can you please check my work.
The time in minutes that it took five students to complete the math test was 45, 27, 30, 25, and 48. What is the mean absolute deviation of the times?
I did 25+27+30+45+48= 175
then I divided it by the 5 students. 175/5= 35
so now I did the absolute value of 25-35=10
27-35=8, 30-35=5, 45-35=10
and 48-35=13
I add the results 10+8+5+10+13=46
46/5 ( the 5 students)= 9.2 being the MAD
Then they asked what conclusion can you make from the mad value you found?
I am not sure of this but I said the MAD of 9.2 is lower than the mean, median and mode, but I am not sure if that is what they are looking for.
Thanks for checking my work!
careful with the notation:
A statement such as 25-35 = 10 is incorrect , you have to say
|25-35| = 10
that is where the "absolute" part of the definition comes in.
Your arithmetic is fine.
Thank you, I know I didn't know what symbol to use for absolute value, that is why I said I did the absolute value of...,
but what are they asking for in the second part when asking What conclusion can you make from the mad value you found?
I am not sure what they want.
Thank you for your help.
Let's check your work and calculations step by step to determine the mean absolute deviation (MAD) and its implications.
First, you correctly found the sum of the five students' test times: 45 + 27 + 30 + 25 + 48 = 175.
Next, you divided the sum by the number of students (5) to find the mean: 175 / 5 = 35. So, the mean test time is 35 minutes.
To calculate the absolute deviation for each student, you correctly subtracted the mean from each individual test time. Here are the absolute deviations for each student:
|25 - 35| = 10
|27 - 35| = 8
|30 - 35| = 5
|45 - 35| = 10
|48 - 35| = 13
To find the MAD, you correctly added up these absolute deviations: 10 + 8 + 5 + 10 + 13 = 46.
Finally, you divided the total absolute deviation by the number of students (5) to get the MAD: 46 / 5 = 9.2.
Your calculations for finding the MAD appear to be correct.
Regarding the conclusion that can be made from the MAD value, you mentioned that the MAD of 9.2 is lower than the mean, median, and mode. However, without additional information about the mean, median, and mode of the data set, it's difficult to draw conclusions based solely on the MAD value.
The MAD measures the average distance between each data point and the mean. A lower MAD indicates that the data points are relatively close to the mean, suggesting less variability or dispersion in the test times. However, since we don't know the other measures of central tendency, it's not possible to make deeper conclusions.
In summary, your calculations for the MAD are correct, but more information is needed to make meaningful conclusions based on the MAD value alone.