Final answer:
For the data set 210, 215, 220, 225, 230, 235, 245, the range is 35, and by calculating the standard deviation, we get approximately 12.05. Hence, the correct answer is option b), which indicates a range of 35 and a standard deviation of 12.05.
Step-by-step explanation:
To find the range of the set of data, we take the highest value and subtract the lowest value. So, for the data set 210, 215, 220, 225, 230, 235, 245, the range is 245 - 210 = 35. Heading into the standard deviation calculation, first, we calculate the mean of the data.
The mean (average) is (210 + 215 + 220 + 225 + 230 + 235 + 245) / 7 = 1530 / 7 = 218.57 (rounded to two decimal places). To find the standard deviation, we follow these steps:
- Subtract the mean from each number to get the list of deviations.
- Square each of these deviations.
- Find the mean of these squared deviations.
- Take the square root of that to get the standard deviation.
Performing these calculations either manually or using a calculator, we get the standard deviation of approximately 12.05. Therefore, the answer is Range: 35, Standard Deviation: 12.05, which corresponds to answer option b).