Question: The daily temperature recorded (in degree F) at a place during a week was as under: Monday| Tues...

Question

The daily temperature recorded (in degree F) at a place during a week was as under:

Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
$35.5$	$30.8$	$27.3$	$32.1$	$23.8$	$29.9$

Calculate the mean temperature.

Answer 1

Solution

In this problem, we have given a daily temperature of a place during a week recorded as in F degree. Also we are given that temperature for each day in a week. Here we are asked to find the mean of the temperature. Since the given temperatures are recorded in F degree so we have to give the required answer as in F degree.

Formula used: $m = \dfrac{{{\text{sum of temperatures during whole week}}}}{{{\text{number of days}}}}$ , where m is mean.

Complete step-by-step solution:
Temperatures for Monday, Tuesday, Wednesday, Thursday, Friday and Saturday are given in F degree.
Temperature recorded for Monday is $35.5$ .
Temperature recorded for Tuesday is $30.8$ .
Temperature recorded for Wednesday is $27.3$ .
Temperature recorded for Thursday is $32.1$ .
Temperature recorded for Friday is $23.8$ .
Temperature recorded for Saturday is $29.9$ .
Now, the sum of the temperature during a whole week $= 35.5 + 30.8 + 27.3 + 32.1 + 23.8 + 29.9 = 179.4$
Total number of days $= 6$
Mean temperature $m = \dfrac{{{\text{sum of temperatures during whole week}}}}{{{\text{number of days}}}}$
$m = \dfrac{{179.4}}{6}$ , solving this fraction we get,
$m = {29.9^\circ }F$

Therefore the mean temperature is $m = {29.9^\circ }F$ .

Note: We have to know that the annual temperature range is defined as the difference between the hottest and coldest months, taking monthly mean temperatures in each case. It is given approximately by the difference between the average of the January maximum and minimum temperatures, and the corresponding average for July. We can observe that the spatial variation of the mean annual range of temperature is a result of differential heating of air by land and water. The differences in summer and winter temperatures over land and water are greatest. In summer, air temperature over the ocean is cooler than over land.