Answer :
The mean of the given scores is 77.62, the median is 77, the mode is 71, the IQR is 12, the variance is 137, the standard deviation is 11.7, and the mean absolute deviation is 8.61.
To find the mean, you need to add up all the numbers in the given list and then divide the sum by the total number of values. In this case, the sum is 1630 and there are 21 values, so the mean is 1630/21 = 77.62 (rounded to two decimal places).
To find the median, you need to arrange the numbers in ascending order and then find the middle value. In this case, the middle two values are 77 and 77, so the median is 77.
To find the mode, you need to identify the value(s) that occur most frequently in the list. In this case, the mode is 71 as it appears three times, more than any other value.
To find the IQR, you need to find the difference between the third quartile (Q3) and the first quartile (Q1). First, you need to find Q1 and Q3 by finding the median of the lower half and upper half of the data respectively. Q1 is 71 and Q3 is 83, so the IQR is 83 - 71 = 12.
To find the variance of the scores, you need to find the average of the squared differences between each score and the mean. The variance in this case is 137 (rounded to one decimal place).
To find the standard deviation of the scores, you need to take the square root of the variance. The standard deviation in this case is approximately 11.7 (rounded to one decimal place).
To find the mean absolute deviation of the scores, you need to find the average of the absolute differences between each score and the mean. The mean absolute deviation in this case is approximately 8.61 (rounded to two decimal places).
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