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If the 26 English alphabets are taken su...

If the 26 English alphabets are taken such that A=1,B=2,C=3 …………Z=26 then find
(I)The mean and the medain of the numbers corresponding to the vowels.
(ii) Which alphabet corresponds to the medain.

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The correct Answer is:
To solve the problem, we need to find the mean and median of the numbers corresponding to the vowels in the English alphabet. The vowels are A, E, I, O, and U. ### Step-by-step Solution: **Step 1: Identify the numerical values of the vowels.** - A = 1 - E = 5 - I = 9 - O = 15 - U = 21 **Step 2: List the values of the vowels.** The values corresponding to the vowels are: - A = 1 - E = 5 - I = 9 - O = 15 - U = 21 So, the list of values is: 1, 5, 9, 15, 21. **Step 3: Calculate the mean of the vowel values.** To find the mean, we use the formula: \[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Total number of observations}} \] - **Sum of observations**: \[ 1 + 5 + 9 + 15 + 21 = 51 \] - **Total number of observations**: 5 (since there are 5 vowels) Now, substituting the values into the mean formula: \[ \text{Mean} = \frac{51}{5} = 10.2 \] **Step 4: Calculate the median of the vowel values.** To find the median, we first arrange the values in ascending order (which they already are): 1, 5, 9, 15, 21. Since there are 5 values (an odd number), the median is the middle value. The middle value is the 3rd value in the ordered list: - Median = 9 **Step 5: Identify the alphabet corresponding to the median.** The median value is 9. Referring back to our vowel values: - The alphabet corresponding to 9 is I. ### Final Answers: (I) The mean of the numbers corresponding to the vowels is **10.2**. (II) The alphabet corresponding to the median is **I**.
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