Answer
Option C is correct.
The mean, median and mode are all within two minutes of each other.
Step-by-step explanation
To know which statement is correct, we have to compute a number of the terms mentioned in these statements.
65, 45, 110, 90, 95, 90, 60, 88, 120, 125
The mean is the sum of variables divided by the number of variables
Mean = (Σx)/N
x = each variable
N = number of variables
Σx = 65 + 45 + 110 + 90 + 95 + 90 + 60 + 88 + 120 + 125 = 888
N = 10
Mean = (888/10) = 88.8
The median is the variable in the middle of the distribution when the variables are arranged in descending or ascending order.
45, 60, 65, 88, 90, 90, 95, 110, 120, 125
Since there are 10 variables, the median will be the average of the two numbers in the middle, the 5th and 6th variable.
Median = (90 + 90)/2 = 90
The mode is the variable that occurs the most number of times in the distribution.
For this data, all the variables except 90 occur only once. So,
Mode = 90
Range is the difference between the highest and the lowest variable.
Range = 125 - 45 = 80
Interquartile range is the difference between the third and first quartile.
Third quartile is the variable at the 3(N + 1)/4 position in the distribution.
3(10 + 1)/4 = (33/4) = 8.25th variable.
This will be between the 8th and 9th variable.
Third quartile = (110 + 120)/2 = 115
First quartile is the variable at the (N + 1)/4 position in the distribution.
(10 + 1)/4 = (11/4) = 2.75th variable.
This will be between the 2nd and 3rd variable.
First quartile = (60 + 65)/2 = 62.5
Interquartile range = (Third quartile) - (First quartile) = 115 - 62.5 = 52.5
Now checking the statements, one at a time,
A.) The interquartile range is half the mean.
Interquartile range = 52.5
Mean = 88.8
We can see that 52.5 isn't half of 88.
So, the interquartile range is not half of the mean.
Option A is not correct.
B.) The range of the data is twice the interquartile range.
Range = 80
Interquartile range = 52.5
We can see that 80 is not twice of 52.5.
So, the range is not twice the interquartile range.
Option B is not correct.
C.) The mean, median and mode are all within two minutes of each other.
Mean = 88.8
Median = 90
Mode = 90
88.8, 90 and 90 are all within 2 minutes of each other.
So, the mean, median and mode are within two minutes of one another.
Option C is correct.
D.) If the 3 students who studied the least each added 15 minutes of study time, the median would increase by 5.
This is not true.
The 3 students with the least minutes will have 60, 75 and 80 minutes if 15 minutes is added to their times. And this doesn't touch the median at all.
Hope this Helps!!!