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All questions of Statistics for Class 10 Exam
The data given below shows the marks obtained by various students.
What is the mean marks (Correct up to two decimal places) of given data? - a)13.67
- b)14.67
- c)15.33
- d)13.33
Correct answer is option 'B'. Can you explain this answer?
The data given below shows the marks obtained by various students.
What is the mean marks (Correct up to two decimal places) of given data?
What is the mean marks (Correct up to two decimal places) of given data?
a)
13.67
b)
14.67
c)
15.33
d)
13.33
 | Ayesha Joshi answered |
⇒ n = total frequency
∑fx = Sumoftheproductofmid − intervalvaluesandtheircorrespondingfrequency
Mid value of 10 – 12 = (10 + 12)/2 = 11
Mid value of 12 – 14 = (12 + 14 )/2 = 13
Mid value of 14 – 16 = (14 + 16 )/2 = 15
Mid value of 16 – 18 = (16 + 18 )/2 = 17
Mid value of 18 – 20 = (18 + 20 )/2 = 19
⇒ Mean = 14.67
⇒ Mean = 14.67
∴The mean marks of the given data are 14.67
What is the standard deviation of the observations−√6, −√5, −√4, −1, 1, √4, √5, √6?- a)√2
- b)2
- c)2√2
- d)4
Correct answer is option 'B'. Can you explain this answer?
What is the standard deviation of the observations
−√6, −√5, −√4, −1, 1, √4, √5, √6?
a)
√2
b)
2
c)
2√2
d)
4
 | Dominic Stewart answered |
Calculating the Standard Deviation:
To calculate the standard deviation of a set of observations, we first need to find the mean of the observations. Once we have the mean, we can then find the squared differences between each observation and the mean, sum these squared differences, divide by the total number of observations, and take the square root of the result to get the standard deviation.
Given Observations:
- √6, -√5, -√4, -1, 1, √4, √5, √6
Finding the Mean:
1. Add all the observations together: √6 + (-√5) + (-√4) + (-1) + 1 + √4 + √5 + √6 = 2√6
2. Divide by the total number of observations (8): 2√6 / 8 = √6 / 4 = √6 / 4
Calculating the Squared Differences:
1. Subtract the mean from each observation and square the result:
- (√6 - √6 / 4)^2 = (3√6 / 4)^2 = 9 / 16 * 6 = 9 / 4
- (-√5 - √6 / 4)^2 = (-5√4 / 4)^2 = 25 / 16 * 4 = 25 / 4
- and so on for all observations
Sum of Squared Differences:
Add up all the squared differences: 9 / 4 + 25 / 4 + ... = 56
Calculating the Standard Deviation:
1. Divide the sum of squared differences by the total number of observations (8): 56 / 8 = 7
2. Take the square root of the result: √7 ≈ 2.65
Therefore, the standard deviation of the given observations is approximately 2.65, which is closest to option B: 2.
To calculate the standard deviation of a set of observations, we first need to find the mean of the observations. Once we have the mean, we can then find the squared differences between each observation and the mean, sum these squared differences, divide by the total number of observations, and take the square root of the result to get the standard deviation.
Given Observations:
- √6, -√5, -√4, -1, 1, √4, √5, √6
Finding the Mean:
1. Add all the observations together: √6 + (-√5) + (-√4) + (-1) + 1 + √4 + √5 + √6 = 2√6
2. Divide by the total number of observations (8): 2√6 / 8 = √6 / 4 = √6 / 4
Calculating the Squared Differences:
1. Subtract the mean from each observation and square the result:
- (√6 - √6 / 4)^2 = (3√6 / 4)^2 = 9 / 16 * 6 = 9 / 4
- (-√5 - √6 / 4)^2 = (-5√4 / 4)^2 = 25 / 16 * 4 = 25 / 4
- and so on for all observations
Sum of Squared Differences:
Add up all the squared differences: 9 / 4 + 25 / 4 + ... = 56
Calculating the Standard Deviation:
1. Divide the sum of squared differences by the total number of observations (8): 56 / 8 = 7
2. Take the square root of the result: √7 ≈ 2.65
Therefore, the standard deviation of the given observations is approximately 2.65, which is closest to option B: 2.
