Mean Median Mode And Standard Deviation

To solve the problem, we need to determine the value of given that the mean of the numbers is 9.

1. Formula for Mean:
The mean of a set of numbers is the sum of the numbers divided by the total count of the numbers. Here, the mean is given as 9, and the numbers are . The total count of numbers is 6. Therefore, the formula for the mean is:

Substitute the given values:

2. Simplifying the Equation:
First, calculate the sum of the known numbers and :

So the equation becomes:

Multiply both sides by 6 to eliminate the denominator:

3. Solving for :
Subtract 35 from both sides:

4. Final Answer:
The value of is .

To solve the problem, we need to find the arithmetic mean (A.M.) of the remaining students after excluding two students who scored zero marks. Here's the step-by-step solution:

Step 1: Understand the given information.
The arithmetic mean (A.M.) of the scores of 30 students is 42. This means the total sum of their scores is:

Step 2: Account for the two students who scored zero.
Since two students scored zero, their contribution to the total sum is zero. Therefore, the total sum of the scores of the remaining 28 students is still 1260.

Step 3: Calculate the A.M. of the remaining 28 students.
The arithmetic mean of the remaining 28 students is given by:

Step 4: Perform the division.
Calculate :

Final Answer:
The arithmetic mean of the remaining students is .

To solve the problem, we need to determine the median of the given set of numbers: .

1. Definition of Median:
The median is the middle value of a data set when the numbers are arranged in ascending order. If the data set has an odd number of elements, the median is the middle number. If the data set has an even number of elements, the median is the average of the two middle numbers.

2. Arranging the Numbers in Ascending Order:
First, arrange the given numbers in ascending order:

3. Identifying the Median:
Since there are 7 numbers (an odd count), the median is the middle number. The middle position is the -th number in the ordered list.

From the ordered list , the 4-th number is:

4. Final Answer:
The median of the given numbers is .

To solve the problem, we need to determine the mode of the sequence .

1. Understanding the Sequence:
The sequence consists of the 26 letters of the English alphabet in order. Each letter appears exactly once in the sequence.

2. Definition of Mode:
The mode of a data set is the value that appears most frequently. If no value repeats, then the data set has no mode.

3. Analyzing the Frequency:
In the given sequence, each letter (from to ) appears exactly once. Since no letter repeats, there is no value that occurs more frequently than any other.

4. Conclusion:
Since no letter in the sequence repeats, the sequence has no mode.

Final Answer:
The mode of the sequence is .

To solve the problem, we need to find the median using the given values of mode and mean.

1. Recall the Empirical Relationship:

There is an empirical relationship between mean, median, and mode for a moderately skewed distribution:

2. Substituting the Known Values:

Mode = 29, Mean = 32

Using the formula:

3. Solving for Median:

Final Answer:
The median is