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All questions of Statistics for SSC CGL Exam
If the mode of the following data is 7, then the value of k in the data set 3, 8, 6, 7, 1, 6, 10, 6, 7, 2k + 5, 9, 7, and 13 is:- a)3
- b)7
- c)4
- d)1
Correct answer is option 'D'. Can you explain this answer?
If the mode of the following data is 7, then the value of k in the data set 3, 8, 6, 7, 1, 6, 10, 6, 7, 2k + 5, 9, 7, and 13 is:
a)
3
b)
7
c)
4
d)
1
 | EduRev SSC CGL answered |
Concept:
Mode is the value that occurs most often in the data set of values.
Calculation:
Given data values are 3, 8, 6, 7, 1, 6, 10, 6, 7, 2k + 5, 9, 7, and 13
In the above data set, values 6, and 7 have occurred more times i.e., 3 times
But given that mode is 7.
So, 7 should occur more times than 6.
Hence the variable 2k + 5 must be 7
⇒ 2k + 5 = 7
⇒ 2k = 2
∴ k = 1
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
 | Ssc Cgl answered |
Given:
The given data is 5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4
Concept used:
The mode is the value that appears most frequently in a data set
At the time of finding Median
First, arrange the given data in the ascending order and then find the term
Formula used:
Mean = Sum of all the terms/Total number of terms
Median = {(n + 1)/2}th term when n is odd
Median = 1/2[(n/2)th term + {(n/2) + 1}th] term when n is even
Range = Maximum value – Minimum value
Calculation:
Arranging the given data in ascending order
2, 3, 3, 4, 4, 4, 5, 6, 8, 9, 9, 10, 11, 15, 19
Here, Most frequent data is 4 so
Mode = 4
Total terms in the given data, (n) = 15 (It is odd)
Median = {(n + 1)/2}th term when n is odd
⇒ {(15 + 1)/2}th term
⇒ (8)th term
⇒ 6
Now, Range = Maximum value – Minimum value
⇒ 19 – 2 = 17
Mean of Range, Mode and median = (Range + Mode + Median)/3
⇒ (17 + 4 + 6)/3
⇒ 27/3 = 9
∴ The mean of the Range, Mode and Median is 9
The number of observations smaller than _________ is the same as the number of observations larger than it.- a)median
- b)mode
- c)mean
- d)More than one of the above
Correct answer is option 'A'. Can you explain this answer?
The number of observations smaller than _________ is the same as the number of observations larger than it.
a)
median
b)
mode
c)
mean
d)
More than one of the above
 | Nilesh Banerjee answered |
Understanding the Concept of Median
The median is a statistical measure that represents the middle value of a dataset when it is organized in ascending order. Here’s why the median is significant in terms of observations:
Equal Distribution of Observations
- The median divides the dataset into two equal halves.
- By definition, 50% of observations are less than the median, and 50% are greater than it.
- This property makes the median a robust measure of central tendency, especially in skewed distributions.
Comparison with Mode and Mean
- Mode: The mode is the value that appears most frequently in a dataset. It does not necessarily divide the data into equal halves.
- Mean: The mean is the average of all observations. In distributions that are not symmetrical, the mean can be skewed by extreme values, leading to unequal numbers of observations on either side.
- Both mode and mean do not guarantee that an equal number of observations are below and above them.
Conclusion
- Since the median inherently divides the data into two equal parts, it is the only measure among the options that satisfies the condition of having the same number of observations smaller and larger than it.
- Therefore, the correct answer is option 'A', the median.
The median is a statistical measure that represents the middle value of a dataset when it is organized in ascending order. Here’s why the median is significant in terms of observations:
Equal Distribution of Observations
- The median divides the dataset into two equal halves.
- By definition, 50% of observations are less than the median, and 50% are greater than it.
- This property makes the median a robust measure of central tendency, especially in skewed distributions.
Comparison with Mode and Mean
- Mode: The mode is the value that appears most frequently in a dataset. It does not necessarily divide the data into equal halves.
- Mean: The mean is the average of all observations. In distributions that are not symmetrical, the mean can be skewed by extreme values, leading to unequal numbers of observations on either side.
- Both mode and mean do not guarantee that an equal number of observations are below and above them.
Conclusion
- Since the median inherently divides the data into two equal parts, it is the only measure among the options that satisfies the condition of having the same number of observations smaller and larger than it.
- Therefore, the correct answer is option 'A', the median.
The mean of 20 numbers is zero. Of them, at the most, how many may be greater than zero?- a)19
- b)1
- c)10
- d)More than one of the above
Correct answer is option 'A'. Can you explain this answer?
The mean of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
a)
19
b)
1
c)
10
d)
More than one of the above
 | Ishaan Roy answered |
Understanding the Problem
To solve the problem, we start with the information provided: the mean of 20 numbers is zero. This means that the sum of these 20 numbers must also be zero.