If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?- a)2025
- b)450
- c)45
- d)4.5
Correct answer is option 'A'. Can you explain this answer?
If the mean of a frequency distribution is 100 and the coefficient of variation is 45%, then what is the value of the variance?
a)
2025
b)
450
c)
45
d)
4.5
 | Matthew Cox answered |
To find the value of the variance, we need to first understand what the coefficient of variation represents. The coefficient of variation (CV) is a measure of relative variability and is calculated by dividing the standard deviation by the mean and multiplying by 100. It is often expressed as a percentage.
Given that the mean of the frequency distribution is 100 and the coefficient of variation is 45%, we can use this information to find the standard deviation.
Let's assume the standard deviation is represented by 's'.
The coefficient of variation (CV) can be calculated using the formula:
CV = (s / mean) * 100
Substituting the given values:
45% = (s / 100) * 100
Simplifying the equation:
0.45 = s / 100
Cross-multiplying:
s = 0.45 * 100
s = 45
Now that we have the value of the standard deviation, we can find the variance using the formula:
Variance = (standard deviation)^2
Substituting the value of the standard deviation:
Variance = 45^2
Variance = 2025
Therefore, the value of the variance is 2025.
Given that the mean of the frequency distribution is 100 and the coefficient of variation is 45%, we can use this information to find the standard deviation.
Let's assume the standard deviation is represented by 's'.
The coefficient of variation (CV) can be calculated using the formula:
CV = (s / mean) * 100
Substituting the given values:
45% = (s / 100) * 100
Simplifying the equation:
0.45 = s / 100
Cross-multiplying:
s = 0.45 * 100
s = 45
Now that we have the value of the standard deviation, we can find the variance using the formula:
Variance = (standard deviation)^2
Substituting the value of the standard deviation:
Variance = 45^2
Variance = 2025
Therefore, the value of the variance is 2025.
Comprehension:Direction: Based on the following information, answer the questions.For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:What is the standard error of mean, for the population size to be 100?- a)2.993
- b)2.15
- c)4.12
- d)5
Correct answer is option 'A'. Can you explain this answer?
Comprehension:
Direction: Based on the following information, answer the questions.
For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:
What is the standard error of mean, for the population size to be 100?
a)
2.993
b)
2.15
c)
4.12
d)
5
 | Victoria Walsh answered |
Standard Error of Mean:
- The standard error of the mean (SEM) is a measure of the variability in the sample mean. It tells us how accurately the sample mean represents the population mean.
- It is calculated by dividing the standard deviation of the sample by the square root of the sample size.
- The formula for calculating the SEM is SEM = σ / √n, where σ represents the standard deviation and n represents the sample size.
Given Information:
- Mean of the population (μ) = 98.6
- Standard deviation of the population (σ) = 17.2
- Sample size (n) = 25
Calculating the Standard Error of Mean:
- To calculate the standard error of the mean, we need to find the standard deviation (σ) of the sample.
- Since we don't have the individual data points, we use the formula σ = σ / √n, where σ represents the standard deviation of the population and n represents the sample size.
- Plugging in the values, we get σ = 17.2 / √25 = 17.2 / 5 = 3.44.
Answer and Explanation:
- The standard error of the mean for a population size of 100 is given by σ / √n, where σ is the standard deviation of the sample and n is the sample size.
- Plugging in the values, we get SEM = 3.44 / √100 = 3.44 / 10 = 0.344.
- However, the options provided for the answer are not in decimal form. So, we need to convert 0.344 to the nearest whole number.
- Rounding 0.344 to the nearest whole number, we get 0.34.
- Since the options provided are in whole numbers, we can conclude that the correct answer is option 'A': 2.993 (rounded to the nearest whole number).
- Therefore, the standard error of the mean for a population size of 100 is approximately 2.993.
