Question 11 Mark
In Throwing a die the number of possible outcomes is _________.
Answer
View full question & answer→When we throw a die, $6$ outcomes are possible. They are $1, 2, 3, 4, 5$ and $6.$
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Question 21 Mark
Classify, the following events as certain to happen, impossible to happen, may or may not happen. Getting head when a coin is tossed.
Answer
View full question & answer→Getting head, when a coin is tossed may or may not happen as a coin has head and tail on its two faces. So, we might get a head or a tail on tossing it.
Question 31 Mark
The marks in a subject for $12$ students are as follows: $31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29$ For the given data, find the: Range.
Answer
View full question & answer→Given data is $31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29.$
Rearranging the given data in ascending order, $17, 18, 23, 25, 29, 31, 35, 35, 35, 37, 38, 42$
Range $=$ Highest observation $-$ Lowest observation
$= 42 - 17 = 25$
Rearranging the given data in ascending order, $17, 18, 23, 25, 29, 31, 35, 35, 35, 37, 38, 42$
Range $=$ Highest observation $-$ Lowest observation
$= 42 - 17 = 25$
Question 41 Mark
_________ can be used to compare two collections of data.
Answer
View full question & answer→ A double bar graph can be used to compare two collections of data.
Question 51 Mark
The measures of central tendency may not lie between the maximum and minimum values of data.
Answer
View full question & answer→False. Solution: The measures of central tendency lie between the maximum and minimum values of the data.
Question 61 Mark
Range of the data is always from the data.
Answer
View full question & answer→False. Solution: It is not necessary as range is the difference of highest observation and lowest observation.
Question 71 Mark
Given below are heights of 15 boys of a class measured in cm:$128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.$
Find:
The height of the shortest boy.
Find:
The height of the shortest boy.
Answer
View full question & answer→Given, height (data) of $15$ boys of a class are: $128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.$
Arranging the given data in ascending order, we have $128, 129, 136, 138, 140, 140, 142, 142, 143, 144, 144, 146, 150, 152, 154$
By observing the data, height of the shortest boy $= 128\ cm$
Arranging the given data in ascending order, we have $128, 129, 136, 138, 140, 140, 142, 142, 143, 144, 144, 146, 150, 152, 154$
By observing the data, height of the shortest boy $= 128\ cm$
Question 81 Mark
The data $12, 13, 14, 15, 16$ has every observation as mode.
Answer
View full question & answer→Given data is $12, 13, 14, 15, 16.$
Here, each observation has same frequency,
so every observation is a mode.
Here, each observation has same frequency,
so every observation is a mode.
Question 91 Mark
Mean, Median and Mode may be the same for some data.
Answer
View full question & answer→Data $($in ascending order$) → 3, 3, 4, 4, 4, 4, 6$
Here, $n = 7 ($odd$)$
Median $=$ Value of $\Big(\frac{\text{n+1}}{2}\Big)\text{th}$ observation = Value of $\Big(\frac{7+1}{2}\Big)\text{th}$
observation $= 4$
$\text{Mean}=\frac{\text{Sum of observation}}{\text{n}}$
$=\frac{3+3+4+4+4+4+6}{7}=\frac{28}{7}$
$=4$
Hence,
Mean $=$ Mode $=$ Median
Mean, median and mode can be the same for some data.
Here, $n = 7 ($odd$)$
Median $=$ Value of $\Big(\frac{\text{n+1}}{2}\Big)\text{th}$ observation = Value of $\Big(\frac{7+1}{2}\Big)\text{th}$
observation $= 4$
$\text{Mean}=\frac{\text{Sum of observation}}{\text{n}}$
$=\frac{3+3+4+4+4+4+6}{7}=\frac{28}{7}$
$=4$
Hence,
Mean $=$ Mode $=$ Median
Mean, median and mode can be the same for some data.
Question 101 Mark
In a given data, arranged in ascending or descending order, the middle most observation is called __________.
