Answers and Data Analysis:
Summary:
Mean = 62.50
Median = 58.00
Mode = 58 & 72
Range = 38
Sample Standard Deviation = 12.49
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Mean:
The mean is the sum of all values divided by the number of values.
Add all the values: 64 + 34 + 72 + 48 + 42 + 58 + 58 + 72 + 72 + 55 = 625
Divide the sum by the number of values (10): 625 / 10 = 62.5
Median:
The median is the "middle" value when the data is ordered from least to greatest.
Order the data: 34, 42, 48, 55, 58, 58, 64, 72, 72, 72
Since we have two middle values (58 and 58), the median is the average of those two numbers: (58 + 58) / 2 = 58
Mode:
The mode is the most frequent value in the data set.
In this case, both 58 and 72 appear three times each. Therefore, the data set has two modes (58 and 72).
Range:
The range is the difference between the largest and smallest values.
Largest value: 72
Smallest value: 34
Range: 72 - 34 = 38
Sample Standard Deviation:
The sample standard deviation measures how spread out the data is from the mean.
Calculating the standard deviation involves several steps:
Calculate the squared deviations from the mean for each data point. (Value - Mean)^2
Find the sum of the squared deviations from the mean.
Divide the sum of squared deviations by the number of values minus one (n-1). This is because we are estimating the population standard deviation from a sample.
Take the square root of the result from step 3.
This can be a lengthy calculation by hand. Here, you can use a calculator or spreadsheet to find the sample standard deviation: (rounded to nearest hundredth) = 12.49