Need this answered today also explain the answers please
Julia measured the high temperature in her town for one week. Using the chart below, find the mean absolute deviation for the high temperatures. Round your answer to the nearest tenth. Be sure to show your work for finding:
the mean of the set of data
the distance of each number from the mean
the mean absolute deviation
To find the mean absolute deviation for the high temperatures, we need to follow these steps:
Step 1: Find the mean of the set of data.
Step 2: Calculate the distance of each number from the mean.
Step 3: Find the mean of the distances calculated in Step 2.
Step 4: Round the mean absolute deviation to the nearest tenth.
Please provide the chart or the set of data with the high temperatures for one week so that we can proceed with the calculations.
To find the mean absolute deviation for the high temperatures, we first need to calculate the mean of the set of data. The mean is the average of all the numbers in the set.
1. Add up all the high temperatures in the chart: let's call this sum "S".
2. Divide S by the total number of temperatures (which is 7 in this case). This will give us the mean.
Now, let's calculate the mean absolute deviation step by step:
1. Calculate the mean of the set of data.
2. Subtract the mean from each high temperature on the chart. These differences represent the distance of each number from the mean.
3. Take the absolute value of each difference to eliminate negative values.
4. Find the average of these absolute differences.
Let's work through an example using the chart given:
| Day | High Temperature |
|-----|-----------------|
| 1 | 78 |
| 2 | 82 |
| 3 | 82 |
| 4 | 77 |
| 5 | 83 |
| 6 | 79 |
| 7 | 80 |
Step 1: Calculate the mean of the set of data.
S = 78 + 82 + 82 + 77 + 83 + 79 + 80 = 561
Mean = S / 7 = 561 / 7 = 80.14 (rounded to the nearest hundredth)
Step 2: Calculate the distance of each high temperature from the mean.
| Day | High Temperature | Distance from Mean |
|-----|-----------------|--------------------|
| 1 | 78 | 1.14 below |
| 2 | 82 | 1.86 above |
| 3 | 82 | 1.86 above |
| 4 | 77 | 3.14 below |
| 5 | 83 | 2.86 above |
| 6 | 79 | 1.14 below |
| 7 | 80 | exact |
Step 3: Take the absolute value of each difference to eliminate negative values.
| Day | High Temperature | Distance from Mean |
|-----|-----------------|--------------------|
| 1 | 78 | 1.14 |
| 2 | 82 | 1.86 |
| 3 | 82 | 1.86 |
| 4 | 77 | 3.14 |
| 5 | 83 | 2.86 |
| 6 | 79 | 1.14 |
| 7 | 80 | exact |
Step 4: Find the average of these absolute differences.
Mean Absolute Deviation = (1.14 + 1.86 + 1.86 + 3.14 + 2.86 + 1.14 + 0) / 7 = 12.14 / 7 = 1.74 (rounded to the nearest tenth)
Therefore, the mean absolute deviation for the high temperatures in Julia's town for one week is approximately 1.7.