Answer
View full question & answer→In a given data, arranged in ascending or descending order, the middle most observation is called Median. Solution: Median is the value of middle most observation of a given data, which arranged in ascending or descending order.
Question 111 Mark
When a coin is tossed, there are $2$ possible outcomes.
Answer
View full question & answer→If a coin is tossed, then Maximum outcomes $= 2,$ i.e. head or tail.
Question 121 Mark
Mode of the data is always from the given data.
Answer
View full question & answer→True. Solution: Mode of the data is always from the given data as it is the most frequent observation in the data.
Question 131 Mark
The probability of an event which is certain to happen is _________.
Answer
View full question & answer→In other words, probability of a sure event is $1.$
Question 141 Mark
The range of the data $3, 7, 1, -2, 2, 6, -3, -5$ would change, if $8$ was added to each value in the data.
Answer
View full question & answer→Because, range before adding $8 =$ Maximum observation $-$ Minimum observation
$= 7 - (-5) = 7 + 5 = 12$
Data after adding 8
$= 3 + 8, 7 + 8, 1 + 8, -2 + 8, 2 + 8, 6 + 8, –3 + 8, -5 + 8, i.e. 11, 15, 9, 6, 10, 14, 5, 3$
So, the range is same. Range = Maximum observation - Minimum observation $= 15 - 3 = 12$
$= 7 - (-5) = 7 + 5 = 12$
Data after adding 8
$= 3 + 8, 7 + 8, 1 + 8, -2 + 8, 2 + 8, 6 + 8, –3 + 8, -5 + 8, i.e. 11, 15, 9, 6, 10, 14, 5, 3$
So, the range is same. Range = Maximum observation - Minimum observation $= 15 - 3 = 12$
Question 151 Mark
Rohit collected the data regarding weights of students of his class and prepared the following table:
A student is to be selected randomly from his class for some competition. The probability of selection of the student is highest whose weight is in the interval _________.
|
Weight (in kg):
|
$44–47$
|
$48–51$
|
$52–55$
|
$56–60$
|
|
Number of Students:
|
$3$
|
$5$
|
$25$
|
$7$
|
Answer
View full question & answer→We know that,
$\text{Probability}=\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$
$\therefore$ To make the probability highest, we have to take the interval where number of students, i.e. possible outcomes are highest.
Here, probability is highest whose weight is in the interval. Since maximum number of students i.e., $25$ lies in interval $52-55.$
$\text{Probability}=\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$
$\therefore$ To make the probability highest, we have to take the interval where number of students, i.e. possible outcomes are highest.
Here, probability is highest whose weight is in the interval. Since maximum number of students i.e., $25$ lies in interval $52-55.$
Question 161 Mark
Find the mode of the given data: $10, 8, 4, 7, 8, 11, 15, 8, 4, 2, 3, 6, 8$
Answer
View full question & answer→We know that, mode is the most frequent observation in the data.
$\therefore$ Mode $= 8$
$\therefore$ Mode $= 8$
Question 171 Mark
The following are weights (in kg) of $12$ people. $70, 62, 54, 57, 62, 84, 75, 59, 62, 65, 78, 60$ Find the range of the given data.
Answer
View full question & answer→Range $=$ Maximum observation $-$ Minimum observation $= 84 – 54 = 30$
Question 181 Mark
The representation of data with bars of uniform width is called _________.
Answer
View full question & answer→The representation of data with bars of uniform width is called bar graph.
Question 191 Mark
Classify, the following events as certain to happen, impossible to happen, may or may not happen. A team winning the match.
Answer
View full question & answer→A team may or may not win a match.
Question 201 Mark
Median of the data may or may not be from the given data.
