Question:
Find the mean deviation about the mean for the given data.
\(x_i\) 5 10 15 20 25 \(f_i\) 7 4 6 3 5
Find the mean deviation about the mean for the given data.
| \(x_i\) | 5 | 10 | 15 | 20 | 25 |
| \(f_i\) | 7 | 4 | 6 | 3 | 5 |
Updated On: Nov 2, 2023
Hide Solution
Verified By Collegedunia
Solution and Explanation
| \(x_i\) | \(f_i\) | \(f_ix_i\) | \(|x_i-\bar{x}|\) | \(f_i|x_i-\bar{x}|\) |
| 5 | 7 | 35 | 9 | 63 |
| 10 | 4 | 40 | 4 | 16 |
| 15 | 6 | 90 | 1 | 6 |
| 20 | 3 | 60 | 6 | 18 |
| 25 | 5 | 125 | 11 | 55 |
| 25 | 350 | 158 |
\(N=\sum_{I=1}^{5}f_i=25\)
\(N=\sum_{I=1}^{5}f_ix_i=350\)
∴ \(\bar{x}=\frac{1}{N}\sum_{I=1}^{5}f_ix_i=\frac{1}{25}×350=14\)
∴ \(=MD\bar{(x)}=\frac{1}{N}\sum_{i=1}^{5}f_i|x_i-\bar{x}|=\frac{1}{25}×158=6.32\)
Was this answer helpful?
0
0
Top Questions on Statistics
- Calculate the mean of the following data :
Class : 4 – 6 7 – 9 10 – 12 13 – 15 Frequency : 5 4 9 10 - For the above distribution, the modal class is :
Marks : Below 10 Below 20 Below 30 Below 40 Below 50 Number of Students : 3 12 27 57 75 - The mean and median of a statistical data are 21 and 23 respectively. The mode of the data is:
- If a certain variable \(x\) divides a statistical data arranged in order into two equal parts; then the value of \(x\) is called the:
- Gurpreet is very fond of doing research on plants. She collected some leaves from different plants and measured their lengths in mm.
The length of the leaves from different plants are recorded in the following table.Based on the above information, answer the following questions :\(\text{Length (in mm)}\) 70-80 80-90 90-100 100-110 110-120 120-130 130-140 \(\text{Number of leaves}\) 3 5 9 12 5 4 2
View More Questions
Questions Asked in CBSE CLASS XII exam
- Find the inverse of each of the matrices, if it exists. \(\begin{bmatrix} 1 & 3\\ 2 & 7\end{bmatrix}\)
- For what values of x,\(\begin{bmatrix} 1 & 2 & 1 \end{bmatrix}\)\(\begin{bmatrix} 1 & 2 & 0\\ 2 & 0 & 1 \\1&0&2 \end{bmatrix}\)\(\begin{bmatrix} 0 \\2\\x\end{bmatrix}\)=O?
- Find the inverse of each of the matrices,if it exists \(\begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix}\)
What is the Planning Process?
- CBSE CLASS XII - 2023
- Planning process steps
- Find the inverse of each of the matrices,if it exists. \(\begin{bmatrix} 2 & 3\\ 5 & 7 \end{bmatrix}\)
View More Questions
Concepts Used:
Mean Deviation
A statistical measure that is used to calculate the average deviation from the mean value of the given data set is called the mean deviation.
The Formula for Mean Deviation:
The mean deviation for the given data set is calculated as:
Mean Deviation = [Σ |X – µ|]/N
Where,
- Σ represents the addition of values
- X represents each value in the data set
- µ represents the mean of the data set
- N represents the number of data values
Grouping of data is very much possible in two ways:
- Discrete Frequency Distribution
- Continuous Frequency Distribution