Final answer:
To find the standard deviation, variance, and quartiles for the given data, you can use the mean, squared differences from the mean, the sum of squared differences, and the formula for variance and standard deviation. The first and third quartiles can be found by sorting the data and calculating the corresponding percentages. The standard deviation for the given data is 64.54, the variance is 4160.56, the first quartile is 193, and the third quartile is 260.
Step-by-step explanation:
To find the standard deviation, variance, and quartiles for the given data, we can use the following steps:
- Find the mean of the data set.
- Subtract the mean from each data value and square the result.
- Calculate the sum of the squared values.
- Divide the sum by the total number of data values to find the variance.
- Take the square root of the variance to find the standard deviation.
- Arrange the data in increasing order.
- Find the first quartile by calculating 25% of the total number of data values and finding the corresponding value in the sorted data set.
- Find the third quartile by calculating 75% of the total number of data values and finding the corresponding value in the sorted data set.
Using these steps, the standard deviation for the given data is 64.54, the variance is 4160.56, the first quartile is 193, and the third quartile is 260.