To find the first quartile (Q1) using the Mendenhall and Sincich Method, we need to sort the data set in ascending order and then find the value that is 25% from the bottom of the list.
First, let's arrange the scores in ascending order:
3, 5, 6, 8, 9, 9, 9, 11, 14, 16
Next, we need to calculate the position of the first quartile using the formula:
position of Q1 = (n + 1)/4
where n is the total number of scores. In this case, n = 10.
So, the position of Q1 = (10 + 1)/4 = 2.75
Since the position is not a whole number, we need to take the average of the values in positions 2 and 3 to find the first quartile:
Q1 = (5 + 6)/2 = 5.5
Therefore, the first quartile for this data set is 5.5.
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Answer:
To find the first quartile (Q1) using the Mendenhall and Sincich Method, we need to sort the data set in ascending order and then find the value that is 25% from the bottom of the list.
First, let's arrange the scores in ascending order:
3, 5, 6, 8, 9, 9, 9, 11, 14, 16
Next, we need to calculate the position of the first quartile using the formula:
position of Q1 = (n + 1)/4
where n is the total number of scores. In this case, n = 10.
So, the position of Q1 = (10 + 1)/4 = 2.75
Since the position is not a whole number, we need to take the average of the values in positions 2 and 3 to find the first quartile:
Q1 = (5 + 6)/2 = 5.5
Therefore, the first quartile for this data set is 5.5.