Mean Calculation
- Mean = (Sum of all numbers) / (Total numbers)
- Given that the mean is zero:
- Sum of all numbers = 0
Implications of the Sum Being Zero
- If we have numbers greater than zero, we need corresponding numbers that are less than zero (or negative) to balance the sum back to zero.
- For instance, if there are more positive numbers, the negative numbers must compensate sufficiently to maintain a zero sum.
Maximum Positive Numbers
- If we want to maximize the count of positive numbers, we can have 19 numbers greater than zero.
- However, to maintain the sum of zero, the 20th number must be negative, and its value must equal the sum of the positive numbers.
Example Scenario
- Let’s consider an example:
- If 19 numbers are 1, the sum of these would be 19.
- To keep the total sum zero, the 20th number must be -19.
- This ensures that the sum remains zero (19 + (-19) = 0).
Conclusion
- Therefore, the maximum number of numbers that can be greater than zero, while still keeping the sum of all numbers zero, is 19.
- Hence, the correct answer is option 'A' – at most 19 numbers can be greater than zero.
To solve the problem, we start with the information provided: the mean of 20 numbers is zero. This means that the sum of these 20 numbers must also be zero.
Mean Calculation
- Mean = (Sum of all numbers) / (Total numbers)
- Given that the mean is zero:
- Sum of all numbers = 0
Implications of the Sum Being Zero
- If we have numbers greater than zero, we need corresponding numbers that are less than zero (or negative) to balance the sum back to zero.
- For instance, if there are more positive numbers, the negative numbers must compensate sufficiently to maintain a zero sum.
Maximum Positive Numbers
- If we want to maximize the count of positive numbers, we can have 19 numbers greater than zero.
- However, to maintain the sum of zero, the 20th number must be negative, and its value must equal the sum of the positive numbers.
Example Scenario
- Let’s consider an example:
- If 19 numbers are 1, the sum of these would be 19.
- To keep the total sum zero, the 20th number must be -19.
- This ensures that the sum remains zero (19 + (-19) = 0).
Conclusion
- Therefore, the maximum number of numbers that can be greater than zero, while still keeping the sum of all numbers zero, is 19.
- Hence, the correct answer is option 'A' – at most 19 numbers can be greater than zero.
Let the average of three numbers be 16. If two of the numbers are 8 and 10, what is the remaining number?- a)-30
- b)18
- c)12
- d)30
Correct answer is option 'D'. Can you explain this answer?
Let the average of three numbers be 16. If two of the numbers are 8 and 10, what is the remaining number?
a)
-30
b)
18
c)
12
d)
30
| | Ssc Cgl answered |
Concept:
Calculation:
Here n = 3. Let's say that the third number is x.
⇒ x + 18 = 48
⇒ x = 30.
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
 | Pioneer Academy 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
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
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
| | EduRev SSC CGL 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
Hence, the mean of the grouped data is 35.7
Which of the following is the correct formula for the arithmetic mean?- a)The formula for arithmetic mean is the total sum of values of observations divided by the number of observations
- b)The formula for arithmetic mean is the total sum of values of observations plus the number of observations
- c)The formula for arithmetic mean is the total sum of values of observations multiplied by the number of observations
- d)More than one of the above
Correct answer is option 'A'. Can you explain this answer?
Which of the following is the correct formula for the arithmetic mean?
a)
The formula for arithmetic mean is the total sum of values of observations divided by the number of observations
b)
The formula for arithmetic mean is the total sum of values of observations plus the number of observations
c)
The formula for arithmetic mean is the total sum of values of observations multiplied by the number of observations
d)
More than one of the above
| | Pioneer Academy answered |
The correct answer is The formula for arithmetic mean is the total sum of values of observations divided by the number of observations.
Key Points
The correct formula for the arithmetic mean is:
Arithmetic mean = (Sum of all observations) / (Total number of observations)
This formula can be used to calculate the arithmetic mean of any set of numbers, regardless of whether the numbers are grouped or ungrouped.
This formula can be used to calculate the arithmetic mean of any set of numbers, regardless of whether the numbers are grouped or ungrouped.
Here is an example of how to use the formula:
Suppose we have the following set of numbers: 1, 2, 3, 4, 5.
To calculate the arithmetic mean, we would first sum all of the numbers:
1 + 2 + 3 + 4 + 5 = 15
Then, we would divide the sum by the total number of observations:
15 / 5 = 3
Therefore, the arithmetic mean of the set of numbers is 3.
The arithmetic mean is a useful measure of central tendency, and it is often used to summarize data and to make comparisons between different groups of data.
The arithmetic mean is a useful measure of central tendency, and it is often used to summarize data and to make comparisons between different groups of data.
The mean monthly salary paid to 77 employees in a company was Rs. 78. The mean salary of 32 of them was Rs. 45 and of the other 25 was Rs. 82. What was the mean salary of the remaining? - a)Rs. 124.8
- b)Rs. 125.8
- c)Rs. 126.8
- d)More than one of the above
Correct answer is option 'B'. Can you explain this answer?
