Median
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SAT Math › Median
The number n is to be added to the list {3, 4, 5, 6, 10, 12}. If n is an integer, which of the following could be the median of the new list of seven numbers?
I) 5
II) 5.5
III) 6
I and III only
I, II, and III
I and II only
II and III only
I only
Explanation
Before n is added to the list, the median is 5.5 (the average of 5 and 6). When n is added to the list, the number of elements becomes odd, so the median will be a value directly from the list, not the average of two values. All of the values in the old list are integers and n is an integer, so the new median must be an integer; therefore, 5.5 cannot be the median of the new list.
Considering some possible values of n, we see that in cases where n is less than or equal to 5, the fourth element in the new list would be 5, making the new median 5. In cases where n is greater than or equal to 6, the fourth element in the new list would be 6, making the new median 6. The possible values for the median of the new list are therefore 5 and 6, but not 5.5.
The number n is to be added to the list {3, 4, 5, 6, 10, 12}. If n is an integer, which of the following could be the median of the new list of seven numbers?
I) 5
II) 5.5
III) 6
I and III only
I, II, and III
I and II only
II and III only
I only
Explanation
Before n is added to the list, the median is 5.5 (the average of 5 and 6). When n is added to the list, the number of elements becomes odd, so the median will be a value directly from the list, not the average of two values. All of the values in the old list are integers and n is an integer, so the new median must be an integer; therefore, 5.5 cannot be the median of the new list.
Considering some possible values of n, we see that in cases where n is less than or equal to 5, the fourth element in the new list would be 5, making the new median 5. In cases where n is greater than or equal to 6, the fourth element in the new list would be 6, making the new median 6. The possible values for the median of the new list are therefore 5 and 6, but not 5.5.
The Brenner cousins' heights, in inches, are as follows:
Jeremy: 64
Vanessa: 69
Tracie: 60
Samuel: 70
Raymond: 74
Justin: 72
Patty: 55
Lauren: 52
Keith: 58
What is the median height of the cousins?
52
58
60
64
74
Explanation
To find the median, one must arrange all the heights from the lowest to the highest value and then pick the middle value.
All values: 64 69 60 70 74 72 55 52 58
In order from lowest: 52 55 58 60 64 69 70 72 74
Median: 64
Find the median of the data set:
25, 37, 13, 58, 52, 83, 21, 51
44
13
83
70
42.5
Explanation
42.5 is the mean of the data. 13 is the minimum. 83 is the maximum. 70 is the range.
To find the median, list all numbers in order:
13, 21, 25, 37, 51, 52, 58, 83
and find the middle value. In cases like this where there are two middle numbers (37 and 51), find the mean of these two numbers.
(37+51)/2 = 88/2 = 44
A car travels at 60 miles per hour for 3 hours, 55 miles per hour for 2 hours, and 40 miles per hour for 3 hours. What (to the closest hundreth) is its average speed over the whole course of this trip?
51.67 miles per hour
58.13 miles per hour
55 miles per hour
19.38 miles per hour
51.25 miles per hour
Explanation
The easiest way to solve this is to find the total number of miles traveled by the car and divide that by the total time travelled.
Recall that D = rt; therefore, for each of these three periods, we can calculate the distance and sum those products:
Dtotal = 60 * 3 + 55 * 2 + 40 * 3 = 180 + 110 + 120 = 410
The total amount of time travelled is: 3 + 2 + 3 = 8
Therefore, the average rate is 410 / 8 = 51.25 miles per hour.
Find the median
Explanation
To find the median, arrange the numbers from lowest to highest then find the middle number.
There are two numbers in the middle in this set (
In this case, the median is 6 but you would typically find the average of the two numbers in the middle.
The Brenner cousins' heights, in inches, are as follows:
Jeremy: 64
Vanessa: 69
Tracie: 60
Samuel: 70
Raymond: 74
Justin: 72
Patty: 55
Lauren: 52
Keith: 58
What is the median height of the cousins?
52
58
60
64
74
Explanation
To find the median, one must arrange all the heights from the lowest to the highest value and then pick the middle value.
All values: 64 69 60 70 74 72 55 52 58
In order from lowest: 52 55 58 60 64 69 70 72 74
Median: 64
A car travels at 60 miles per hour for 3 hours, 55 miles per hour for 2 hours, and 40 miles per hour for 3 hours. What (to the closest hundreth) is its average speed over the whole course of this trip?
51.67 miles per hour
58.13 miles per hour
55 miles per hour
19.38 miles per hour
51.25 miles per hour
Explanation
The easiest way to solve this is to find the total number of miles traveled by the car and divide that by the total time travelled.
Recall that D = rt; therefore, for each of these three periods, we can calculate the distance and sum those products:
Dtotal = 60 * 3 + 55 * 2 + 40 * 3 = 180 + 110 + 120 = 410
The total amount of time travelled is: 3 + 2 + 3 = 8
Therefore, the average rate is 410 / 8 = 51.25 miles per hour.
Find the median of the data set:
25, 37, 13, 58, 52, 83, 21, 51
44
13
83
70
42.5
Explanation
42.5 is the mean of the data. 13 is the minimum. 83 is the maximum. 70 is the range.
To find the median, list all numbers in order:
13, 21, 25, 37, 51, 52, 58, 83
and find the middle value. In cases like this where there are two middle numbers (37 and 51), find the mean of these two numbers.
(37+51)/2 = 88/2 = 44
Find the median
Explanation
To find the median, arrange the numbers from lowest to highest then find the middle number.
There are two numbers in the middle in this set (
In this case, the median is 6 but you would typically find the average of the two numbers in the middle.