Answer:
The standard deviation of the given data set is approximately 0.5818, the mean is 59.44, the median is 59.25, and there is no mode.
Step-by-step explanation:
To calculate the standard deviation, mean, median, and mode of the given data set, we'll follow these steps:
Step 1: Calculate the mean (average):
Mean = (58.7 + 60.0 + 58.8 + 59.1 + 59.2 + 60.4 + 59.8 + 59.3 + 59.8 + 60.3) / 10
Mean = 594.4 / 10
Mean = 59.44
Step 2: Calculate the median:
To find the median, we need to arrange the data set in ascending order:
58.7, 58.8, 59.1, 59.2, 59.3, 59.8, 59.8, 60.0, 60.3, 60.4
Since we have 10 data points, the median will be the average of the two middle values:
Median = (59.2 + 59.3) / 2
Median = 118.5 / 2
Median = 59.25
Step 3: Calculate the mode:
The mode is the value(s) that appears most frequently in the data set.
In this case, there is no value that appears more than once, so there is no mode.
Step 4: Calculate the standard deviation:
To calculate the standard deviation, we'll use the formula:
Standard Deviation = sqrt((sum of (x - mean)^2) / n)
where x is each data point, mean is the mean value we calculated earlier, and n is the number of data points.
First, calculate the squared differences from the mean for each data point:
(58.7 - 59.44)^2, (58.8 - 59.44)^2, (59.1 - 59.44)^2, (59.2 - 59.44)^2, (59.3 - 59.44)^2, (59.8 - 59.44)^2, (59.8 - 59.44)^2, (60.0 - 59.44)^2, (60.3 - 59.44)^2, (60.4 - 59.44)^2
Next, sum up the squared differences:
Sum of (x - mean)^2 = (0.74)^2 + (0.64)^2 + (0.34)^2 + (0.24)^2 + (0.14)^2 + (0.36)^2 + (0.36)^2 + (0.56)^2 + (0.86)^2 + (0.96)^2
Sum of (x - mean)^2 = 0.5476 + 0.4096 + 0.1156 + 0.0576 + 0.0196 + 0.1296 + 0.1296 + 0.3136 + 0.7396 + 0.9216
Sum of (x - mean)^2 = 3.384
Finally, calculate the standard deviation:
Standard Deviation = sqrt(3.384 / 10)
Standard Deviation = sqrt(0.3384)
Standard Deviation ≈ 0.5818
Therefore, the standard deviation of the given data set is approximately 0.5818, the mean is 59.44, the median is 59.25, and there is no mode.
