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Question: If mode is 400 and median is 500 mean is: A. \(450\) B. \(480\) C. \(500\) D. \(550\)...

If mode is 400 and median is 500 mean is:
A. 450450
B. 480480
C. 500500
D. 550550

Explanation

Solution

According to the question given in the question we have to determine the mean if mode = 400 and median = 500. So, first of all we have to understand about the mean which is as explained below:
Mean: The mean or we can say that the average of a data set which can be found by adding all the given numbers in the data set and then dividing by the number of the values in the set.
Now, as we know that the mode is given 400 and median is given 500 so, with the help of mode and median we can determine the mean as asked in the question with the help of the formula as mentioned below:
Mode = 3 median – 2 mean ……………….(A)
Now, to determine the value of mean we have to substitute the values of mode and median in the formula (A) as mentioned above.

Complete step-by-step solution:
Step 1: First of all we have to determine the mean we have to understand about the mean which is the average of a data set which can be found by adding all the given numbers in the data set and then dividing by the number of the values in the set as mentioned in the solution hint.
Step 2: Now, to determine the value of mean we have to substitute the values of mode and median in the formula (A) as mentioned in the solution hint. Hence, on substituting all the values in the formula.
⇒400=3×500−2×Mean\Rightarrow 400 = 3 \times 500 - 2 \times Mean…………………..(1)
Step 3: Now, to determine the mean we have to rearrange the terms of the expression (1) as obtained in the solution step 2. Hence,
⇒Mean=3×500−4002 ⇒Mean=1500−4002 ⇒Mean=11002 ⇒Mean=550 \Rightarrow Mean = \dfrac{{3 \times 500 - 400}}{2} \\\ \Rightarrow Mean = \dfrac{{1500 - 400}}{2} \\\ \Rightarrow Mean = \dfrac{{1100}}{2} \\\ \Rightarrow Mean = 550
Final solution: Hence, with the help of the formula (A) as mentioned in the solution hint we have determined the mean = 550.

Therefore option (D) is correct.

Note: Mean is basically the same as the average for the given data set in which first of all we have to determine the sum of all the given numbers or data and then we have to divide the sum by the total number of data sets.
The median is the middle value in the list of numbers of no number in the list is repeated, then there is no mode for the list.