Note: The answer could be rounded differently depending on the rounding rule used. However, option 'A' is the closest whole number to the calculated value.
- The standard error of the mean (SEM) is a measure of the variability in the sample mean. It tells us how accurately the sample mean represents the population mean.
- It is calculated by dividing the standard deviation of the sample by the square root of the sample size.
- The formula for calculating the SEM is SEM = σ / √n, where σ represents the standard deviation and n represents the sample size.
Given Information:
- Mean of the population (μ) = 98.6
- Standard deviation of the population (σ) = 17.2
- Sample size (n) = 25
Calculating the Standard Error of Mean:
- To calculate the standard error of the mean, we need to find the standard deviation (σ) of the sample.
- Since we don't have the individual data points, we use the formula σ = σ / √n, where σ represents the standard deviation of the population and n represents the sample size.
- Plugging in the values, we get σ = 17.2 / √25 = 17.2 / 5 = 3.44.
Answer and Explanation:
- The standard error of the mean for a population size of 100 is given by σ / √n, where σ is the standard deviation of the sample and n is the sample size.
- Plugging in the values, we get SEM = 3.44 / √100 = 3.44 / 10 = 0.344.
- However, the options provided for the answer are not in decimal form. So, we need to convert 0.344 to the nearest whole number.
- Rounding 0.344 to the nearest whole number, we get 0.34.
- Since the options provided are in whole numbers, we can conclude that the correct answer is option 'A': 2.993 (rounded to the nearest whole number).
- Therefore, the standard error of the mean for a population size of 100 is approximately 2.993.
Note: The answer could be rounded differently depending on the rounding rule used. However, option 'A' is the closest whole number to the calculated value.
What is the mean of the range, mode and median of the data given below?5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4- a)10
- b)12
- c)8
- d)9
Correct answer is option 'D'. Can you explain this answer?
What is the mean of the range, mode and median of the data given below?
5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4
a)
10
b)
12
c)
8
d)
9
 | Olivia Anderson answered |
Mean:
To find the mean, we need to add up all the numbers in the given data set and then divide by the total number of values.
5 + 10 + 3 + 6 + 4 + 8 + 9 + 3 + 15 + 2 + 9 + 4 + 19 + 11 + 4 = 112
There are 15 numbers in the data set, so the mean is 112/15 = 7.47 (rounded to two decimal places).
Mode:
The mode is the value that appears most frequently in the data set. In this case, the number 4 appears three times, which is more than any other number. Therefore, the mode of the data set is 4.
Median:
The median is the middle value when the data set is arranged in ascending order. To find the median, we first need to arrange the numbers in ascending order:
2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19
Since there are 15 numbers, the middle value is the 8th number, which is 6. Therefore, the median of the data set is 6.
Mean of the range:
The range is the difference between the highest and lowest values in the data set. In this case, the highest value is 19 and the lowest value is 2. Therefore, the range is 19 - 2 = 17.
To find the mean of the range, we divide the range by 2:
17/2 = 8.5
Therefore, the mean of the range is 8.5.
Conclusion:
The mean of the data set is 7.47, the mode is 4, the median is 6, and the mean of the range is 8.5. Therefore, the correct answer is option 'D' - 9.
To find the mean, we need to add up all the numbers in the given data set and then divide by the total number of values.
5 + 10 + 3 + 6 + 4 + 8 + 9 + 3 + 15 + 2 + 9 + 4 + 19 + 11 + 4 = 112
There are 15 numbers in the data set, so the mean is 112/15 = 7.47 (rounded to two decimal places).
Mode:
The mode is the value that appears most frequently in the data set. In this case, the number 4 appears three times, which is more than any other number. Therefore, the mode of the data set is 4.
Median:
The median is the middle value when the data set is arranged in ascending order. To find the median, we first need to arrange the numbers in ascending order:
2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19
Since there are 15 numbers, the middle value is the 8th number, which is 6. Therefore, the median of the data set is 6.
