viii) The number of students scoring less than 50 is 5 (i.e. 37, 39, 44, 48, 48).