GSEB Class 12 Statistics Question Paper February 2025
The GSEB Class 12 Statistics February 2025 board paper is available in both Gujarati and English medium. Download and practice probability, time series, and index number questions.
0
Questions
0
Marks
3h
Duration
Interactive Practice
Answer 0 questions interactively. Get your score instantly.
Review Answer Key
Read all questions with correctly marked answers and full explanations.
Paper Profile
Category / Board
GSEB
Level / Std
Std 12
Subject
Statistics
Total Questions
0
Total Marks
0
Negative Marking
None โ
Practice Mode
MCQ and True/False questions are interactive. Other question types show the model answer directly.
Which prices are considered in the construction of the cost of living index number?
If the purchase power of money is 0.75 in the year 2024 with respect to the base year 2023 then what will be the price index number for the year 2024?
What is the range of the correlation coefficient $r$?
In the method of rank correlation, in usual notations if $R_{x} = R_{y}$ for each pair of observations then what is the value of the $r$?
The regression line always passes through which point?
What is coefficient of determination in the study of regression for two variables?
Which variation is shown in increase in the sale of umbrellas of a company due to monsoon?
State the independent variable of time series.
Which random experiment from the following random experiments has an infinite sample space?
What is the probability of having 5 Mondays in the month of February in a year which is not a leap year?
Which variable of the following will be an illustration of continuous variable?
For the probability distribution of a discrete random variable $X$, $E(X) = 5$ and $E(X^2) = 35$, what will be the variance of this distribution?
The binomial distribution has mean 6 and variance $\frac{12}{7}$. What will be the type of this distribution?
Which of the following are mean and variance of standard normal variable?
What is the area under the normal curve to the right hand side of perpendicular line at $X = \mu$?
Mean and the first quartile for a normal distribution are 15 and 11 respectively. Which of the following is the value of the third quartile?
What is the neighbourhood form of $|x - 5| < 0.25$?
If $y = 10 - 3x$ and $x \to -3$ then $y$ tends to which value?
What is $\frac{dy}{dx}$ if $y = ax^n$, $a$ is constant?
What is the formula for elasticity of demand?
Write the formula to find the rate of inflation.
What is the main limitation of scatter diagram method?
Will the regression coefficient change if the values of both the variables $x$ and $y$ are doubled with the help of transformation of scale?
The linear equation fitted using the data of 7 weeks for a variable $y$ is $\hat{y} = 25.1 - 1.5t$. Estimate the value of $y$ for the eighth week.
Define mutually exclusive events.
Mean of a symmetrical binomial distribution is 9. Find the value of its parameter $n$.
"Standard score is independent of unit of measurement". Is this statement true or false?
The approximate value of mean deviation for a normal distribution is 12. Find its standard deviation.
If $\lim_{x \to -1} 4x + k = 6$ then find the value of $k$.
Define marginal cost.
The cost of living index numbers and average monthly wage from the year 2020 to 2023 are given as follows. Find the real wage for each year: | Year | 2020 | 2021 | 2022 | 2023 | | --- | --- | --- | --- | --- | | Average monthly wage (โน) | 36,000 | 40,000 | 52,000 | 56,000 | | Cost of living index number | 120 | 150 | 130 | 160 |
If the correlation coefficient between two variables $X$ and $Y$ is 0.8, find the value of the following: (i) $r(x, -y)$ (ii) $r(-x, -y)$
If $\bar{x} = 30, \bar{y} = 20$ and $b = 0.5$, find the intercept of the regression line of $Y$ on $X$ and write equation of the line.
State the components of time series.
If two balanced coins are tossed, then find the probability of: (i) getting one head and one tail. (ii) getting at least one head.
State any four properties of binomial distribution.
Express $N(16, 0.5)$ in the interval and modulus form.
Find the value of $\lim_{x \to -2} \frac{x^7 + 128}{x + 2}$
Determine whether the function $y = 12 + 4x - 7x^2$ is increasing or decreasing at $x = 2$.
The chain base index numbers of sales of a certain type of scooter from the year 2020 to 2024 are as follows. Find fixed base index numbers: | Year | 2020 | 2021 | 2022 | 2023 | 2024 | | --- | --- | --- | --- | --- | --- | | Index Number of Sale | 110 | 112 | 109 | 108 | 105 |
The prices of three items among five fuel items were increased by 50%, 90% and 110% in the year 2024 as compared to the base year 2023. The prices of other two items were decreased by 5% and 2% respectively. If the ratio of importance of these five items is $5:4:3:2:1$, find the index number of fuel prices for the year 2024.
The following results are obtained from a bivariate data, $n = 10$, $\Sigma (x - \bar{x})(y - \bar{y}) = 72$, $S_{x} = 3$, and $\Sigma (y - \bar{y})^{2} = 360$, find the correlation coefficient.
