Task: Solve Professor Ashton's Task and Determine True or False for Each Statement
We will analyze each statement one by one and determine whether it is
TRUE or
FALSE. Let's go through them step by step.
---
####
1. Average is also known as the mean.
-
Analysis: The term "average" is often used interchangeably with "mean" in mathematics. The mean is calculated by summing all the values in a dataset and dividing by the number of values.
-
Conclusion:
TRUE
---
####
2. In finding the mode of a data, you should arrange the data from highest to lowest or vice-versa.
-
Analysis: The mode is the value that appears most frequently in a dataset. Arranging the data in ascending or descending order is not necessary to find the mode. You can identify the mode simply by counting the frequency of each value.
-
Conclusion:
FALSE
---
####
3. Mode is the number that occurred the least in a set of data.
-
Analysis: The mode is actually the number that occurs most frequently in a dataset, not the least frequently. The least frequent value would be related to the concept of the "minimum" or "rarest" value, but not the mode.
-
Conclusion:
FALSE
---
####
4. Median is finding the middle number.
-
Analysis: The median is indeed the middle number when the data is arranged in ascending or descending order. If there is an even number of data points, the median is the average of the two middle numbers.
-
Conclusion:
TRUE
---
####
5. If you have two numbers in the middle, you should get the difference and divide it by two.
-
Analysis: When there are two middle numbers (which happens when the dataset has an even number of values), the median is calculated by taking the
average of these two numbers, not by finding their difference and dividing by two.
-
Conclusion:
FALSE
---
####
6. The mean of 23, 56, 45, and 30 is 38.5.
-
Analysis: To find the mean, we sum the values and divide by the number of values:
\[
\text{Mean} = \frac{23 + 56 + 45 + 30}{4} = \frac{154}{4} = 38.5
\]
-
Conclusion:
TRUE
---
####
7. The median of the set of data 18, 22, 19, 26, and 35 is 19.
-
Analysis: To find the median, we first arrange the data in ascending order:
\[
18, 19, 22, 26, 35
\]
Since there are 5 values (an odd number), the median is the middle value, which is 22.
-
Conclusion:
FALSE
---
####
8. The mode/s of the given data 11, 10, 12, 12, 11 is/are 11 and 12.
-
Analysis: The mode is the value that appears most frequently. In the dataset \(11, 10, 12, 12, 11\):
- 11 appears twice.
- 12 appears twice.
- 10 appears once.
Since both 11 and 12 appear with the highest frequency (twice), they are both modes.
-
Conclusion:
TRUE
---
Final Answers:
1.
TRUE
2.
FALSE
3.
FALSE
4.
TRUE
5.
FALSE
6.
TRUE
7.
FALSE
8.
TRUE
Boxed Answer:
\[
\boxed{
\begin{array}{c|c}
1. & \text{TRUE} \\
2. & \text{FALSE} \\
3. & \text{FALSE} \\
4. & \text{TRUE} \\
5. & \text{FALSE} \\
6. & \text{TRUE} \\
7. & \text{FALSE} \\
8. & \text{TRUE} \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of central tendency worksheet.
