Question 1 :
For drawing a frequency polygon of a continous frequency distribution, we plot the points whose ordinates are the frequencies of the respective classes and abcissae are respectively :
Question 2 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d16af59b460d7261f441.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 more than 10?
Question 3 :
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 4 :
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 5 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d15ff59b460d7261f430.jpg' />
30 children were asked about the number of hours they watched TV programmes last week. The results are recorded as shown in the above table. Can we say that the number of children who watched TV for 10 or more hours a week is 22?
Question 6 :
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 7 :
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:
Question 8 : <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 9 :
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 10 :
The class marks of a frequency distribution are given as follows : 15, 20, 25, ... The class corresponding to the class mark 20 is :
Question 11 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d179f59b460d7261f457.jpg' />
The mean of the following distribution shown in the above image is 50. Find the value of frequency for x=30.
Question 12 :
If $\overline {x}$ represents the mean of n observations $x_1,\ x_2,\ ...,\ x_n$ , then value of $\sum_{i=1}^n\left(x_i-\overline{x}\right)$ is
Question 13 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d168f59b460d7261f43e.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 earning Rs 25000 and more per year and owning 2 televisions.
Question 14 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d15cf59b460d7261f42c.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. The probability that bulbs selected randomly from the lot has life less than 900 hours is :
Question 15 :
If $\overline {x}$ is the mean of $x_1,\ x_2,\ ...,\ x_n$ , then for a ≠ 0, the mean of, $ax_1,\ ax_2,\ ...,\ ax_n,\frac{x_1}{a},\ \frac{x_2}{a},\ ...,\ \frac{x_n}{a}$ is:
Question 16 :
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, $the\ median\ =\ \frac{\left(5th\ observation\ +6th\ observation\right)}{2}=\frac{\left(8+6\right)}{2}=7$.
Is it the correct answer ?
Question 17 :
In a histogram, the areas of the rectangles are proportional to the frequencies. Can we say that the lengths of the rectangles are also proportional to the frequencies?
Question 18 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d170f59b460d7261f449.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 not more than 5 defective parts.
Question 19 :
State true or false: The observation that occurs most frequently, i.e., the observation with maximum frequency is called mode.
Question 20 :
The median of the data 78, 56, 22, 34, 45, 54, 39, 68, 54, 84 is
Question 22 :
If each observation of the data is increased by 5, then their mean is:
Question 23 :
Median of the following numbers : 4, 4, 5, 7, 6, 7, 7, 12, 3 is:
Question 24 :
The mean of the data : 2, 8, 6, 5, 4, 5, 6, 3, 6, 4, 9, 1, 5, 6, 5 is given to be 5. Based on this information, is it correct to say that the mean of the data: 10, 12, 10, 2, 18, 8, 12, 6, 12, 10, 8, 10, 12, 16, 4 is 10?
Question 25 :
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 :
Question 26 :
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 27 :
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.
Question 28 :
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 29 :
State true or false: Mode of ungrouped data can be determined by observation/ inspection.
Question 30 :
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 31 : <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 33 :
Histograms of uniform width and of varying widths is a type of graphical representation of data
Question 34 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d15af59b460d7261f42a.jpg' />
In a medical examination of students of a class, the following blood groups are recorded in the above table shown. A student is selected at random from the class. The probability that he/she has blood group B, is :
Question 35 :
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 :
Question 36 :
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 13 observations is 40, the 13th observation is :
Question 37 :
State true or false: Frequency polygons is a type of graphical representation of data
Question 38 :
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.
Question 39 :
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 40 : <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 41 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d16ff59b460d7261f447.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 no defective part.
Question 42 :
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 43 :
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 :
Question 44 : <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 45 : <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 46 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d15df59b460d7261f42e.jpg' />
<img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61cc1ad678c526e972caf082.jpg' />
The data of the given frequency distribution has been represented graphically in the figure above. Do you think this representation is correct?
Question 47 :
The mean of five numbers is 30. If one number is excluded, their mean becomes 28. The excluded number is :
Question 48 : <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 49 : <img style='object-fit:contain' src='https://teachmint.storage.googleapis.com/question_assets/cbse_ncert/61b1d168f59b460d7261f43d.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 earning Rs 10000 – Rs 14999 per year and having exactly one television.
Question 50 :
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.