The information of price (in โน) of a ball pen and the supply of ball pen (in units) at the end of each month of a year for a company making ball pen is given below. Estimate the supply of ball pen when its price is โน 40: | Detail | Price (x) | Supply (y) | | --- | --- | --- | | Average | 30 | 500 | | Variance | 25 | 10,000 | | Co-variance = 400 | |
If the regression line of $Y$ on $X$ is $\hat{y} = 11 + 3x$ and $S_{x}: S_{y} = 3:10$, find the coefficient of determination.
State any three merits of graphical method of time series.
State the characteristics of random experiment.
If $P(B) = \frac{3}{5}$ and $P(A' \cap B) = \frac{1}{2}$, for two events $A$ and $B$, find $P\left(\frac{A}{B}\right)$ and $P(A' \cup B')$.
One number is randomly selected from the natural number 1 to 100. Find the probability that the number selected is either a single digit number or a perfect square.
The mean and variance of the binomial distribution are 2 and $\frac{6}{5}$ respectively. Find $p(2)$ for this binomial distribution.
A random variable $X$ denotes the number of accidents per year in a factory and the probability distribution of $X$ is given below: | X=x | 0 | 1 | 2 | 3 | 4 | | --- | --- | --- | --- | --- | --- | | p(x) | 4K | 15K | 25K | 5K | K | (i) Find the constant $K$. (ii) Find the probability of the event that one or two accidents will occur in this factory during the year.
Find $f'(x)$ if $f(x) = (x^2 + 3x + 4)^7$.
The average monthly expense of students residing in university hostel is โน 2,000 and its standard deviation is โน 500. If the monthly expense of a student follows normal distribution then: (i) Find percentage of students having expense between โน 750 and โน 1,250. (ii) Find percentage of students having expense more than โน 1,800 [Note: Blind students should state any four properties of normal distribution.]
A normal distribution has mean 52 and variance 64. Obtain estimated limits which include exactly middle 60% of the observations. [Note: Blind students should define standard normal variable and write its probability function.]
Find the value of $\lim_{x \to 2} \frac{f(x) - f(2)}{x - 2}$ where $f(x) = x^2 + x$.
The demand function of an item is $P = 30 - \frac{x^2}{10}$. Find the demand and price for maximum revenue.
Find Laspeyre's, Paasche's and Fisher's index numbers for the year 2024 with base year 2023 from the data about price and consumption of food items given below: | Item | Unit | Year 2024 | | Year 2023 | | --- | --- | --- | --- | --- | | | | Price (โน) | Quantity | Price (โน) | Quantity | | Rice | 20 kg. | 800 | 1.5 kg. | 780 | 1 kg. | | Milk | Litre | 44 | 10 Litre | 40 | 12 Litre | | Bread | kg. | 50 | 1.5 kg. | 45 | 2 kg. | | Banana | Dozen | 36 | 1.5 Dozen | 30 | 2 Dozen |
The following information is obtained to study the relationship between the advertisement cost and the sales of electric fans of the companies manufacturing electric fans. Find the *correlation coefficient* between advertisement cost and sales by Karl-Pearsonโs method: | Company | A | B | C | D | E | F | | --- | --- | --- | --- | --- | --- | --- | | Advertisement cost (lakh โน) | 140 | 120 | 80 | 100 | 80 | 180 | | Sales of electric fans (crore โน) | 35 | 45 | 15 | 40 | 20 | 50 |
From the following information, find the *rank correlation coefficient* between the sales (in thousand units) and the profit (in lakh โน): | Sales (thousand Units) | 25 | 58 | 215 | 72 | 58 | 25 | 90 | 162 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Profit (lakh โน) | 65 | 140 | 500 | 115 | 65 | 65 | 220 | 340 |
To study the relationship between the time of usage of cars and its average annual maintenance cost of a car manufacturing company, the following information is obtained: | Car | 1 | 2 | 3 | 4 | 5 | 6 | | --- | --- | --- | --- | --- | --- | --- | | Time of usage of a car (Years) x | 3 | 1 | 2 | 2 | 5 | 3 | | Average annual maintenance cost (thousand โน) y | 10 | 5 | 8 | 7 | 13 | 8 | Obtain the regression line of $Y$ on $X$. Find an estimate of average annual maintenance cost when the usage of a car is 5 years. Also find its error.
