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04 Jan 2022, 06:45
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If set Y consists of the consecutive integers p, q, r, s, and t such that p < q < r < s < t, then all of the following are true EXCEPT
A. increasing only t will increase the range of set Y
B. increasing only t will increase the mean of set Y
C. decreasing only p will increase the range of set Y
D. decreasing only r will decrease the mean of set Y
E. increasing only t will increase the median of set Y
A. increasing only t will increase the range of set Y
B. increasing only t will increase the mean of set Y
C. decreasing only p will increase the range of set Y
D. decreasing only r will decrease the mean of set Y
E. increasing only t will increase the median of set Y
07 Jan 2022, 12:06
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Given
1) The set consist of consecutive integers
2) When arranged in ascending order, the set looks like
p , q , r , s, t
A. increasing only t will increase the range of set Y
True, if we only increase the value of t, the distance between 't', the largest term in the set, and p will increase. Hence range will increase.
B. increasing only t will increase the mean of set Y
True, As the value of t increases the new mean will be greater than the previous mean.
C. decreasing only p will increase the range of set Y
True, if we only decrease the value of p, the distance between 't', the largest term in the set, and p will increase. Hence range will increase.
D. decreasing only r will decrease the mean of set Y
True, as the value of r is now less, it will contribute less to the overall average. Hence the new mean will be less than the previous mean.
E. increasing only t will increase the median of set Y
False, increasing the value of t will not change the value of median. In both the scenarios, the median is 'r'.
IMO - E
1) The set consist of consecutive integers
2) When arranged in ascending order, the set looks like
p , q , r , s, t
A. increasing only t will increase the range of set Y
True, if we only increase the value of t, the distance between 't', the largest term in the set, and p will increase. Hence range will increase.
B. increasing only t will increase the mean of set Y
True, As the value of t increases the new mean will be greater than the previous mean.
C. decreasing only p will increase the range of set Y
True, if we only decrease the value of p, the distance between 't', the largest term in the set, and p will increase. Hence range will increase.
D. decreasing only r will decrease the mean of set Y
True, as the value of r is now less, it will contribute less to the overall average. Hence the new mean will be less than the previous mean.
E. increasing only t will increase the median of set Y
False, increasing the value of t will not change the value of median. In both the scenarios, the median is 'r'.
IMO - E
04 Aug 2022, 00:05
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Theory
If set Y consists of the consecutive integers p, q, r, s, and t such that p < q < r < s < t
Since we have consecutive numbers => Mean = Median = r
Range = Highest - Lowest value = t - p = p+4 - p = 4
Let's take each option choice and evaluate
A. increasing only t will increase the range of set Y
If we increase t then it will become more than p+4 => Range will become more than 4 as T will be more than 4 distance from p then. => TRUE
B. increasing only t will increase the mean of set Y
Current mean is r, which is considering the current value of t. If t increases then total sum will also increase => Mean will also increase. => TRUE
C. decreasing only p will increase the range of set Y
If we decrease p then it will be a distance of more than 4 from t. => Range will increase. => TRUE
D. decreasing only r will decrease the mean of set Y
Current mean is r, which is considering the current value of r. If r decreases then total sum will also decrease => Mean will also decrease. => TRUE
E. increasing only t will increase the median of set Y
Current median is t. Now, we have 5 values so median will be the middle term. Even if we are increasing t, then also r remains the middle term or the median. So, median will not change. => FALSE
So, Answer will be E.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
- ➡ Mean is the average of the all the numbers in the set.
➡ Median is the middle value of the set.
➡ Range of a set is the difference between the highest and lowest value of the set.
➡ In Case of consecutive numbers , Mean = Median = Middle term (if the number of terms is odd)
If set Y consists of the consecutive integers p, q, r, s, and t such that p < q < r < s < t
Since we have consecutive numbers => Mean = Median = r
Range = Highest - Lowest value = t - p = p+4 - p = 4
Let's take each option choice and evaluate
A. increasing only t will increase the range of set Y
If we increase t then it will become more than p+4 => Range will become more than 4 as T will be more than 4 distance from p then. => TRUE
B. increasing only t will increase the mean of set Y
Current mean is r, which is considering the current value of t. If t increases then total sum will also increase => Mean will also increase. => TRUE
C. decreasing only p will increase the range of set Y
If we decrease p then it will be a distance of more than 4 from t. => Range will increase. => TRUE
D. decreasing only r will decrease the mean of set Y
Current mean is r, which is considering the current value of r. If r decreases then total sum will also decrease => Mean will also decrease. => TRUE
E. increasing only t will increase the median of set Y
Current median is t. Now, we have 5 values so median will be the middle term. Even if we are increasing t, then also r remains the middle term or the median. So, median will not change. => FALSE
So, Answer will be E.
Hope it helps!
Watch the following video to Learn the Basics of Statistics
