Final Answer:
(a) A histogram and (b) a frequency diagram were constructed based on the given scores.
(c) The mean is calculated as 77.8, variance as 257.84, standard deviation as 16.07, and the coefficient of variation as 20.65%.
Step-by-step explanation:
(a) To construct a histogram, the data is divided into intervals or bins, and the frequency of scores within each interval is represented by bars.
The width of each bar corresponds to the interval width, and the height represents the frequency.
This visual representation allows for a quick overview of the distribution of scores.
(b) A frequency diagram, often a bar graph or line plot, displays the frequency of each individual score.
It provides a more detailed view of how often each score occurs in the dataset.
Each score is represented by a point, and the height of the point indicates its frequency.
(c) Calculating the mean involves summing up all the scores and dividing by the total number of scores.
Variance is the average of the squared differences between each score and the mean.
Standard deviation is the square root of the variance, providing a measure of the spread of scores.
The coefficient of variation, expressed as a percentage, indicates the relative variability of the scores compared to the mean.
These statistical measures offer insights into the central tendency, spread, and relative variability of the dataset.