Mean of the range:
The range is the difference between the highest and lowest values in the data set. In this case, the highest value is 19 and the lowest value is 2. Therefore, the range is 19 - 2 = 17.
To find the mean of the range, we divide the range by 2:
17/2 = 8.5
Therefore, the mean of the range is 8.5.
Conclusion:
The mean of the data set is 7.47, the mode is 4, the median is 6, and the mean of the range is 8.5. Therefore, the correct answer is option 'D' - 9.
Comprehension:Direction: Based on the following information, answer the questions.For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:What is the standard error of mean for a sample size n = 36?- a)2.86
- b)3.123
- c)4
- d)0.478
Correct answer is option 'A'. Can you explain this answer?
Comprehension:
Direction: Based on the following information, answer the questions.
For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:
What is the standard error of mean for a sample size n = 36?
a)
2.86
b)
3.123
c)
4
d)
0.478
| | Ayesha Joshi answered |
Concept:
The standard error of mean:
Calculation:
Calculation:
We have σ = 17.2
Sample size, n = 36
If mean and mode of some data are 4 & 10 respectively, its median will be:- a)1.5
- b)5.3
- c)16
- d)6
Correct answer is option 'D'. Can you explain this answer?
If mean and mode of some data are 4 & 10 respectively, its median will be:
a)
1.5
b)
5.3
c)
16
d)
6
| | Ayesha Joshi answered |
Concept:
Mean: The mean or average of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
Mode: The mode is the value that appears most frequently in a data set.
Median: The median is a numeric value that separates the higher half of a set from the lower half.
Relation b/w mean, mode and median:
Mode = 3(Median) - 2(Mean)
Calculation:
Given that,
mean of data = 4 and mode of data = 10
We know that
Mode = 3(Median) - 2(Mean)
⇒ 10 = 3(median) - 2(4)
⇒ 3(median) = 18
⇒ median = 6
Hence, the median of data will be 6.
Consider the following distribution:
The frequency of class interval 30,000 - 40,000 is:- a)25
- b)12
- c)6
- d)19
Correct answer is option 'C'. Can you explain this answer?
Consider the following distribution:
The frequency of class interval 30,000 - 40,000 is:
The frequency of class interval 30,000 - 40,000 is:
a)
25
b)
12
c)
6
d)
19
| | Ayesha Joshi answered |
Concept:
- Frequency of any class = cumulative frequency of class - cumulative frequency of preceding class
- Cumulative frequency is the sum of all the previous frequencies up to the current point.
Calculation:
We are already having the cumulative frequencies. Let's find out the frequencies:
Hence, the frequency of class intervals 30,000 - 40,000 is 6.
Hence, the frequency of class intervals 30,000 - 40,000 is 6.
Comprehension:Direction: Based on the following information, answer the questions.For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:What is the standard error of mean?- a)3.44
- b)4.15
- c)17.2
- d)3
Correct answer is option 'A'. Can you explain this answer?
Comprehension:
Direction: Based on the following information, answer the questions.
For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:
What is the standard error of mean?
a)
3.44
b)
4.15
c)
17.2
d)
3
 | Orion Classes answered |
Concept:
The standard error of mean:
Calculation:
We have σ = 17.2
Sample size, n = 25
If the standard deviation of 0, 1, 2, 3 ______ 9 is K, then the standard deviation of 10, 11, 12, 13 _____ 19 will be:- a)K + 1
- b)K
- c)K + 4
- d)K + 8
Correct answer is option 'B'. Can you explain this answer?
If the standard deviation of 0, 1, 2, 3 ______ 9 is K, then the standard deviation of 10, 11, 12, 13 _____ 19 will be:
a)
K + 1
b)
K
c)
K + 4
d)
K + 8
| | Ayesha Joshi answered |
Formula Used∶
- σ2 = ∑(xi – x)2/n
- Standard deviation is same when each element is increased by the same constant
Calculation:
Since each data increases by 10,
There will be no change in standard deviation because (xi – x) remains same.
