Question
Marcel recorded the total number of pages he read each week for 5 weeks.
The mean and mean absolute deviation of the data are shown.
Mean: 120
Mean absolute deviation: 5
all the possible numbers of pages Marcel read in the 6th week that are within the mean absolute deviation.
The mean and mean absolute deviation of the data are shown.
Mean: 120
Mean absolute deviation: 5
all the possible numbers of pages Marcel read in the 6th week that are within the mean absolute deviation.
Answers
Answered by
GPT-4o mini
The mean absolute deviation (MAD) tells us how much the values deviate from the mean on average. Since Marcel has a mean of 120 pages for the first 5 weeks and a MAD of 5, we can calculate the range of values for the 6th week that fall within the mean absolute deviation.
The mean absolute deviation of 5 indicates that the values for the total pages read can vary from the mean by up to 5 pages either above or below.
So, we can calculate the possible range of values for the 6th week as follows:
- Minimum value: \( 120 - 5 = 115 \)
- Maximum value: \( 120 + 5 = 125 \)
Thus, all possible numbers of pages Marcel could have read in the 6th week that are within the mean absolute deviation are:
- 115 pages
- 116 pages
- 117 pages
- 118 pages
- 119 pages
- 120 pages
- 121 pages
- 122 pages
- 123 pages
- 124 pages
- 125 pages
In conclusion, the possible numbers of pages Marcel read in the 6th week that are within the mean absolute deviation range are any whole values from 115 to 125, inclusive.
The mean absolute deviation of 5 indicates that the values for the total pages read can vary from the mean by up to 5 pages either above or below.
So, we can calculate the possible range of values for the 6th week as follows:
- Minimum value: \( 120 - 5 = 115 \)
- Maximum value: \( 120 + 5 = 125 \)
Thus, all possible numbers of pages Marcel could have read in the 6th week that are within the mean absolute deviation are:
- 115 pages
- 116 pages
- 117 pages
- 118 pages
- 119 pages
- 120 pages
- 121 pages
- 122 pages
- 123 pages
- 124 pages
- 125 pages
In conclusion, the possible numbers of pages Marcel read in the 6th week that are within the mean absolute deviation range are any whole values from 115 to 125, inclusive.