Question 1 :
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 :
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d16bf59b460d7261f442.jpg' />
Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on their tops is noted and recorded as given in the table shown above. If the dice are thrown once more, what is the probability of getting a sum less than or equal to 5?
Question 3 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d15df59b460d7261f42d.jpg' />
80 bulbs are selected at random from a lot and their life time (in hrs) is recorded in the form of a frequency table given above. One bulb is selected at random from the lot. The probability that its life is 1150 hours, is:
Question 4 :
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:
Question 5 :
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:
Question 6 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d17af59b460d7261f458.jpg' />
The mean of the following distribution shown in the above image is 50. Find the value of frequency for x=70.
Question 7 :
A total of 25 patients admitted to a hospital are tested for levels of blood sugar, (mg/dl) and the results obtained were as follows : 87, 71, 83, 67, 85, 77, 69, 76, 65, 85, 85, 54, 70, 68, 80, 73, 78, 68, 85, 73, 81, 78, 81, 77, 75. Find median (mg/dl) of the above data.
Question 8 :
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
Question 9 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d16cf59b460d7261f444.jpg' />
Bulbs are packed in cartons each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs and the results are given in the table shown in the above image. One carton was selected at random. What is the probability that it has no defective bulb?
Question 10 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d162f59b460d7261f435.jpg' />
The given frequency distribution in the above image is converted into a continuous grouped frequency distribution. In which intervals would 153.5 be included?
Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d173f59b460d7261f44d.jpg' />
A recent survey found that the ages of workers in a factory is distributed as shown in the figure above. If a person is selected at random, find the probability that the person is 40 years or more.
Question 12 :
A total of 25 patients admitted to a hospital are tested for levels of blood sugar, (mg/dl) and the results obtained were as follows : 87, 71, 83, 67, 85, 77, 69, 76, 65, 85, 85, 54, 70, 68, 80, 73, 78, 68, 85, 73, 81, 78, 81, 77, 75. Find mode (mg/dl) of the above data.
Question 13 :
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 :
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d173f59b460d7261f44e.jpg' />
A recent survey found that the ages of workers in a factory is distributed as shown in the figure above. If a person is selected at random, find the probability that the person is under 40 years.
Question 15 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d17bf59b460d7261f459.jpg' />
The mean of the following distribution shown in the above image is 50. Find the value of a.
Question 16 :
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?
Question 17 :
In the class intervals 10-20, 20-30, the number 20 is included in :
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d17cf59b460d7261f45b.jpg' />
A die is thrown 1000 times and the outcomes were recorded as shown in the above data. If the die is thrown once more, then the probability that it shows 5 is :
Question 19 :
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?
Question 20 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d16df59b460d7261f445.jpg' />
Bulbs are packed in cartons each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs and the results are given in the table shown in the above image. One carton was selected at random. What is the probability that it has defective bulbs from 2 to 6?
Question 21 :
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 :
Question 22 :
Median of the following numbers : 4, 4, 5, 7, 6, 7, 7, 12, 3 is:
Question 23 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d15bf59b460d7261f42b.jpg' />
Two coins are tossed 1000 times and the outcomes are recorded as shown in the above figure. Based on this information, the probability for at most one head is:
Question 24 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d17df59b460d7261f45c.jpg' />
Above image shows an extract from a mortality table. Based on this information, what is the probability of a person ‘aged 60’ of dying within a year?
Question 25 :
The following observations are arranged in ascending order : 26, 29, 42, 53, x, x + 2, 70, 75, 82, 93. If the median is 65, find the value of x.
Question 26 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d161f59b460d7261f433.jpg' />
A continuous grouped frequency distribution can be prepared from the following data shown in the above image. Find the size of class intervals.
Question 27 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d17df59b460d7261f45d.jpg' />
Above image shows an extract from a mortality table. Based on this information, what is the probability that a person ‘aged 61’ will live for 4 years?
Question 28 :
The marks obtained by 17 students in a mathematics test (out of 100) are given as follows:
91, 82, 100, 100, 96, 65, 82, 76, 79, 90, 46, 64, 72, 68, 66, 48, 49. The range of the data is ?
Question 29 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d172f59b460d7261f44c.jpg' />
A recent survey found that the ages of workers in a factory is distributed as shown in the figure above. If a person is selected at random, find the probability that the person is having age from 30 to 39 years.
Question 30 :
Mode of the data 15, 14, 19, 20, 14, 15, 16, 14, 15, 18, 14, 19, 15, 17, 15 is:
Question 31 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d163f59b460d7261f436.jpg' />
The given frequency distribution in the above image is converted into a continuous grouped frequency distribution. In which intervals would 157.5 be included?
Question 32 :
The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is :
Question 33 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d169f59b460d7261f43f.jpg' />
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 shown above. Find the probability of a household not having any television.
Question 34 :
State true or false: The probability of an event E can be any number from 0 to 1. It can also be 0 or 1 in some special cases.
Question 35 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d16ff59b460d7261f448.jpg' />
Over the past 200 working days, the number of defective parts produced by a machine is given in the table shown above. Determine the probability that tomorrow’s output will have atleast one defective part.
Question 36 :
A total of 25 patients admitted to a hospital are tested for levels of blood sugar, (mg/dl) and the results obtained were as follows : 87, 71, 83, 67, 85, 77, 69, 76, 65, 85, 85, 54, 70, 68, 80, 73, 78, 68, 85, 73, 81, 78, 81, 77, 75. Find mean (mg/dl) of the above data.
Question 37 :
The points scored by a basket ball team in a series of matches are as follows: 17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28 Find the mode for the data.
Question 38 :
Histograms of uniform width and of varying widths is a type of graphical representation of data
Question 39 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d16ef59b460d7261f446.jpg' />
Bulbs are packed in cartons each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs and the results are given in the table shown in the above image. One carton was selected at random. What is the probability that it has defective bulbs less than 4?
Question 40 :
If $\overline{x}_1,\ \overline{x}_2,\ \overline{x}_3,\ ...,\ \overline{x}_n$ are the means of n groups with $n_1,\ n_2,\ ...,\ n_n$ number of observations respectively, then the mean $\overline {x}$ of all the groups taken together is given by :
