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Answer :
After calculating the measures of central tendency and variability, the mean is 82.4, median is 82, mode is 88, and midrange is 78.5 for the given collection of class test scores.
To determine the mean, median, mode, and midrange for a collection of class test scores, it's important to first organize the data effectively. We will work through these measures of central tendency and variability step by step.
Calculating the Mean
The mean is the arithmetic average of all the scores. To find this, all test scores should be added together, and then divided by the total number of scores. For the set provided, the sum of the scores is:
88 + 82 + 97 + 76 + 79 + 92 + 65 + 84 + 79 + 90 + 75 + 82 + 78 + 77 + 93 + 88 + 95 + 73 + 69 + 89 + 93 + 78 + 60 + 95 + 88 + 72 + 80 + 94 + 88 + 74 = 2473
Since there are 30 scores, the mean is 2473 divided by 30, which is 82.4.
Calculating the Median
The median is the middle value when all scores are arranged from lowest to highest. With 30 values, we will find the mean of the 15th and 16th scores. After arranging the scores, we find the 15th and 16th scores are 82 and 82, so the median is also 82.
Calculating the Mode
The mode is the score that appears most frequently in the dataset. In this case, the score of 88 appears four times, which is more frequent than any other score, making 88 the mode.
Calculating the Midrange
The midrange is the mean of the highest and lowest scores in the dataset. The lowest score is 60, and the highest is 97. Thus, the midrange is (60 + 97) / 2, which equals 78.5.
Based on these calculations, the correct answer is: Mean is 82.4, median is 82, mode is 88, midrange is 78.5.
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Rewritten by : Barada
Mean of a given set of data = Sum of all observations ÷ Total number of observations
Mean of this data set = 88 + 82 + 97 + 76 + 79 + 92 + 65 + 84 + 79 + 90 + 75 + 82 + 78 + 77 + 93 + 88 + 95 + 73 + 69 89 + 93 + 78 + 60 + 95 + 88 + 72 + 80 + 94 + 88 + 74
Mean = 2729 ÷ 30
Mean = 82.4
Median = the middle observation in a given set of data
Median of these test scores = 60 , 65 , 69 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 78 , 79 , 79 , 80 , 82 , 82 , 84 , 88 , 88 , 88 , 88 , 89 , 90 , 92 , 93 , 93 , 94 , 95 , 95 , 97 .
Median = 82 + 82 / 2
= 164 ÷ 2
= 82
Median = 82
Mode = most frequently occurring number in a given set of data .
Mode of these test scores =
= 60 = 1 time
= 65 = 1 time
= 69 = 1 time
= 72 = 1 time
= 73 = 1 time
= 74 = 1 time
= 75 = 1 time
= 76 = 1 time
= 77 = 1 time
= 78 = 2 times
= 79 = 2 times
= 80 = 1 time
= 82 = 2 times
= 84 = 1 time
= 88 = 4 times
= 89 = 1 time
= 90 = 1 time
= 92 = 1 time
= 93 = 2 times
= 94 = 1 time
= 95 = 2 times
= 97 = 1 time
Mode = 88
Midrange = average of the largest and smallest number in a given set of data
Midrange of these test scores = 97 + 60 / 2
= 97 + 60 / 2
= 157 ÷ 2
= 78.5
Midrange = 78.5
Therefore , the correct option is :-
