Complete guide to "Statistics and Probability" for Math students. Below you will find important questions and model answers to help you prepare.
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The marks obtained by 17 students in a mathematics test (out of 100) are given below: 91, 82, 100, 100, 96, 65, 82, 76, 79, 90, 46, 64, 72, 68, 66, 48, 49. The range of the data is:
46
54
90
100
The class-mark of the class 130-150 is:
130
135
140
145
A die is thrown 1000 times, and the outcomes were recorded as follows. Now if the die is thrown once more, then the probability that it shows 5 is:
9/50
3/20
4/25
7/25
The class mark of the class 90-120 is
90
105
115
120
The range of the data: 25, 18, 20, 22, 16, 6, 17, 15, 12, 30, 32, 10, 19, 8, 11, 20
10
15
18
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:
6
7
8
12
The width of each of five continuous classes in a frequency distribution is 5 and the lower class-limit of the lowest class is 10. The upper class-limit of the highest class is:
15
25
35
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:
2m + l
2m – l
m – l
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:
12.5 – 17.5
17.5 – 22.5
18.5 – 21.5
19.5 – 20.5
In the class intervals 10-20, 20-30, the number 20 is included in:
10-20
20-30
both the intervals
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:
4
5
6
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:
9
10
11
12
To draw a histogram to represent the following frequency distribution, the adjusted frequency for the class 25-45 is:
6
5
3
2
The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is:
28
30
35
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
If each observation of the data is increased by 5, then their mean
remains the same
becomes 5 times the original mean
is decreased by 5
is increased by 5
The mean of 100 observations is 50. If one of the observations which was 50 is replaced by 150, the resulting mean will be:
50.5
51
51.5
52
There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be –3.5. The mean of the given numbers is:
46.5
49.5
53.5
56.5
The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is 32 and that of the last 13th observations is 40, the 13th observation is:
23
36
38
40
The median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54, 84 is
45
49.5
54
56
For drawing a frequency polygon of a continuous frequency distribution, we plot the points whose ordinates are the frequencies of the respective classes and abscissae are respectively:
upper limits of the classes
lower limits of the classes
class marks of the classes
upper limits of preceding classes
Median of the following numbers 4, 4, 5, 7, 6, 7, 7, 12, 3 is
4
5
6
7
Mode of the data 15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is
14
15
16
17
In a sample study of 642 people, it was found that 514 people have a high school certificate. If a person is selected at random, the probability that the person has a high school certificate is:
0.5
0.6
0.7
0.8
In a survey of 364 children aged 19-36 months, it was found that 91 liked to eat potato chips. If a child is selected at random, the probability that he/she does not like to eat potato chips is:
0.25
0.50
0.75
0.80
In a medical examination of students of a class, the following blood groups are recorded. And a student is selected at random from the class. The probability that he/she has blood group B, is:
1/4
13/40
3/10
1/8
Two coins are tossed 1000 times, and the outcomes are recorded as below. Based on this information, the probability for at most one head is:
1/5
1/4
4/5
3/4
80 bulbs are selected at random from a lot and their lifetime (in hours) is recorded in the form of a frequency table given below. One bulb is selected at random from the lot. The probability that its life is 1150 hours, is
1/80
7/16
0
1
80 bulbs are selected at random from a lot and their lifetime (in hours) is recorded in the form of a frequency table given below. The probability that bulbs selected randomly from the lot has life less than 900 hours is:
11/40
5/16
7/16
9/16