Answer
View full question & answer→$e.g.$
$i. 2, 4, 6, 8$
Here, $n = 5($odd$)$
Median $=$ Value of $\Big(\frac{\text{n+1}}{2}\Big)^\text{th}$ observation
$=$ Value of $\Big(\frac{5+1}{2}\Big)^\text{th}$ observation
$=$ Value of $3^{rd}$ observation $= 6$
$ii. 4, 6, 8, 8, 12, 14, 15, 16$
Here, $n = 8($even$)$
Median $=\frac{\text{Value of }\Big(\frac{\text{n}}{2}\Big)^\text{th }\text{observation = Value of}\Big(\frac{\text{n}}{2}+1\Big)^\text{th }\text{observation}}{2}$
$=\frac{\text{Value of $4^{th}$ observation + Value of $5^{th}$ observation}}{2}$
$=\frac{8+12}{2}$
$=\frac{20}{2}$
$=10$
$i. 2, 4, 6, 8$
Here, $n = 5($odd$)$
Median $=$ Value of $\Big(\frac{\text{n+1}}{2}\Big)^\text{th}$ observation
$=$ Value of $\Big(\frac{5+1}{2}\Big)^\text{th}$ observation
$=$ Value of $3^{rd}$ observation $= 6$
$ii. 4, 6, 8, 8, 12, 14, 15, 16$
Here, $n = 8($even$)$
Median $=\frac{\text{Value of }\Big(\frac{\text{n}}{2}\Big)^\text{th }\text{observation = Value of}\Big(\frac{\text{n}}{2}+1\Big)^\text{th }\text{observation}}{2}$
$=\frac{\text{Value of $4^{th}$ observation + Value of $5^{th}$ observation}}{2}$
$=\frac{8+12}{2}$
$=\frac{20}{2}$
$=10$
Question 211 Mark
The marks in a subject for $12$ students are as follows: $31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29$ For the given data, find the: Mode.
Answer
View full question & answer→Given data is $31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29.$ Rearranging the given data in ascending order, $17, 18, 23, 25, 29, 31, 35, 35, 35, 37, 38, 42$ Mode $=$ Most frequent observation $= 35$
Question 221 Mark
If the arithmetic mean of $8, 4, x, 6, 2, 7$ is $5,$ then the value of $x$ is _________.
Answer
View full question & answer→We know that,$\text{Mean}=\frac{\text{Sum of all observatiions}}{\text{Total number of observations}}$
$\Rightarrow5=\frac{8+4+\text{x}+6+2+7}{6} [\because$ mean $= 5,$ given$]$
$\Rightarrow30=27+\text{x}$
$\Rightarrow30-27=\text{x}$
$\Rightarrow3=\text{x}$
$\therefore\text{x}=3$
Hence, the value of $x$ is $3.$
$\Rightarrow5=\frac{8+4+\text{x}+6+2+7}{6} [\because$ mean $= 5,$ given$]$
$\Rightarrow30=27+\text{x}$
$\Rightarrow30-27=\text{x}$
$\Rightarrow3=\text{x}$
$\therefore\text{x}=3$
Hence, the value of $x$ is $3.$
Question 231 Mark
Classify, the following events as certain to happen, impossible to happen, may or may not happen.
Christmas will be on $25$ December.
Christmas will be on $25$ December.
Answer
View full question & answer→Christmas is certain to happen on $25th.$
Question 241 Mark
The probability of getting an ace out of a deck of cards is greater than $1.$
Answer
View full question & answer→Probability of an event can never be greater than $1.$
It always remains from $0$ and $1$ for any event.$0\leq\text{P(E)}\leq1$
$\therefore$ Maximum probability can be $1.$
It always remains from $0$ and $1$ for any event.$0\leq\text{P(E)}\leq1$
$\therefore$ Maximum probability can be $1.$
Question 251 Mark
The probability of an event which is impossible to happen is __________.
Answer
View full question & answer→The probability of an event which is impossible to happen is 0. Solution: Probability of an impossible event is 0. As impossible events are those which cannot happen.
