Questions: The stem-and-leaf display represents scores achieved on a 100-point biology exam by the 32 members of the class. Identify the mean, median and mode for the data represented. 4 7 5 2 5 6 6 2 3 3 6 6 8 7 0 2 3 3 3 3 5 5 6 6 The mean for the data is (Round to the nearest tenth)

Solution Steps

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

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

where \( N \) is the number of scores and \( x_i \) are the individual scores. The total sum of the scores is \( 1334 \) and the number of scores is \( 20 \):

\[ \mu = \frac{1334}{20} = 66.7 \]

Thus, the mean for the data is \( 66.7 \).

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

\[ \text{Sorted data} = [47, 52, 55, 56, 62, 63, 63, 66, 66, 68, 70, 72, 73, 73, 73, 73, 75, 75, 76, 76] \]

The formula for the rank of the median is:

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

Since the rank is \( 10.5 \), we take the average of the 10th and 11th values in the sorted list:

\[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{68 + 70}{2} = 69.0 \]

Thus, the median for the data is \( 69.0 \).

The mode is the value that appears most frequently in the dataset. By examining the sorted data, we find that the score \( 73 \) appears most frequently:

\[ \text{Mode} = 73 \]

Final Answer