Statistics and Probability Maths - Statistics and Probability

Write the correct answer in the following:
If each observation of the data is increased by 5, then their mean:

1. Remains the same.
2. Becomes 5 times the original mean.
3. Is decreased by 5.
4. Is increased by 5.

Write the correct answer in the following:
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:

1. 4
2. 5
3. 6
4. 7

Write the correct answer in the following:
The range of the data: 25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20 is:

1. 10
2. 15
3. 18
4. 26

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

Can the experimental probability of an event be greater than 1? Justify your anwer.

Can the experimental probability of an event be a negative number? If not, 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.

30 children were asked about the number of hours they watched TV programmes last week. The results are recorded as under:

Number of hours	0-5	5-10	10-15	15-20
Frequency	8	16	4	2

Can we say that the number of children who watched TV for 10 or more hours a week is 22? Justify your answer.

Mean of 50 observations was found to be 80.4. But later on, it was discovered that 96 was misread as 69 at one place. Find the correct mean.

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?

The class marks of a continuous distribution are:
1.04, 1.14, 1.24, 1.34, 1.44, 1.54 and 1.64
Is it correct to say that the last interval will be 1.55 - 1.73? Justify your answer.

In there is a histogram depicting daily wages of workers in a factory. Construct the frequency distribution table.

Bulbs are packed in cartons each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs and the results are given in the following table:

Number of defective bulbs	0	1	2	3	4	5	6	more than 6
Frequency	400	180	48	41	18	8	3	2

One carton was selected at random. What is the probability that it has:

1. No defective bulb?
2. Defective bulbs from 2 to 6?
3. Defective bulbs less than 4?

A company selected 4000 households at random and surveyed them to find out a relationship between income level and the number of television sets in a home. The information so obtained is listed in the following table:

Monthly income (in Rs.)	Number of Televisions/ household
	0	1	2	Above 2
<10000 10000-14999 15000-19999 20000-24999 25000 and above	20 10 0 0 0	80 240 380 520 1100	10 60 120 370 760	0 0 30 80 220

Find the probability:

1. Of a household earning Rs. 10000 - Rs 14999 per year and having exactly one television.
2. Of a household earning Rs. 25000 and more per year and owning 2 televisions.
3. Of a household not having any television.

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

Letter	a	e	i	o	r	t	u
Frequency	75	125	80	70	80	95	75

Represent the information above by a bar graph.

Obtain the mean of the following distribution:

Frequency	Varible
4 8 14 11 3	4 6 8 10 12

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, 84000 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.

The mean of the following distribution is 50.

X	f
10 30 50 70 90	17 5a + 3 32 7a - 11 19

Find the value of a and hence the frequencies of 30 and 70.

A recent survey found that the ages of workers in a factory is distributed as follows:

Age (in years)	20-39	30-39	40-49	50-59	60 and above
Number of workers	38	27	86	46	3

If a person is selected at random, find the probability that the person is:

1. 40 years or more.
2. Under 40 years.
3. Having age from 30 to 39 years.
4. Under 60 but over 39 years.

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

Head	Food	Education	Clothing	House Rent	Others	Savings
Expenditure(in Rs.)	4000	2500	1000	3500	2500	1500

Draw a bar graph to represent the data above.

The mean marks (out of 100) of boys and girls in an examination are 70 and 73, respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.

Prepare a continuous grouped frequency distribution from the following data:

Mid-point	Frequency
5 15 25 35 45	4 8 13 12 6

Also find the size of class intervals.

Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them.

Section A		Section B
Marks	Frequency	Marks	Frequency
0-15 15-30 30-45 45-60 60-75 75-90	5 12 28 30 35 13	0-15 15-30 30-45 45-60 60-75 75-90	3 16 25 27 40 10

Represent the marks of the students of both the sections on the same graph by two frequency polygons.What do you observe?