Questions: The marks of seven students in a test were: 90% 80% 71% 85% 74% 67% 55% Find the mean mark and the median mark. The mean test score is %. (Type an integer or decimal rounded to one decimal place as needed.)

Solution Steps

To find the mean test score, we use the formula:

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

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

\[ \sum_{i=1}^7 x_i = 90 + 80 + 71 + 85 + 74 + 67 + 55 = 522 \]

Thus, the mean is calculated as follows:

\[ \mu = \frac{522}{7} \approx 74.6 \]

The mean test score is \( 74.6 \% \).

To find the median, we first sort the test scores:

\[ \text{Sorted data} = [55, 67, 71, 74, 80, 85, 90] \]

The median is the value at the position given by the formula:

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

For the median (\( Q = 0.5 \)) and \( N = 7 \):

\[ \text{Rank} = 0.5 \times (7 + 1) = 4.0 \]

The median is the value at position 4 in the sorted list, which corresponds to:

\[ \text{Median} = 74 \]

The median test score is \( 74 \% \).

Final Answer