Answer :
Certainly! Let's analyze the body temperature data set and determine the mean and median.
### Step 1: Understanding the Data Set
We are provided with 48 body temperature readings. We will use these readings to calculate the mean and median temperature.
### Step 2: Calculating the Mean
The mean (average) is found by summing all the values and then dividing by the number of values.
- Sum of all body temperatures = [tex]\( (97.2 + 99.4 + 99.2 + ... + 98.7 + 98.3) \)[/tex]
- Number of values (n) = 48
Using the provided numerical result:
- The sum of the data set values divided by 48 gives us a mean (average) body temperature of approximately [tex]\( 98.12^{\circ} F \)[/tex].
### Step 3: Calculating the Median
The median is the middle value when all values are arranged in ascending order. If the number of observations (n) is even, the median is the average of the two middle numbers.
Given:
- The ordered list of body temperatures allows us to find the middle values.
- For 48 data points (even number), the median will be the average of the 24th and 25th values in the ordered list.
Using the provided numerical result:
- The median body temperature turns out to be [tex]\( 98.3^{\circ} F \)[/tex].
### Step 4: Comparing the Results with the Common Belief
The common belief is that the mean body temperature is [tex]\( 98.6^{\circ} F \)[/tex].
We found:
- Mean = [tex]\( 98.12^{\circ} F \)[/tex]
- Median = [tex]\( 98.3^{\circ} F \)[/tex]
### Conclusion
The results show that the average (mean) body temperature of [tex]\( 98.12^{\circ} F \)[/tex] is slightly lower than the commonly believed [tex]\( 98.6^{\circ} F \)[/tex]. Similarly, the median temperature of [tex]\( 98.3^{\circ} F \)[/tex] is also lower than the common belief. Therefore, these findings do not support the common belief that the mean body temperature is [tex]\( 98.6^{\circ} F \)[/tex].
Summary:
- Mean body temperature: [tex]\( 98.12^{\circ} F \)[/tex]
- Median body temperature: [tex]\( 98.3^{\circ} F \)[/tex]
These calculations indicate that the actual mean and median body temperatures based on the given data set are both lower than the traditionally accepted [tex]\( 98.6^{\circ} F \)[/tex].
### Step 1: Understanding the Data Set
We are provided with 48 body temperature readings. We will use these readings to calculate the mean and median temperature.
### Step 2: Calculating the Mean
The mean (average) is found by summing all the values and then dividing by the number of values.
- Sum of all body temperatures = [tex]\( (97.2 + 99.4 + 99.2 + ... + 98.7 + 98.3) \)[/tex]
- Number of values (n) = 48
Using the provided numerical result:
- The sum of the data set values divided by 48 gives us a mean (average) body temperature of approximately [tex]\( 98.12^{\circ} F \)[/tex].
### Step 3: Calculating the Median
The median is the middle value when all values are arranged in ascending order. If the number of observations (n) is even, the median is the average of the two middle numbers.
Given:
- The ordered list of body temperatures allows us to find the middle values.
- For 48 data points (even number), the median will be the average of the 24th and 25th values in the ordered list.
Using the provided numerical result:
- The median body temperature turns out to be [tex]\( 98.3^{\circ} F \)[/tex].
### Step 4: Comparing the Results with the Common Belief
The common belief is that the mean body temperature is [tex]\( 98.6^{\circ} F \)[/tex].
We found:
- Mean = [tex]\( 98.12^{\circ} F \)[/tex]
- Median = [tex]\( 98.3^{\circ} F \)[/tex]
### Conclusion
The results show that the average (mean) body temperature of [tex]\( 98.12^{\circ} F \)[/tex] is slightly lower than the commonly believed [tex]\( 98.6^{\circ} F \)[/tex]. Similarly, the median temperature of [tex]\( 98.3^{\circ} F \)[/tex] is also lower than the common belief. Therefore, these findings do not support the common belief that the mean body temperature is [tex]\( 98.6^{\circ} F \)[/tex].
Summary:
- Mean body temperature: [tex]\( 98.12^{\circ} F \)[/tex]
- Median body temperature: [tex]\( 98.3^{\circ} F \)[/tex]
These calculations indicate that the actual mean and median body temperatures based on the given data set are both lower than the traditionally accepted [tex]\( 98.6^{\circ} F \)[/tex].