CAT Q1. The following are CATS scores of students in mathematics. \( 7,15,19,34,37,6,17,16,39,20 \). a) Calculate mean, mode and median. ( 3 mks ) b) Calculate standard deviation. ( 3 mks ) c) Draw a distribution to represent the scores. ( 3 mks ) d) Interpret the results in a,b and c. ( 3 mks ) e) How would the information in a,b and c help you as a teacher in your class. ( 3 mks )

To tackle this data set effectively, let’s break down the various parts of the question systematically! 1. First, let's calculate the mean, mode, and median based on the scores provided: - **Mean**: Add all scores together: \( 7 + 15 + 19 + 34 + 37 + 6 + 17 + 16 + 39 + 20 = 200 \). Divide by 10 (the number of students): \( \text{Mean} = \frac{200}{10} = 20 \). - **Mode**: This is the score that appears most frequently. From the list, no score appears more than once, so there is no mode. - **Median**: To find the median, first arrange the scores in ascending order: \(6, 7, 15, 16, 17, 19, 20, 34, 37, 39\). Since there are 10 scores (an even number), the median will be the average of the 5th and 6th scores: \( \frac{17 + 19}{2} = 18 \). 2. Next, the standard deviation measures how spread out the numbers are: - Calculate the variance by finding the difference of each score from the mean, squaring it, and averaging those squared differences: \[ \sigma^2 = \frac{(7-20)^2 + (15-20)^2 + (19-20)^2 + (34-20)^2 + (37-20)^2 + (6-20)^2 + (17-20)^2 + (16-20)^2 + (39-20)^2 + (20-20)^2}{10} \] After calculations, we find \( \sigma^2 = 182.8 \) and thus \( \sigma = \sqrt{182.8} \approx 13.52 \). 3. To represent the distribution, you could create a histogram by plotting the scores on the x-axis and their frequency on the y-axis. 4. Interpretation: - The mean score of 20 suggests that on average, students scored below the maximum. The absence of a mode indicates all the students performed at different levels, while the median shows that half the students scored below 18, indicating overall lower performance. 5. As a teacher, examining these statistics allows you to identify which areas require more focus in terms of teaching methods or supplemental resources. For example, if many students score well below the mean, it suggests a need for review or different instructional strategies. Moreover, understanding the variation through standard deviation helps in recognizing how widely students' scores vary, guiding differentiated instruction. Keep in mind that the visualization of the data is also crucial; it gives a clear picture at a glance and can engage the students more when discussing performance and learning gaps.