Indicate with Yes or No whether the given statement could apply to a data set consisting of 1,000 values that are all different.
a.The 29th percentile is greater than the 30th percentile.b.The median is greater than the first quartile.c.The third quartile is greater than the first quartile.d.The mean is equal to the median.e.The range is zero.
B and C are always true by definition.
a.no
b.yes
c.yes
d.yes
e.no
To determine whether the given statements could apply to a data set consisting of 1,000 different values, we need to understand the concepts of percentiles, quartiles, mean, median, and range:
a. The 29th percentile is greater than the 30th percentile.
To determine if this statement could apply, we need to consider the properties of percentiles. Percentiles divide a dataset into 100 equal parts. Since the data set consists of 1,000 different values, each percentile would represent 10 values. Therefore, it is not possible for the 29th percentile to be greater than the 30th percentile. The answer is No.
b. The median is greater than the first quartile.
The first quartile represents the 25th percentile, which would be the value that divides the lower 25% of the data from the upper 75%. The median represents the 50th percentile, which divides the dataset into two equal parts. Therefore, if all the 1,000 values are different, it is likely that the median (50th percentile) will be greater than the first quartile (25th percentile). The answer is Yes.
c. The third quartile is greater than the first quartile.
Similar to the previous statement, if all the 1,000 values are different, it is likely that the third quartile (75th percentile) will be greater than the first quartile (25th percentile). The answer is Yes.
d. The mean is equal to the median.
To calculate the mean, add up all the values in the data set and divide by the number of values (in this case, 1,000). The median is the middle value in the data set, after arranging the values in ascending or descending order. Since the data set consists of 1,000 different values, it is highly unlikely that the mean and median will be exactly equal. The answer is No.
e. The range is zero.
The range is the difference between the largest and smallest values in the data set. Since the data set consists of 1,000 different values, it is highly improbable that the largest and smallest values will be the same, resulting in a range of zero. Therefore, the answer is No.
In summary:
a. No
b. Yes
c. Yes
d. No
e. No