Question

use technology to find the requested measures of center and spread for the following sample data set. you should be able to select the data and copy it directly to excel. if you are using a graphing or statistical calculator, you will need to enter the data by hand. 35.6, 44.3, 45.9, 51.4, 58.7, 63.9, 66.6, 73.4, 51.5, 59.9, 55.2, 53, 36.4, 41.8, 38.6, 47.4, 59.4, 50.6, 57.7, 52.8, 48.5, 56.6, 53.2, 63.3, 62.6, 48.3, 58.7, 65.3, 54, 59.7, 50.1, 64.4, 47, 55.2, 56.2, 71.4, 47, 66.8, 63.6, 51.7, 53.4, 48.5, 54.8, 55.4, 65.7, 50.3, 46, 54.4, 56.2, 43.2, 47.4, 59, 41, 65.3, 36.4, 60.9, 52.6, 58.5, 68.2, 61.7, 63.6, 63.3, 43.2, 60.7, 69, 60.7, 50.1, 54.6, 46.4, 60.7. what is the mean of this data set? mean = report answer to 2 decimal places. what is the median of this data set? median = report answer to 2 decimal places. what is the maximum of this data set? max = what is the minimum of this data set? min = what is the mid - range of this data set? (recall that the mid - range is the arithmetic mean of the maximum and minimum values.) mid - range = what is the range of this data set? range = report the standard deviation to two more decimal places than the data reports. standard deviation = report answer to 3 decimal places.

Explanation:

Step1: Count total data points

Total \( n = 80 \)

Step2: Calculate the mean

Sum all values, divide by \( n \):
\( \text{mean} = \frac{\sum x_i}{80} = \frac{4314.4}{80} = 53.93 \)

Step3: Find the median

Sort data, average 40th & 41st values:
\( \text{median} = \frac{53.3 + 53.4}{2} = 53.35 \)

Step4: Identify maximum value

Largest value in dataset: \( \text{max} = 69 \)

Step5: Identify minimum value

Smallest value in dataset: \( \text{min} = 35.6 \)

Step6: Calculate mid-range

Average max and min:
\( \text{mid-range} = \frac{69 + 35.6}{2} = 52.30 \)

Step7: Calculate range

Subtract min from max:
\( \text{range} = 69 - 35.6 = 33.4 \)

Step8: Calculate sample standard deviation

Use sample SD formula:
\( s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}} = \sqrt{\frac{7493.204}{79}} \approx 9.723 \)

Answer:

mean = 53.93
median = 53.35
max = 69
min = 35.6
mid-range = 52.30
range = 33.4
standard deviation = 9.723