For the data set: 12, 8, 6, 6, 9, 8, 7, 11, 6, “6” is the value for which measure? Select two answers.
A. IQR
B. range
C. mode
D. median
E.mean
clearly you need to review these terms and their meanings.
Hint: 6 occurs the most times, right?
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but wait is it like b
and c?
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To determine which measure the value "6" represents in the given data set, we need to understand the definitions of the measures.
1. IQR (Interquartile Range): It is the range between the first quartile (Q1) and the third quartile (Q3) and measures the spread of the middle 50% of the data. To find the IQR, we need to arrange the data in ascending order.
2. Range: It is the difference between the largest and smallest values in the data set.
3. Mode: It is the value that appears most frequently in the data set.
4. Median: It is the middle value of the data set when arranged in ascending or descending order.
5. Mean: It is calculated by summing all the values in the data set and dividing by the number of values.
Now, let's examine the given data set: 12, 8, 6, 6, 9, 8, 7, 11, 6.
Step 1: Arrange the data in ascending order: 6, 6, 6, 7, 8, 8, 9, 11, 12.
Step 2: Analyze the measures based on the given value "6".
A. IQR: To find the IQR, we need to look for the range between Q1 and Q3. Since the value "6" appears multiple times in the data set, it could potentially be either the first quartile or the third quartile. However, we cannot determine the IQR based solely on the given value. Therefore, "6" is not related to the IQR.
B. Range: The range is determined by the difference between the smallest and largest values in the data set. In this case, the smallest value is 6, and the largest value is 12. The range is 12 - 6 = 6. Since the value "6" is present in the data set, it is related to the range.
C. Mode: The mode is the value that appears most frequently in the data set. In this case, the value "6" appears three times, more than any other value. Therefore, "6" is related to the mode.
D. Median: The median is the middle value of the data set. In this case, there are nine values, and when arranged in ascending order, the middle value is 8. Since "6" is not the median, it is not related to the median.
E. Mean: The mean is calculated by summing all the values in the data set and dividing by the number of values. In this case, the sum of all the values is 12 + 8 + 6 + 6 + 9 + 8 + 7 + 11 + 6 = 73. There are nine values in the data set. So, the mean is 73 / 9 = 8.11 (rounded to two decimal places). Since the value "6" is present in the data set and contributes to the sum, it is related to the mean.
Based on the above analysis, the value "6" is related to the range (B) and the mean (E).