Final answer:
The question pertains to the calculation of mean, median, mode, range, and sample standard deviation for a set of data in Mathematics at a High School level. The calculations reveal a mean of 68.10, a median of 66.50, a mode of 85, a range of 37, and a sample standard deviation of 13.94.
Step-by-step explanation:
The subject of the question is Mathematics, and the level is suitable for High School. We are asked to calculate the mean, median, mode, range, and sample standard deviation for a given set of data. First, let's organize the data in ascending order: 48, 54, 58, 61, 66, 67, 72, 85, 85, 85. Now, let's calculate each measurement:
- Mean: The average of all the numbers: (48 + 54 + 58 + 61 + 66 + 67 + 72 + 85 + 85 + 85) / 10 = 681 / 10 = 68.10.
- Median: The middle number in an ordered set. With 10 numbers, the median will be the average of the two middle numbers, which are 66 and 67. Thus, Median = (66 + 67) / 2 = 66.50.
- Mode: The number that appears most frequently, which is 85.
- Range: The difference between the highest and lowest values: 85 - 48 = 37.
- To find the Sample Standard Deviation, you can use a calculator or software: The calculation results in approximately 13.94 (rounded here, for accurate calculation, use precise values).
- To find the value that is one standard deviation below the mean, subtract the standard deviation from the mean: 68.10 - 13.94 = 54.16.
Thus, the Mean is 68.10, the Median is 66.50, the Mode is 85, the Range is 37, and the Sample Standard Deviation is 13.94.