Question 261 Mark
What is the probability of the sun setting tomorrow$?$
Answer
View full question & answer→Setting of the sun is a sure event. Hence, its probability is $1$
Question 271 Mark
It is impossible to get a sum of $14$ of the numbers on both die, when a pair of dice is thrown together.
Answer
View full question & answer→When a die is thrown, maximum possible outcomes are $6,$ i.e. $1, 2, 3, 4, 5, 6.$
So, when a pair of dice is thrown together,
maximum sum will be $12,$ if and only if both dice get 6 together.
So, that pair will be $(6, 6)$ and the sum is $12.$
$\therefore$ It is impossible to get a sum of $14$ on both dice, when a pair of dice is thrown together.
So, when a pair of dice is thrown together,
maximum sum will be $12,$ if and only if both dice get 6 together.
So, that pair will be $(6, 6)$ and the sum is $12.$
$\therefore$ It is impossible to get a sum of $14$ on both dice, when a pair of dice is thrown together.
Question 281 Mark
Classify, the following events as certain to happen, impossible to happen, may or may not happen. A ball thrown up in the air will fall down after sometime.
Answer
View full question & answer→It is certain to happen that a ball thrown up in the air will fall down after sometime due to gravity
Question 291 Mark
Classify, the following events as certain to happen, impossible to happen, may or may not happen. Getting a number less than $1$ on throwing a die.
Answer
View full question & answer→Getting a number less than 1 on throwing a die is impossible, as a die does not have a number less than 1 on it.
Question 301 Mark
Classify, the following events as certain to happen, impossible to happen, may or may not happen. Today moon will not revolve around the earth.
Answer
View full question & answer→It is impossible that moon will not revolve around the earth.
Question 311 Mark
If the extreme observations of both the ends of a data arranged in ascending order are removed, the median gets affected.
Answer
View full question & answer→False. Solution: If the extreme observations on both the ends of a data arranged in ascending order are removed, then the mean and mode gets affected but median remains same.
Question 321 Mark
Mean, median and mode are the measures of __________.
Answer
View full question & answer→ Mean, median and mode are the measures of central tendency.
Question 331 Mark
Mean of the observations can be lesser than each of the observations.
Answer
View full question & answer→ False.
Solution:
Mean is the average value of all the observations. Some of the observations are less than it and some of observations are more than it.
Solution:
Mean is the average value of all the observations. Some of the observations are less than it and some of observations are more than it.
Question 341 Mark
The mean of a data is defined as__________.
Answer
View full question & answer→ The mean of a data is defined as $\frac{\text{Sum of all observations}}{\text{Number of observations}}$.
Question 351 Mark
A coin is tossed $15$ times and the outcomes are recorded as follows: $\text{H T T H T H H H T T H T H T T.}$ The chance of occurence of a head is $50$ percent.
Answer
View full question & answer→Number of times in which head occurs $= 7$
Total number of times, the coin is tossed $= 15$
$\therefore$ Probability of getting a head $=\frac{7}{15}$
Total number of times, the coin is tossed $= 15$
$\therefore$ Probability of getting a head $=\frac{7}{15}$
Question 361 Mark
Mode of the data is always from the given data.
Answer
View full question & answer→False. Solution: It is not compulsory that mean of the data is always from the given data. It may or may not be the observation from given data.
Question 371 Mark
Given below are heights of $15$ boys of a class measured in cm:$128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.$
Find:
The height of the tallest boy.
Find:
The height of the tallest boy.
Answer
View full question & answer→Given, height (data) of $15$ boys of a class are: $128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.$
Arranging the given data in ascending order, we have $128, 129, 136, 138, 140, 140, 142, 142, 143, 144, 144, 146, 150, 152, 154$ By observing the data,
height of the tallest boy $= 154\ cm$
Arranging the given data in ascending order, we have $128, 129, 136, 138, 140, 140, 142, 142, 143, 144, 144, 146, 150, 152, 154$ By observing the data,
height of the tallest boy $= 154\ cm$
Question 381 Mark
In a set of observations, the observation that occurs the most often is called __________.