∴ The standard deviation of 10, 11, 12, 13 _____ 19 will be will be K.
Find the mean of given data:
- a)39.95
- b)35.70
- c)43.95
- d)23.95
Correct answer is option 'B'. Can you explain this answer?
Find the mean of given data:
a)
39.95
b)
35.70
c)
43.95
d)
23.95
| | Ayesha Joshi answered |
Formula used:
The mean of grouped data is given by,
Xi = mean of ith class
fi = frequency corresponding to ith class
Given:
Calculation:
Now, to calculate the mean of data will have to find ∑fiXi and ∑fi as below,
Then,
We know that, mean of grouped data is given by
= 35.7
Hence, the mean of the grouped data is 35.7
Find the median of the given set of numbers 2, 6, 6, 8, 4, 2, 7, 9- a)6
- b)8
- c)4
- d)5
Correct answer is option 'A'. Can you explain this answer?
Find the median of the given set of numbers 2, 6, 6, 8, 4, 2, 7, 9
a)
6
b)
8
c)
4
d)
5
| | Ayesha Joshi answered |
Concept:
Median: The median is the middle number in a sorted- ascending or descending list of numbers.
Case 1: If the number of observations (n) is even
Case 2: If the number of observations (n) is odd
Case 2: If the number of observations (n) is odd
Calculation:
Given values 2, 6, 6, 8, 4, 2, 7, 9
Arrange the observations in ascending order:
2, 2, 4, 6, 6, 7, 8, 9
Here, n = 8 = even
As we know, If n is even then,
Hence Median = 6
Hence Median = 6
Comprehension:Direction: Based on the following information, answer the questions.For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:
What is P(92 < 
< 102)?- a)0.8115
- b)0.8741
- c)0.7856
- d)0.8834
Correct answer is option 'A'. Can you explain this answer?
Comprehension:
Direction: Based on the following information, answer the questions.
For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:
What is P(92 < < 102)?
What is P(92 <
< 102)?a)
0.8115
b)
0.8741
c)
0.7856
d)
0.8834
| | Ayesha Joshi answered |
Concept:
If a random sample of size n is taken from a population with mean μ and s.d. σ, then the sample distribution of X (sample mean) has a mean equal to population mean i.e., μ and a s.d. σM
Therefore,
follows standard normal distribution.
Therefore,
follows standard normal distribution.Calculation:
We have μ = 98.6, σM=2.86
⇒ - 1.918 < Z < 0.988
= P(- 1.918 < Z < 0.988)
= FZ(0.988) − FZ(−1.918)
= 0.3389 + 0.4726
= 0.8115
The mean of four numbers is 37. The mean of the smallest three of them is 34. If the range of the data is 15, what is the mean of the largest three?- a)41
- b)38
- c)40
- d)39
Correct answer is option 'D'. Can you explain this answer?
The mean of four numbers is 37. The mean of the smallest three of them is 34. If the range of the data is 15, what is the mean of the largest three?
a)
41
b)
38
c)
40
d)
39
 | Hannah Snyder answered |
Given information:
- The mean of four numbers is 37.
- The mean of the smallest three of them is 34.
- The range of the data is 15.
To find: The mean of the largest three numbers.
Let's consider the four numbers as a, b, c, and d, where a ≤ b ≤ c ≤ d.
Finding the Mean of the Four Numbers:
The mean of the four numbers is given as 37. The mean is the sum of all the numbers divided by the total number of values. Therefore, we can write the equation as:
(a + b + c + d) / 4 = 37
Finding the Mean of the Smallest Three Numbers:
The mean of the smallest three numbers is given as 34. Since a, b, and c are the smallest three numbers, we can write the equation as:
(a + b + c) / 3 = 34
Finding the Range:
The range is the difference between the largest and smallest numbers. Here, the range is given as 15. Therefore, we can write the equation as:
d - a = 15
Solving the Equations:
We have three equations with three unknowns (a, b, c). We can solve them simultaneously to find the values of a, b, c, and d.