The mean monthly salary paid to 77 employees in a company was Rs. 78. The mean salary of 32 of them was Rs. 45 and of the other 25 was Rs. 82. What was the mean salary of the remaining?
a)
Rs. 124.8
b)
Rs. 125.8
c)
Rs. 126.8
d)
More than one of the above
| | Pioneer Academy answered |
Given:
Total number of employees (n) = 77
Mean salary of all employees = Rs. 78
Number of employees with salary Rs. 45 = 32
Number of employees with salary Rs. 82 = 25
Concept used:
Total sum of salaries = Mean salary × Total number of employees
Calculation:
Total salaries for employees with salary Rs. 45
⇒ 45 × 32 = Rs. 1440
Total salaries for employees with salary Rs. 82
⇒ 82 × 25 = Rs. 2050
Total sum of salaries = 78 × 77 = Rs. 6006
Total salaries of remaining employees
⇒ Total sum of salaries - Sum of salaries for known employees
⇒ 6006 - 1440 - 2050 = Rs. 2516
⇒ 6006 - 1440 - 2050 = Rs. 2516
Now, Mean salary of the remaining employees
⇒ 2516/(77 - 32 - 25) = 2516/20 = 125.8
∴ The mean salary is 125.8
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
| | Pioneer Academy 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.
Find the no. of observations between 250 and 300 from the following data:
- a)56
- b)23
- c)15
- d)8
Correct answer is option 'B'. Can you explain this answer?
Find the no. of observations between 250 and 300 from the following data:
a)
56
b)
23
c)
15
d)
8
| | Pioneer Academy answered |
Concept:
To find number of observations between 250 and 300.
first we have to draw a frequency distribution table from this data.
∴ The Number of observation in between 250-300 = 38 - 15 = 23.
For the given set of data: 4, 4, 5, 6, 6 which of the following is true?- a)Mean = Mode
- b)Median = Mode
- c)Mean = Median
- d)Mean < Median
Correct answer is option 'C'. Can you explain this answer?
For the given set of data: 4, 4, 5, 6, 6 which of the following is true?
a)
Mean = Mode
b)
Median = Mode
c)
Mean = Median
d)
Mean < Median
| | Ssc Cgl answered |
Let's calculate the mean, median, and mode for the given set of data: 4, 4, 5, 6, 6.
- Mean: Mean = 4 + 4 + 5 + 6 + 65 = 255 = 5" id="MathJax-Element-1-Frame" role="presentation" style="position: relative;" tabindex="-1">Mean = 4 + 4 + 5 + 6 + 65 = 255 = 5" id="MathJax-Element-24-Frame" role="presentation" style="position: relative;" tabindex="0">
- Median:
- Since the data set is already sorted (4, 4, 5, 6, 6), the median is the middle value, which is 5.
- Mode:
- The mode is the value(s) that occur most frequently. In this case, both 4 and 6 occur twice, so the data set is bimodal, and there is no single mode.
Now, let's check the options:
- Mean = Median: This is true since both the mean and median are 5.
- Mean = Mode: This is not true because there is no single mode in this dataset.
- Mode = Median: This is not true since the data is bimodal (two modes), and the median is 5.
- Mean is less than Median: This is not true since the mean (5) is equal to the median (5).
Therefore, the correct statement is "Mean = Median."
What is the mean of first 99 natural numbers?- a)100
- b)50.5
- c)50
- d)99
Correct answer is option 'C'. Can you explain this answer?
What is the mean of first 99 natural numbers?
a)
100
b)
50.5
c)
50
d)
99
| | EduRev SSC CGL answered |
Concept:
Suppose there are ‘n’ observations {x1, x2, x3,…, xn}
Sum of the first n natural numbers 
Calculation:
To find: Mean of the first 99 natural numbers
As we know, Sum of first n natural numbers 
Find the mode and the median of the following frequency distribution respectively.
- a)13, 12
- b)14, 13
- c)17, 16
- d)14, 11
Correct answer is option 'B'. Can you explain this answer?
Find the mode and the median of the following frequency distribution respectively.
a)
13, 12
b)
14, 13
c)
17, 16
d)
14, 11
| | Ssc Cgl answered |
Formula used:
If the total number of observations given is odd, then the formula to calculate the median is:
Median = {(n+1)/2}th term
If the total number of observations is even, then the median formula is:
Median = [(n/2)th term + {(n/2)+1}th term]/2
where n is the number of observations.
Mode
The mode is the value that appears most frequently in a data set.
Given:
Calculation:
Since the frequency of x = 14 is 9 which is the maximum.
So, mode = 14
for frequency distribution,
So, the total number of observation = (1 + 4 + 7 + 5 + 9 + 3) = 29
So, 29 is ODD number, For odd number, the Median formula is,
⇒ Median = 15th term
⇒ Frequency of the 15th term
According to the table, the value of 15th is at x = 13
so the median = 13
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