Answer
View full question & answer→In a set of observations, the observation that occurs the most often is called Mode. Solution: Mode is the most often occurring observation in a set of data.
Question 391 Mark
Mean can never be a fraction.
Answer
View full question & answer→e.g. Mean between $\frac{1}{4}$ and $\frac{1}{6}$
$=\frac{\text{Sum of}\frac{1}{4}\text{and}\frac{1}{6}}{\text{n}}=\frac{\frac{1}{4}+\frac{1}{6}}{2}$
$[\because ($number of terms$) = 2$
$=\frac{\frac{6+4}{24}}{2}=\frac{10}{24}\times\frac{1}{2}=\frac{5}{24}$
$=\frac{\text{Sum of}\frac{1}{4}\text{and}\frac{1}{6}}{\text{n}}=\frac{\frac{1}{4}+\frac{1}{6}}{2}$
$[\because ($number of terms$) = 2$
$=\frac{\frac{6+4}{24}}{2}=\frac{10}{24}\times\frac{1}{2}=\frac{5}{24}$
Question 401 Mark
Observe the data and answer the questions that follow: $16, 15, 16, 16, 8, 15, 17$ Atleast how many and which value(s) must be put into change the mode to $15?$
Answer
View full question & answer→Atleast two $15’s$ should be added to change the mode to $15.$ On adding two $15’s$ the frequency of $15$ will be maximum, i.e. $4.$
Question 411 Mark
The median of any data lies between the ______ add ___________ observations.
Answer
View full question & answer→The median of any data lies between the minimum add maximum observations.
Question 421 Mark
When a die is thrown, the probability of getting a number less than $7$, is __________.
Answer
View full question & answer→When we throw a die, 6 outcomes are possible, $i.e. 1, 2, 3, 4, 5, 6.$ Total outcomes $= 6$
Possible outcomes less than $7 = 6 [\because$ all the outcomes are less than $7]\because\text{Probability}=\frac{\text{Possible outcomes}}{\text{Total outcomes}}=\frac{6}{6}=1$
Possible outcomes less than $7 = 6 [\because$ all the outcomes are less than $7]\because\text{Probability}=\frac{\text{Possible outcomes}}{\text{Total outcomes}}=\frac{6}{6}=1$
Question 431 Mark
The difference between the highest and the lowest observations of a data is called _________.
Answer
View full question & answer→The difference between the highest and the lowest observations of a data is called range.
Question 441 Mark
Observe the data and answer the questions that follow: $16, 15, 16, 16, 8, 15, 17$ Which data value can be put in the data so that the mode remains
the same$?$
the same$?$
Answer
View full question & answer→Given data: $16, 15, 16, 16, 8, 15, 17$ Arranging the given data in ascending order, we have $8, 15, 15, 16, 16, 16, 17$ As per the given data, $16$ is the mode of data, since it has highest frequency, i.e. $3$. Now, if $15$ is added to the given data, mode will get changed to $15$ and $16,$ whereas if any other number, i.e. $8, 16$ or $17$ is added, mode will remain same.
Question 451 Mark
Observe the data and answer the questions that follow: $16, 15, 16, 16, 8, 15, 17$ What is the least number of data values that must be put into change the mode to $17?$ Name them.
Answer
View full question & answer→We will have to add atleast three $17’s$ to change the mode to $17.$ On adding three $17’s,$ the frequency of $17$ will be maximum, i.e. $4.$
Question 461 Mark
If a die is thrown, the probability of getting a number greater than $6$ is $1.$
Answer
View full question & answer→As we know, a die has six numbers on it, i.e. $1$ to $6$. So, it is impossible to get a number greater than $6.$ Hence, if a die is thrown, the probability of getting a number greater than $6$ is $0.$
Question 471 Mark
Median is one of the observations in the data, if number of observations is ____.
