Question

For the following data items given: 8, 10, 12, 14, 16, 18, 20 find: mean range standard deviation

Options:
a) 2, 8, 4
b) 12, 12, 4
c) 14, 12, 6
d) 14, 8, 4

Answer 1

The mean of the data set is 14, the range is 12, and the standard deviation, calculated to two decimal places, is approximately 7.48. However, the closest match from the provided options is 14 (mean), 12 (range), and 4 (standard deviation).

Step-by-step explanation:

To find the mean, range, and standard deviation of the given data items (8, 10, 12, 14, 16, 18, 20), we start with the mean:

1. Add all the numbers together: 8 + 10 + 12 + 14 + 16 + 18 + 20 = 98.
2. Divide the sum by the number of data items: 98 \u00f7 7 = 14. So, the mean is 14.
3. The range is the difference between the largest and smallest values: 20 - 8 = 12.
4. To find standard deviation, we first find the variance by averaging the squared differences from the mean, and then take the square root of the variance.

• Variance = [(8-14)^2 + (10-14)^2 + (12-14)^2 + (14-14)^2 + (16-14)^2 + (18-14)^2 + (20-14)^2] / 7 = 56.
• Standard Deviation = \u221a56 = 7.48 (to two decimal places). The listed options do not provide this exact number, suggesting a possible error in the options or that the list is only an approximation. However, we will choose the closest option.

Therefore, the closest matching set for mean, range, and standard deviation from the options provided is: 14 (mean), 12 (range), 4 (standard deviation).