The birth rates of a state in different years are given in the following table. Fit a linear trend for these data. Also find the estimates for birth rates in the year 2025. | Year | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | | --- | --- | --- | --- | --- | --- | --- | --- | | Birth rate | 22.2 | 21.8 | 21.3 | 20.9 | 20.6 | 20.2 | 19.9 |
Find the trend using four yearly moving averages for the following data showing yearly sales (in lakh โน) of a shop: | Year | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Sales (lakh โน) | 5 | 3 | 7 | 6 | 4 | 8 | 9 | 10 | 8 | 9 |
Official Answer Key
All answers and explanations are shown below.
Which prices are considered in the construction of the cost of living index number?
If the purchase power of money is 0.75 in the year 2024 with respect to the base year 2023 then what will be the price index number for the year 2024?
What is the range of the correlation coefficient $r$?
In the method of rank correlation, in usual notations if $R_{x} = R_{y}$ for each pair of observations then what is the value of the $r$?
The regression line always passes through which point?
What is coefficient of determination in the study of regression for two variables?
Which variation is shown in increase in the sale of umbrellas of a company due to monsoon?
State the independent variable of time series.
Which random experiment from the following random experiments has an infinite sample space?
What is the probability of having 5 Mondays in the month of February in a year which is not a leap year?
Which variable of the following will be an illustration of continuous variable?
For the probability distribution of a discrete random variable $X$, $E(X) = 5$ and $E(X^2) = 35$, what will be the variance of this distribution?
The binomial distribution has mean 6 and variance $\frac{12}{7}$. What will be the type of this distribution?
Which of the following are mean and variance of standard normal variable?
What is the area under the normal curve to the right hand side of perpendicular line at $X = \mu$?
Mean and the first quartile for a normal distribution are 15 and 11 respectively. Which of the following is the value of the third quartile?
What is the neighbourhood form of $|x - 5| < 0.25$?
If $y = 10 - 3x$ and $x \to -3$ then $y$ tends to which value?
What is $\frac{dy}{dx}$ if $y = ax^n$, $a$ is constant?
What is the formula for elasticity of demand?
Write the formula to find the rate of inflation.
What is the main limitation of scatter diagram method?
Will the regression coefficient change if the values of both the variables $x$ and $y$ are doubled with the help of transformation of scale?
The linear equation fitted using the data of 7 weeks for a variable $y$ is $\hat{y} = 25.1 - 1.5t$. Estimate the value of $y$ for the eighth week.
Define mutually exclusive events.
Mean of a symmetrical binomial distribution is 9. Find the value of its parameter $n$.
"Standard score is independent of unit of measurement". Is this statement true or false?
The approximate value of mean deviation for a normal distribution is 12. Find its standard deviation.
If $\lim_{x \to -1} 4x + k = 6$ then find the value of $k$.
Define marginal cost.
The cost of living index numbers and average monthly wage from the year 2020 to 2023 are given as follows. Find the real wage for each year: | Year | 2020 | 2021 | 2022 | 2023 | | --- | --- | --- | --- | --- | | Average monthly wage (โน) | 36,000 | 40,000 | 52,000 | 56,000 | | Cost of living index number | 120 | 150 | 130 | 160 |
If the correlation coefficient between two variables $X$ and $Y$ is 0.8, find the value of the following: (i) $r(x, -y)$ (ii) $r(-x, -y)$
If $\bar{x} = 30, \bar{y} = 20$ and $b = 0.5$, find the intercept of the regression line of $Y$ on $X$ and write equation of the line.
State the components of time series.
If two balanced coins are tossed, then find the probability of: (i) getting one head and one tail. (ii) getting at least one head.
State any four properties of binomial distribution.
Express $N(16, 0.5)$ in the interval and modulus form.
Find the value of $\lim_{x \to -2} \frac{x^7 + 128}{x + 2}$
Determine whether the function $y = 12 + 4x - 7x^2$ is increasing or decreasing at $x = 2$.
The chain base index numbers of sales of a certain type of scooter from the year 2020 to 2024 are as follows. Find fixed base index numbers: | Year | 2020 | 2021 | 2022 | 2023 | 2024 | | --- | --- | --- | --- | --- | --- | | Index Number of Sale | 110 | 112 | 109 | 108 | 105 |
The prices of three items among five fuel items were increased by 50%, 90% and 110% in the year 2024 as compared to the base year 2023. The prices of other two items were decreased by 5% and 2% respectively. If the ratio of importance of these five items is $5:4:3:2:1$, find the index number of fuel prices for the year 2024.
The following results are obtained from a bivariate data, $n = 10$, $\Sigma (x - \bar{x})(y - \bar{y}) = 72$, $S_{x} = 3$, and $\Sigma (y - \bar{y})^{2} = 360$, find the correlation coefficient.
