The following information is an explanation of the terms for the options available to select in the Header Row.
- Mean – Displays the mean for the column. The mean (average) of a dataset is found by adding all numbers in the dataset and then dividing by the number of values in the set.
If you have eight scores (100, 90, 80, 70, 60, 50, 40, and 30), the average (or mean) score is calculated by adding all the scores together (520) and then dividing that total by the number of scores (8), resulting in an average of 65.
- Median – Displays the median score for the column. The median is the middle value when a dataset is ordered from least to greatest. If there are 2 numbers in the middle, the median is the average of those 2 numbers.
For instance, if the middle two numbers in a dataset are 60 and 70, then the median value is 65, which is calculated as the average of those two middle numbers: (60 + 70) / 2.
- Student Score/Avg. Count – Displays the number of scores in the column. It is the number of values in the dataset.
If eight student scores (100, 90, 80, 70, 60, 50, 40, 30) are entered into the assessment column, the system will return a value of 8, representing the total count of scores entered.
- Range – Displays the range for the column. The range is the difference between the lowest and highest values.
If the highest average score in a dataset is 100 and the lowest average score is 30, the range (or difference) between these averages is 70 (100-30=70).
- Standard Deviation – Displays the standard deviation for the column. Standard deviation is a measure of how wide the grade distribution spreads out from the mean. Representing how the values are changing with comparison or the respect to the mean or the average value (like in a bell curve model). A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range. The Gradebook uses “population standard deviation,” which is a fixed value calculated from every individual in the population. It is reflected in the same units of the measured values (%).
The standard deviation is 22.91. N (total number of values) is 8, the mean μ is 65, and the Variance, σ2 525, The standard deviation is the square root of the variance √525 (22.91). This makes 22.91% (+/-) represents one unit (SD) from the mean. Making 42% SD-1 and 87% SD+1. The scores of 50, 60, 70, and 80 fall within 1 SD +/-.
- Variance – Displays the population variance for the column. It is a measure of dispersion of data points from the mean. It is the average of the squared differences from the Mean. It is a square of the Standard Deviation.
In the example provided, the variance is 525, which is the square of the standard deviation (22.91^2). A large variance, like in this example, means that the students' grades were all over the place in a wide range. A small variance indicates a narrower distribution. If our scores were instead (90, 88, 87, 80, 78, 75, 70, 67) our variance would be 63.48, much smaller by comparison as the distribution is much narrower.
- Interquartile Range – Displays the interquartile range for the column. This is the amount of spread in the middle 50% of a dataset. It is the distance/difference between the Bottom (lower) quartile and the Top (upper) quartile of the data set (IQR=Q3-Q1). Helps to determine outliers.
In the example provided the interquartile range is 40. This represents the distance or difference between the Top Quartile (Q3) and the Bottom Quartile (Q1), 85-45= 40. Because this is a measure of the middle 50% of data it is more resistant to the presence of outliers, unlike the standard deviation and range.
- High Score/Avg.- Displays the Highest score/avg. in the column.
The high score/avg. is 100. - Low Score/Avg.- Displays the Lowest score/avg. in the column.
The low score/avg. is 30.
- Top Quartile- Displays the Top Quartile (or Upper Quartile (Q3)) for the column. This is the value under which 75% of data points are found when arranged in increasing order.
Also known as the Upper Quartile or Q3 of the dataset. In the example data the Top Quartile is 85. This is found by arranging the data high to low and dividing the data into 2 sets (excluding the median) then finding the median of the upper set. In this case the values used would be 100, 90, 80, 70, making 85 the median value and thus the Top Quartile value.
- Bottom Quartile- Displays the Bottom Quartile (or Lower Quartile (Q1) for the column. This is the value under which 25% of data points are found when they are arranged in increasing order.
Also known as the Lower Quartile or Q1 of the dataset. In the example data, the Bottom Quartile is 45. This is found by arranging the data high to low and dividing the data into 2 sets (excluding the median) then finding the median of the lower set. In this case the values used would be 60, 50, 40, 30, making 45 the median value and thus the Bottom Quartile value.