Final Answer:
The sum of the sample data is 314 inches. The sample mean is 44.86 inches.
Step-by-step explanation:
Let's first find the sum of the sample data, which means adding all the heights of the 5th graders together.
Here are the heights given:
42, 48, 45, 41, 48, 50, 40
To find the sum, we add all these numbers together:
42 + 48 + 45 + 41 + 48 + 50 + 40
Calculating this, we get:
42 + 48 = 90
45 + 41 = 86
48 + 50 = 98
40 (still needs to be added)
Now adding all these partial sums together:
90 + 86 + 98 + 40 = 314
So, the sum of the sample data (the total height of the 5th graders) is 314 inches.
Next, we will calculate the sample mean, which is the average of the data. To find the average, we divide the sum of the heights by the number of observations (the number of 5th graders in this case).
There are 7 data points (heights), so we divide the sum by 7.
Mean height = Sum of heights/Number of students
Mean height = 314/7
To divide 314 by 7, you can do long division:
314 divided by 7 equals 44 with a remainder of 6. Hence, the division yields 44 with a fraction of 6/7.
The mean height, therefore, as a mixed number, is 44 6/7 inches, or as a decimal approximately 44.86 inches when rounded to two decimal places.
In summary:
- The sum of the sample data is 314 inches.
- The sample mean (average height) is 44 6/7 inches, or about 44.86 inches.