Suppose the daily high temperature in a town is 3 degrees above average one day, then 5 degrees below average the next day, then 2 degrees above average, then 1 degree below average, then 6 degrees above average, then equal to the average the next day. Find the mean deviation from the average temperature for the 5-day period.
I added 3 + -5 + 2 + -1 + 6 + 0 and divided by 6 to get the mean as .83
The second part of the question I do not understand how to do.
How many degrees above or below average would the temperature need to be the next day to average one degree above over the 7-day period?
Thank you.
To find the mean deviation from the average temperature for the 5-day period, you correctly added up the deviations from the average temperature for each day and divided by the number of days (6). The calculation is correct, and you obtained a mean deviation of 0.83 degrees.
To answer the second part of the question and find out how many degrees above or below average the temperature would need to be on the next day to average one degree above over the 7-day period, we can use the concept of averages.
Given the information, we know that over the 5-day period, the mean deviation from the average was 0.83. This means that if the temperature on the next day is equal to the average temperature, the average over the 6-day period would be 0.83 degrees above the average.
Now we want to find out how many degrees above or below average the temperature should be on the 7th day to make the average over the 7-day period equal to one degree above average.
To do this, we can set up an equation. Let's denote the deviation from average on the 7th day as 'x.' We know that the average temperature over the 6-day period is 0.83, and we want the average temperature over the 7-day period to be 1 degree above average.
So, we can set up the equation:
(3 - 5 + 2 - 1 + 6 + x + 0) / 7 = 1
Simplifying this equation gives:
(5 + x) / 7 = 1
To isolate 'x,' we can multiply both sides of the equation by 7:
5 + x = 7
Now, subtracting 5 from both sides gives:
x = 7 - 5
Therefore, x = 2.
Hence, the temperature on the 7th day should be 2 degrees above average to average one degree above over the 7-day period.