Problem Analysis
The question asks for the sum of 20 numbers, given the median (250) and the mode (295). We need to find the relationship connecting these values to calculate the sum.
- Number of observations (\(N\)): 20
- Median: 250
- Mode: 295
- Required: Sum of the 20 numbers
The sum of numbers is calculated as \(Sum = Mean \times N\). We first need to find the mean using the given median and mode.
Finding the Mean Using Empirical Relationship
For moderately skewed distributions, the empirical relationship between mean, median, and mode is often used. A common form of this relationship is:
\( Mode = 3 \times Median - 2 \times Mean \)
Substitute the given values:
\( 295 = 3 \times 250 - 2 \times Mean \)
\( 295 = 750 - 2 \times Mean \)
Rearrange the equation to solve for the Mean:
\( 2 \times Mean = 750 - 295 \)
\( 2 \times Mean = 455 \)
\( Mean = \frac{455}{2} \)
\( Mean = 227.5 \)
Calculating the Sum of Numbers
Now that the mean is found, calculate the sum using the formula \(Sum = Mean \times N\).
\( Sum = 227.5 \times 20 \)
\( Sum = 4550 \)
Therefore, the sum of the 20 numbers is 4550.
Similar Questions
Find the median of the data 11, 16, 33, 15, 51, 19, 71, 75, 21, 17.
For a data, if the mean is 28.5 and the median is 32, then the mode using empirical formula is:
- If the mean of a distribution is 8.73 and its median is 11, then the mode of the distribution is __________ (using empirical relation).
- What is the mode of the following data?
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70, 79, 66, 89, 68, 80, 82, 80, 71, 84, 69, 68, 61, 85, 71, 84, 68, 86, 73, 75, 83, 88, 64, 88, 65 - The lifetime of certain species is given in the following table. Calculate the modal lifetime (rounded up to one decimal place) in days.
Lifetime (days) 0-10 10-20 20-30 30-40 40-50 50-60 Frequency 10 35 52 61 38 29 - The given data shows the marks obtained by 50 students of a class in a test. What is the mean marks obtained by students?
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Important Questions from Elementary Statistics
In a colony 5 families have 1 child, 7 families have 2 children, 8 families have 3 children and 3 families have 4 children.What is the mode of the number of children.
What will be the difference between mean and median of the given data?
21, 11, 27, 8, 5, 12, 7, 23, 3, 14, 9, 19Find the mode and median of 3, 4, 5, 5, 3, 6, 7, 3, 5, 5, 6.
A. 5 and 5
B. 3 and 5
C. 5 and 4
D. 3 and 4
For which set of numbers do the mean, median and mode all have the same value?
The median of 5, 8, 25, 22, 34, 18 is
