The arithmetic mean of the following data is _________. 23, 17, 20, 19, 21
20
How to Calculate the Arithmetic Mean
This problem asks us to find the arithmetic mean of a given set of numbers. The arithmetic mean, often simply called the mean or average, is a fundamental concept in statistics used to represent the central value of a set of numbers.
Understanding Arithmetic Mean
The arithmetic mean is calculated by summing all the numbers in a dataset and then dividing the sum by the total count of numbers in the dataset. It gives us a single value that represents the typical value in the set.
Given Data for Mean Calculation
The dataset provided is:
- 23
- 17
- 20
- 19
- 21
We have a total of 5 numbers in this dataset.
Formula for Arithmetic Mean Calculation
The formula for calculating the arithmetic mean ($\bar{x}$) is:
$$\bar{x} = \frac{\text{Sum of all values}}{\text{Number of values}}$$
In mathematical notation, if the dataset is $x_1, x_2, \dots, x_n$, the arithmetic mean is:
$$\bar{x} = \frac{\sum_{i=1}^{n} x_i}{n}$$
Where $\sum x_i$ is the sum of all values and $n$ is the number of values.
Step-by-Step Arithmetic Mean Calculation
Let's apply the formula to the given data:
- First, sum all the numbers in the dataset:
- Sum = $23 + 17 + 20 + 19 + 21$
- Sum = $100$
- Next, count the total number of values in the dataset:
- Number of values ($n$) = 5
- Now, divide the sum by the number of values:
- Arithmetic Mean = $\frac{100}{5}$
- Arithmetic Mean = $20$
Final Result: Arithmetic Mean
The arithmetic mean of the given data set (23, 17, 20, 19, 21) is 20.
Revision Table: Key Concepts
| Term | Definition | How to Calculate |
|---|---|---|
| Arithmetic Mean | The average of a set of numbers. | Sum of values divided by the count of values. |
| Sum of Values | The result of adding all numbers in the dataset. | Add each number together. |
| Number of Values | The total count of numbers in the dataset. | Count how many numbers are present. |
Additional Information: Measures of Central Tendency
The arithmetic mean is one of several measures of central tendency used to describe the center point of a dataset. Other common measures include:
- Median: The middle value of a dataset when it is ordered from least to greatest. If there is an even number of values, the median is the average of the two middle values.
- Mode: The value that appears most frequently in a dataset. A dataset can have one mode (unimodal), more than one mode (multimodal), or no mode if all values appear with the same frequency.
These measures provide different perspectives on the typical value within a dataset and are used depending on the nature of the data and the analysis required.
Similar Questions
The given table represents the monthly income of 100 families of a locality.
Monthly income range (in Rs.)
Number of families
Income more than Rs. 10,000
100
Income more than Rs. 13,000
85
Income more than Rs. 16,000
69
Income more than Rs. 19,000
50
Income more than Rs. 22,000
33
Income more than Rs. 25,000
15
The number of families having income range (in Rs.) 19000 - 22000 is:
Find the mode for the given distribution (rounded off to two decimal places).
Class Interval 5-10 10-15 15-20 20-25 25-30 30-35 Frequency 8 7 6 9 11 10 The median of the following data will be _________.
32, 25, 33, 27, 35, 29 and 30
For a sample data, mean = 60 and median = 48. For this distribution, the mode is:
The mode of the following data is __________.
13, 15, 31, 12, 27, 13, 27, 30, 27, 28 and 16
The median of a set of 11 distinct observations is 73.2. If each of the largest five observations of the set is increased by 3, then the median of the new set:
What is the mode of the given data?
5, 7, 9, 7, 3, 7, 5, 7, 8, 6, 7
In tossing a coin, let the probability of turning up a head be p . The hypotheses are H 0∶ p = 0.4 vs H 1 ∶ p = 0.6. H 0is rejected if there are five or more heads in six tosses. Then the power of the test is:
For ANOVA two-way classification, to test two types of cloth in fashion trends, we have the following table.
Source of Variations
SS
Df
MSS
F-Ratio
Variety A
280
2
140
42.04
Variety B
α
3
34.03
Error
20
β
3.33
Total
640
11
The values of (α, β) are:The arithematic average of Edgeworth - Marshal index number
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.