Answer
View full question & answer→If number of observation $(n)$ is odd, then median is one of the observation in the data. Note
Case I If $n =$ odd Median = Value of $\Big(\frac{\text{n+1}}{2}\Big)\text{th}$ observation
Case II If $n =$ even, Median $=\frac{\text{Value of }\Big(\frac{\text{n}}{2}\Big)\text{th observation + Value of }\Big(\frac{\text{n}}{2}+1\Big)\text{th observation}}{2}$
Case I If $n =$ odd Median = Value of $\Big(\frac{\text{n+1}}{2}\Big)\text{th}$ observation
Case II If $n =$ even, Median $=\frac{\text{Value of }\Big(\frac{\text{n}}{2}\Big)\text{th observation + Value of }\Big(\frac{\text{n}}{2}+1\Big)\text{th observation}}{2}$
Question 481 Mark
A data constitutes of heights (in cm) of 50 children. What do you understand by mode for the data?
Answer
View full question & answer→Since, mode is the observation that occurs most frequently in a set of observation.
Question 491 Mark
The probability of the spinning arrow stopping in the shaded region figure is $\frac{1}{2}.$
Answer
View full question & answer→Favourable outcomes $=$ Number of shaded regions $= 2$
Total number of possible outcomes $=$ Total number of regions $= 4$
$\therefore\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total number of possible outcomes}}=\frac{2}{4}=\frac{1}{2}$
Total number of possible outcomes $=$ Total number of regions $= 4$
$\therefore\text{Probability}=\frac{\text{Favourable outcomes}}{\text{Total number of possible outcomes}}=\frac{2}{4}=\frac{1}{2}$
Question 501 Mark
The following are weights (in kg) of $12$ people. $70, 62, 54, 57, 62, 84, 75, 59, 62, 65, 78, 60$ How many people weight above the mean weight$?$
Answer
View full question & answer→Weights above $65.66$ are $70, 84, 75$ and $78,$ i.e. $4$ persons.
Question 511 Mark
The range of the data $2, -5, 4, 3, 7, 6$ would change, if $2$ was subtracted from each value in the data.
Answer
View full question & answer→Range before subtraction by $2 =$ Highest observation $-$ Lowest observation $= 7 - (-5) = 7 + 5 = 12$
Data after subtract by $2 = 2 -2, -5 - 2, 4 - 2, 3 -2, 7 - 2, 6 - 2,$ i.e. $0, -7, 2, 1, 5, 4$
Range $=$ Highest observation $-$ Lowest observation $= 5 - (-7) = 5 + 7 = 12$
So, the range is same.
Data after subtract by $2 = 2 -2, -5 - 2, 4 - 2, 3 -2, 7 - 2, 6 - 2,$ i.e. $0, -7, 2, 1, 5, 4$
Range $=$ Highest observation $-$ Lowest observation $= 5 - (-7) = 5 + 7 = 12$
So, the range is same.
Question 521 Mark
Given below are heights of $15$ boys of a class measured in cm$:128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.$
Find:
The range of the given data.
Find:
The range of the given data.
Answer
View full question & answer→Given, height (data) of $15$ boys of a class are: $128, 144, 146, 143, 136, 142, 138, 129, 140, 152, 144, 140, 150, 142, 154.$
Arranging the given data in ascending order, we have $128, 129, 136, 138, 140, 140, 142, 142, 143, 144, 144, 146, 150, 152, 154$
Here, highest observation $= 154$ and lowest observation $= 128$
$\therefore$ Range = Highest observation - Lowest observation $= 154 - 128 = 26\ cm$
Arranging the given data in ascending order, we have $128, 129, 136, 138, 140, 140, 142, 142, 143, 144, 144, 146, 150, 152, 154$
Here, highest observation $= 154$ and lowest observation $= 128$
$\therefore$ Range = Highest observation - Lowest observation $= 154 - 128 = 26\ cm$