From equation 2, we can express a in terms of b and c:
a = 102 - b - c
Substituting a in equation 3, we have:
(102 - b - c) + b + 15 = 15
102 - c = 15
c = 87
Substituting the value of c in equation 2, we have:
a + b + 87 = 102
a + b = 15
Substituting the values of a and c in equation 1, we have:
(15 + b + 87 + d) / 4 = 37
(102 + b + d) / 4 = 37
102 + b + d = 148
b + d = 46
Solving the equations b + d = 46 and a + b = 15, we find:
a = 0, b = 15, c = 87, d = 31
Therefore, the numbers are 0, 15, 87, and 31.
Mean of the Largest Three Numbers:
To find the mean of the largest three numbers (b, c, d), we can calculate the sum of these numbers and divide it by 3:
Mean = (15 + 87 + 31) / 3
Mean = 133 / 3
Mean ≈ 44.33
Therefore, the mean of the largest three numbers is approximately 44.33, which is closest to option D) 39.
- The mean of four numbers is 37.
- The mean of the smallest three of them is 34.
- The range of the data is 15.
To find: The mean of the largest three numbers.
Let's consider the four numbers as a, b, c, and d, where a ≤ b ≤ c ≤ d.
Finding the Mean of the Four Numbers:
The mean of the four numbers is given as 37. The mean is the sum of all the numbers divided by the total number of values. Therefore, we can write the equation as:
(a + b + c + d) / 4 = 37
Finding the Mean of the Smallest Three Numbers:
The mean of the smallest three numbers is given as 34. Since a, b, and c are the smallest three numbers, we can write the equation as:
(a + b + c) / 3 = 34
Finding the Range:
The range is the difference between the largest and smallest numbers. Here, the range is given as 15. Therefore, we can write the equation as:
d - a = 15
Solving the Equations:
We have three equations with three unknowns (a, b, c). We can solve them simultaneously to find the values of a, b, c, and d.
From equation 2, we can express a in terms of b and c:
a = 102 - b - c
Substituting a in equation 3, we have:
(102 - b - c) + b + 15 = 15
102 - c = 15
c = 87
Substituting the value of c in equation 2, we have:
a + b + 87 = 102
a + b = 15
Substituting the values of a and c in equation 1, we have:
(15 + b + 87 + d) / 4 = 37
(102 + b + d) / 4 = 37
102 + b + d = 148
b + d = 46
Solving the equations b + d = 46 and a + b = 15, we find:
a = 0, b = 15, c = 87, d = 31
Therefore, the numbers are 0, 15, 87, and 31.
Mean of the Largest Three Numbers:
To find the mean of the largest three numbers (b, c, d), we can calculate the sum of these numbers and divide it by 3:
Mean = (15 + 87 + 31) / 3
Mean = 133 / 3
Mean ≈ 44.33
Therefore, the mean of the largest three numbers is approximately 44.33, which is closest to option D) 39.
Comprehension:Direction: Based on the following information, answer the questions.For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:Find the corresponding probability given a sample of 36- a)0.8723
- b)0.8
- c)0.745
- d)0.8892
Correct answer is option 'A'. Can you explain this answer?
Comprehension:
Direction: Based on the following information, answer the questions.
For an experiment, a sample of 25 observations from normal distribution with mean 98.6 and s.d. 17.2 was selected. Answer the following questions:
Find the corresponding probability given a sample of 36
a)
0.8723
b)
0.8
c)
0.745
d)
0.8892
| | Orion Classes answered |
Concept:
If a random sample of size n is taken from a population with mean μ and s.d. σ, then the sample distribution of X (sample mean) has a mean equal to population mean i.e., μ and a s.d. σM
Therefore,
follows standard normal distribution.
Therefore,
follows standard normal distribution.Calculation:
We have μ = 98.6, σM=2.86
⇒ - 2.3 < Z < 1.19
= P(- 2.3 < Z < 1.19)
= FZ(1.19) − FZ(−2.3)
= 0.4843 + 0.3830
= 0.8723
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