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
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Important Questions from Elementary Statistics
What is the mode of the given data?
3, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 1, 1, 3, 2What is the mode of the given data?
21, 22, 23, 23, 24, 21, 22, 23, 21, 23, 24, 23, 21, 23A bowler has taken 0, 3, 2, 1, 5, 3, 4, 5, 5, 2, 2, 0, 0, 1 and 2 wickets in 15 consecutive matches. What is the mode of the given data?
The data given below shows the number of people who have saved a certain amount of money.
Saving (In Rs.)
Number of people
5
1
15
3
20
4
25
2
30
1
35
1
40
2
What is the median of the given data?
If the ratio of mean and median of a certain data is 4 : 5, then find the ratio of its mean and mode.