The information of price (in โน) of a ball pen and the supply of ball pen (in units) at the end of each month of a year for a company making ball pen is given below. Estimate the supply of ball pen when its price is โน 40: | Detail | Price (x) | Supply (y) | | --- | --- | --- | | Average | 30 | 500 | | Variance | 25 | 10,000 | | Co-variance = 400 | |
If the regression line of $Y$ on $X$ is $\hat{y} = 11 + 3x$ and $S_{x}: S_{y} = 3:10$, find the coefficient of determination.
State any three merits of graphical method of time series.
State the characteristics of random experiment.
If $P(B) = \frac{3}{5}$ and $P(A' \cap B) = \frac{1}{2}$, for two events $A$ and $B$, find $P\left(\frac{A}{B}\right)$ and $P(A' \cup B')$.
One number is randomly selected from the natural number 1 to 100. Find the probability that the number selected is either a single digit number or a perfect square.
The mean and variance of the binomial distribution are 2 and $\frac{6}{5}$ respectively. Find $p(2)$ for this binomial distribution.
A random variable $X$ denotes the number of accidents per year in a factory and the probability distribution of $X$ is given below: | X=x | 0 | 1 | 2 | 3 | 4 | | --- | --- | --- | --- | --- | --- | | p(x) | 4K | 15K | 25K | 5K | K | (i) Find the constant $K$. (ii) Find the probability of the event that one or two accidents will occur in this factory during the year.
Find $f'(x)$ if $f(x) = (x^2 + 3x + 4)^7$.
The average monthly expense of students residing in university hostel is โน 2,000 and its standard deviation is โน 500. If the monthly expense of a student follows normal distribution then: (i) Find percentage of students having expense between โน 750 and โน 1,250. (ii) Find percentage of students having expense more than โน 1,800 [Note: Blind students should state any four properties of normal distribution.]
A normal distribution has mean 52 and variance 64. Obtain estimated limits which include exactly middle 60% of the observations. [Note: Blind students should define standard normal variable and write its probability function.]
Find the value of $\lim_{x \to 2} \frac{f(x) - f(2)}{x - 2}$ where $f(x) = x^2 + x$.
The demand function of an item is $P = 30 - \frac{x^2}{10}$. Find the demand and price for maximum revenue.
Find Laspeyre's, Paasche's and Fisher's index numbers for the year 2024 with base year 2023 from the data about price and consumption of food items given below: | Item | Unit | Year 2024 | | Year 2023 | | --- | --- | --- | --- | --- | | | | Price (โน) | Quantity | Price (โน) | Quantity | | Rice | 20 kg. | 800 | 1.5 kg. | 780 | 1 kg. | | Milk | Litre | 44 | 10 Litre | 40 | 12 Litre | | Bread | kg. | 50 | 1.5 kg. | 45 | 2 kg. | | Banana | Dozen | 36 | 1.5 Dozen | 30 | 2 Dozen |
The following information is obtained to study the relationship between the advertisement cost and the sales of electric fans of the companies manufacturing electric fans. Find the *correlation coefficient* between advertisement cost and sales by Karl-Pearsonโs method: | Company | A | B | C | D | E | F | | --- | --- | --- | --- | --- | --- | --- | | Advertisement cost (lakh โน) | 140 | 120 | 80 | 100 | 80 | 180 | | Sales of electric fans (crore โน) | 35 | 45 | 15 | 40 | 20 | 50 |
From the following information, find the *rank correlation coefficient* between the sales (in thousand units) and the profit (in lakh โน): | Sales (thousand Units) | 25 | 58 | 215 | 72 | 58 | 25 | 90 | 162 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Profit (lakh โน) | 65 | 140 | 500 | 115 | 65 | 65 | 220 | 340 |
To study the relationship between the time of usage of cars and its average annual maintenance cost of a car manufacturing company, the following information is obtained: | Car | 1 | 2 | 3 | 4 | 5 | 6 | | --- | --- | --- | --- | --- | --- | --- | | Time of usage of a car (Years) x | 3 | 1 | 2 | 2 | 5 | 3 | | Average annual maintenance cost (thousand โน) y | 10 | 5 | 8 | 7 | 13 | 8 | Obtain the regression line of $Y$ on $X$. Find an estimate of average annual maintenance cost when the usage of a car is 5 years. Also find its error.
The birth rates of a state in different years are given in the following table. Fit a linear trend for these data. Also find the estimates for birth rates in the year 2025. | Year | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | | --- | --- | --- | --- | --- | --- | --- | --- | | Birth rate | 22.2 | 21.8 | 21.3 | 20.9 | 20.6 | 20.2 | 19.9 |
Find the trend using four yearly moving averages for the following data showing yearly sales (in lakh โน) of a shop: | Year | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | Sales (lakh โน) | 5 | 3 | 7 | 6 | 4 | 8 | 9 | 10 | 8 | 9 |