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If the sum of the mode and mean of the certain frequency distribution in 129 and the median of the observations is 63, mode and mean are respectively
- a)69 and 60
- b)65 and 64
- c)68 and 61
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If the sum of the mode and mean of the certain frequency distribution ...
Given, Mode+ Mean = 129 .....(1)
and Median =63,
Also we know, Mode = 3. Median − 2. Mean
⇒ Mode=3×63−2. Mean =129−2.Mean ..(2)
Solving (1) and (2) we get, Mean=60 and Mode =69.
and Median =63,
Also we know, Mode = 3. Median − 2. Mean
⇒ Mode=3×63−2. Mean =129−2.Mean ..(2)
Solving (1) and (2) we get, Mean=60 and Mode =69.
Most Upvoted Answer
If the sum of the mode and mean of the certain frequency distribution ...
Given Information:
The sum of the mode and mean of the frequency distribution is 129. The median of the observations is 63.
Calculating the Mean:
Let the mean of the frequency distribution be x.
The sum of the frequencies is equal to the total number of observations. Therefore, the sum of all observations is 3x.
Given that the median is 63, the total number of observations is an odd number. Since the median is the middle value, there should be (n+1)/2 observations below it and (n+1)/2 observations above it.
Therefore, (n+1)/2 observations are less than or equal to 63. This implies that the sum of these observations is (n+1)/2 * 63.
The sum of observations above 63 is 3x - (n+1)/2 * 63.
Given that the mean is x, the total sum of all observations is 3x.
Therefore, we have the equation: (n+1)/2 * 63 + 3x - (n+1)/2 * 63 = 3x.
Solving this equation, we get x = 69.
Calculating the Mode:
Since the sum of the mode and mean is 129, and the mean is 69, we can calculate the mode as 129 - 69 = 60.
Therefore, the mode is 60.
Final Answer:
The mode is 60 and the mean is 69, which matches option A: 69 and 60.
The sum of the mode and mean of the frequency distribution is 129. The median of the observations is 63.
Calculating the Mean:
Let the mean of the frequency distribution be x.
The sum of the frequencies is equal to the total number of observations. Therefore, the sum of all observations is 3x.
Given that the median is 63, the total number of observations is an odd number. Since the median is the middle value, there should be (n+1)/2 observations below it and (n+1)/2 observations above it.
Therefore, (n+1)/2 observations are less than or equal to 63. This implies that the sum of these observations is (n+1)/2 * 63.
The sum of observations above 63 is 3x - (n+1)/2 * 63.
Given that the mean is x, the total sum of all observations is 3x.
Therefore, we have the equation: (n+1)/2 * 63 + 3x - (n+1)/2 * 63 = 3x.
Solving this equation, we get x = 69.
Calculating the Mode:
Since the sum of the mode and mean is 129, and the mean is 69, we can calculate the mode as 129 - 69 = 60.
Therefore, the mode is 60.
Final Answer:
The mode is 60 and the mean is 69, which matches option A: 69 and 60.
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If the sum of the mode and mean of the certain frequency distribution in 129 and the median of the observations is 63, mode and mean are respectivelya)69 and 60b)65 and 64c)68 and 61d)none of theseCorrect answer is option 'A'. Can you explain this answer?
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