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20 Feb 2023, 02:30
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What is the standard deviation of set X, containing consecutive odd integers?
(1) Set consists of 10 elements
(2) The range of set is 18
700-Level Question!!!
(1) Set consists of 10 elements
(2) The range of set is 18
700-Level Question!!!
20 Feb 2023, 11:35
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Few important points on Standard Deviation
1) Standard deviation is simply a measure of how far on average each term in a set is from the mean.
2) If we add or subtract a constant to each term in a set: Mean will increase or decrease by the same constant. But, SD will not change.
3) If we increase or decrease each term in a set by the same percent (multiply all terms by the constant): Mean will increase or decrease by the same percent. SD will increase or decrease by the same percent.
Now with this information lets solve the given question.
What is the standard deviation of set X, containing consecutive odd integers?
(1) Set consists of 10 elements
In a consecutive set, we know that, mean = median and since we know how far each term is from the mean we can definitely get the SD value. Statement 1 is Sufficient
(2) The range of set is 18: Range is the difference of last term and first term.
It implies that we have 10 consecutive odd integers : {1,3,5,.....19} or {9,11,13, .... 27}
So we have the same information as in statement 1.
So statement 2 is also sufficient
Answer D
1) Standard deviation is simply a measure of how far on average each term in a set is from the mean.
2) If we add or subtract a constant to each term in a set: Mean will increase or decrease by the same constant. But, SD will not change.
3) If we increase or decrease each term in a set by the same percent (multiply all terms by the constant): Mean will increase or decrease by the same percent. SD will increase or decrease by the same percent.
Now with this information lets solve the given question.
What is the standard deviation of set X, containing consecutive odd integers?
(1) Set consists of 10 elements
In a consecutive set, we know that, mean = median and since we know how far each term is from the mean we can definitely get the SD value. Statement 1 is Sufficient
(2) The range of set is 18: Range is the difference of last term and first term.
It implies that we have 10 consecutive odd integers : {1,3,5,.....19} or {9,11,13, .... 27}
So we have the same information as in statement 1.
So statement 2 is also sufficient
Answer D
21 Feb 2023, 03:17
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sivakumarm786
To solve this problem, we can use the following property: If we add (or subtract) a constant to each term in a set, the set's standard deviation remains the same.
Both statements in the problem tell us that the set consists of 10 consecutive odd integers.
All sets of 10 consecutive odd integers have the same standard deviation. This is because any set of 10 consecutive odd integers can be obtained by adding a constant to another set of 10 consecutive odd integers. For example, the set {1, 3, 5, ..., 19} consists of 10 consecutive odd integers, and we can obtain it by adding 4 to each term of the set {-3, -1, 1, ..., 15}. So, we can calculate the standard deviation of any set of 10 consecutive odd integers, and it will be the same as the standard deviation of any other set of 10 consecutive odd integers.
