$3, 4, 5, 6, 7$
To calculate the standard deviation for the dataset \(3, 4, 5, 6, 7\), we will follow these steps:
- Calculate the mean (\(\bar{x}\)) of the data.
\(\bar{x} = \frac{3 + 4 + 5 + 6 + 7}{5} = \frac{25}{5} = 5\) - Find the deviations of each data point from the mean and square each deviation.
- \(3 - 5 = -2\quad \rightarrow \quad (-2)^2 = 4\)
- \(4 - 5 = -1\quad \rightarrow \quad (-1)^2 = 1\)
- \(5 - 5 = 0\quad \rightarrow \quad (0)^2 = 0\)
- \(6 - 5 = 1\quad \rightarrow \quad (1)^2 = 1\)
- \(7 - 5 = 2\quad \rightarrow \quad (2)^2 = 4\)
- Calculate the average of these squared deviations.
\(\frac{4 + 1 + 0 + 1 + 4}{5} = \frac{10}{5} = 2\) - The standard deviation (\(\sigma\)) is the square root of the variance.
\(\sigma = \sqrt{2}\)
Therefore, the standard deviation of the given dataset is \(\sqrt{2}\), which matches the correct answer option provided.
Similar Questions
- The standard deviation of 12 values is 3. If each value is increased by 4, then find the variance of the new set of values.
Calculate the standard deviation for the following data.
4, 7, 9, 10, 15
- If the variance of 5 values is 0.64, then what will be its standard deviation?
Important Questions from Standard Deviation
A cold drink bottling plant fills bottles of 500 ml. capacity with mean of 500 ml. and a standard deviation of 5 ml. Atleast what percentage of bottles would contain cold drink between 490 ml. and 510 ml.?
The mean and standard deviation of 100 terms are 50 and 3, respectively. The sum of squares of the 100 terms is:
- Following are the ages (in years) of 6 people in a group: 25, 30, 35, 40, 45 and 50. What is the standard deviation of their ages (rounded to two decimal places)?
If the mean of a random variable X following Poisson distribution is 3, then standard deviation of the distribution is:
If the standard deviation of a population is 100, then based on a sample of size 100, the standard deviation of sample mean is equal to:
