Indicate whether the given statement could apply to the data set consisting of 1000 values that are all different.
1. The 29% is greater then the 30 th percentile.
2. The median is greater then the first quartile.
3. The third quartile is greater then the first quartile.
4. The mean is equal to the median.
5. The range is zero.
I'll be glad to check YOUR answers.
Percentile is proportion score at or below a certain point. Median = 50th percentile. First quartile = 25th percentile.
That should help you.
To determine whether the given statements apply to the data set, we need to understand the concepts of percentiles, quartiles, mean, median, and range.
1. The 29% is greater than the 30th percentile:
To determine this, we first need to calculate the value of the 30th percentile. We can do this by finding the index in the sorted dataset corresponding to the 30th percentile (30% of 1000 is 300). Since all the values in the dataset are different, the 30th percentile will be the value at index 300. If the given statement says that 29% is greater than this value, then the statement is true.
2. The median is greater than the first quartile:
The first quartile (Q1) is the median of the lower half of the dataset. To calculate Q1, we need to find the index corresponding to the median of the lower half. In a dataset of 1000 values, the median will be the value at index 500. If the given statement compares the value of the median to Q1 and claims that the median is greater, then the statement is true.
3. The third quartile is greater than the first quartile:
Similar to the previous statement, we need to calculate the third quartile (Q3). Q3 is the median of the upper half of the dataset. In a dataset of 1000 values, the median will be the value at index 750. If the given statement compares Q3 to Q1 and asserts that Q3 is greater, then the statement is true.
4. The mean is equal to the median:
To calculate the mean, we sum up all the values in the dataset and divide by the total number of values (1000 in this case). The median is the middle value of the sorted dataset. If the given statement claims that the mean is equal to the median, then it would be true only if the dataset is symmetric (no skewness or outliers).
5. The range is zero:
The range is determined by finding the difference between the maximum and minimum values in the dataset. Since the given statement says the range is zero, it implies that the maximum and minimum values are the same. In a dataset of 1000 values that are all different, it is impossible for the range to be zero. Therefore, the statement is false.
In summary:
1. True if 29% is greater than the 30th percentile value.
2. True if the median is greater than the first quartile.
3. True if the third quartile is greater than the first quartile.
4. May be true if the dataset is symmetric.
5. False; the range cannot be zero.