Questions: Find the mean, median, and mode of the following data. If necessary, round to one more decimal place than the largest number of decimal places given in the data. 0.275, 0.318, 0.318, 0.321, 0.327, 0.306, 0.317, 0.284, 0.299, 0.276, 0.328, 0.291, 0.288, 0.297, 0.319, 0.326, 0.274, 0.290, 0.277, 0.276

Solution Steps

To find the mean (\( \mu \)) of the data, we use the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( N \) is the number of data points. For the given data, we have:

\[ \mu = \frac{6.007}{20} = 0.3003 \]

To find the median (\( Q \)), we first sort the data:

\[ \text{Sorted data} = [0.274, 0.275, 0.276, 0.276, 0.277, 0.284, 0.288, 0.290, 0.291, 0.297, 0.299, 0.306, 0.317, 0.318, 0.318, 0.319, 0.321, 0.326, 0.327, 0.328] \]

Since there are \( N = 20 \) data points, the rank for the median is calculated as:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (20 + 1) = 10.5 \]

To find the median, we average the values at positions 10 and 11:

\[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{0.297 + 0.299}{2} = 0.298 \]

The mode is the value that appears most frequently in the data. In this case, the mode is:

\[ \text{Mode} = 0.276 \]

Final Answer