What is the mean of 2, 5, 8, 14, 21?
10
Understanding the Mean of a Dataset
The question asks us to find the mean of a given set of numbers: 2, 5, 8, 14, and 21. The mean is a measure of central tendency, often referred to as the average. It is calculated by summing all the numbers in the dataset and then dividing by the total count of numbers.
Formula for Calculating the Mean
The formula for the arithmetic mean (\(\bar{x}\)) of a set of \(n\) numbers (\(x_1, x_2, ..., x_n\)) is given by:
\[ \bar{x} = \frac{\sum_{i=1}^{n} x_i}{n} \]
Where:
- \(\sum x_i\) represents the sum of all the numbers in the dataset.
- \(n\) represents the total count of numbers in the dataset.
Step-by-Step Mean Calculation
Let's apply the mean formula to the given numbers: 2, 5, 8, 14, and 21.
- List the numbers: The given numbers are 2, 5, 8, 14, 21.
- Count the numbers: There are 5 numbers in the set. So, \(n = 5\).
- Sum the numbers: Add all the numbers together: \[ \text{Sum} = 2 + 5 + 8 + 14 + 21 \] \[ \text{Sum} = 7 + 8 + 14 + 21 \] \[ \text{Sum} = 15 + 14 + 21 \] \[ \text{Sum} = 29 + 21 \] \[ \text{Sum} = 50 \] The sum of the numbers is 50.
- Calculate the mean: Divide the sum by the count of numbers: \[ \text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{50}{5} \] \[ \text{Mean} = 10 \]
Therefore, the mean of the numbers 2, 5, 8, 14, and 21 is 10.
Comparing with Options
Let's check the calculated mean against the provided options:
- Option 1: 10
- Option 2: 9
- Option 3: 8.5
- Option 4: 9.5
Our calculated mean is 10, which matches Option 1.
| Number | Value |
|---|---|
| First | 2 |
| Second | 5 |
| Third | 8 |
| Fourth | 14 |
| Fifth | 21 |
| Total Sum | 50 |
| Count (n) | 5 |
| Mean (Sum/n) | 10 |
Revision Table: Key Statistical Measures
| Measure | Description | Calculation Method |
|---|---|---|
| Mean (Average) | Sum of all values divided by the number of values. | Sum / Count |
| Median | The middle value in a dataset when arranged in ascending or descending order. If there's an even number of values, it's the average of the two middle values. | Order data, find middle value(s) |
| Mode | The value that appears most frequently in the dataset. A dataset can have one mode (unimodal), multiple modes (multimodal), or no mode. | Identify most frequent value(s) |
| Range | The difference between the highest and lowest values in a dataset. | Highest value - Lowest value |
Additional Information: Measures of Central Tendency
The mean, median, and mode are the three most common measures of central tendency. They each provide a different way to describe the "center" or typical value of a dataset. The mean is sensitive to extreme values (outliers), while the median is less affected by them. The mode is useful for identifying the most common category or value, particularly in non-numeric data.
In this specific problem, we were asked to find the mean, which represents the arithmetic average of the numbers.
Similar Questions
In a cricket match, the scores of the players are considered such that coefficient of variation of scores is 16 and mean is 25 .then the variance is:
The mean of the numbers 1, 4, 9, X, 12, 14, 15 and 16 is 10. Find the mode.
The median of the numbers 3, 1, 1, 5, 2 and 7 is:
The median of the numbers 4, 2, 2, 6, 3 and 8 is:
A sequence a, ax, ax 2, _______ ax n, has odd number of terms. Then the median is
In the usual set notation,
A U (B ∩ C) =
- If A, B and C are denoting Mean, Median and Mode of a data and A ∶ B = 9 ∶ 8 then the ratio of B ∶ C is:
If the mean of the following data is 40, then what is the value of x?
Class 10-20 20-30 30-40 40-50 50-60 Frequency 30 27 44 29 X What is the mode of 21, 22, 22, 23, 24, 24, 24?
The median of the following data is :
25, 15, 23, 25, 17, 27, 20, 18, 24, 30, 19, 28, 35, 10, 31, 40
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
