Here is a FDT for a small data set:
data	freq
43	1
44	3
45	2
46	3
47	11
Find the following measures of central tendency.

mean = 


median = 


mode = 
Submit QuestionQuestion 9

To find the **mean**, **median**, and **mode** for the given frequency distribution table (FDT), let's proceed step by step:

### Data:

| Data (x) | Frequency (f) |
|----------|---------------|
| 43       | 1             |
| 44       | 3             |
| 45       | 2             |
| 46       | 3             |
| 47       | 11            |

#### 1. **Mean**:
The formula for the mean is:
\[
\text{Mean} = \frac{\sum (x \cdot f)}{\sum f}
\]
Where:
- \( x \) is the data value
- \( f \) is the frequency of the data value

**Step 1**: Calculate the sum of \( x \cdot f \) for each data point.

\[
(43 \cdot 1) + (44 \cdot 3) + (45 \cdot 2) + (46 \cdot 3) + (47 \cdot 11) = 43 + 132 + 90 + 138 + 517 = 920
\]

**Step 2**: Calculate the total frequency \( \sum f \).
\[
1 + 3 + 2 + 3 + 11 = 20
\]

**Step 3**: Compute the mean.
\[
\text{Mean} = \frac{920}{20} = 46
\]

#### 2. **Median**:
The median is the middle value of the data set when it is arranged in ascending order. For frequency distributions, we locate the median based on cumulative frequencies.

**Step 1**: Find the total frequency (\( N = 20 \)) and determine the median position:
\[
\text{Median Position} = \frac{N + 1}{2} = \frac{20 + 1}{2} = 10.5
\]
So, the median is the 10.5th value in the ordered data set.

**Step 2**: Use the cumulative frequency to locate the median.
- Cumulative frequency for 43: 1
- Cumulative frequency for 44: 4
- Cumulative frequency for 45: 6
- Cumulative frequency for 46: 9
- Cumulative frequency for 47: 20

The 10.5th value falls within the data value 47 (cumulative frequency from 10 to 20).

Thus, the **median** is 47.

#### 3. **Mode**:
The mode is the value that occurs most frequently. 

From the table, the highest frequency is 11, which corresponds to the data value 47.

So, the **mode** is 47.

### Final Answers:
- **Mean** = 46
- **Median** = 47
- **Mode** = 47

Would you like further details or explanations on any of the calculations?

Here are 5 related questions you can explore:
1. How would the mean change if the frequency of 47 increased by 2?
2. How do you calculate the mean if given grouped data instead of a frequency table?
3. Can a data set have more than one mode?
4. How does the median compare to the mean in a skewed distribution?
5. What is the impact of outliers on the mean and median?

**Tip:** The mode is the only measure of central tendency that can be used with categorical data.

Here is a FDT for a small data set: data freq 43 1 44 3 45 2 46 3 47 11 Find the following measures of central tendency. mean = median = mode =

Learn how to calculate the mean, median, and mode for a small data set using a frequency distribution table. This problem covers key statistical concepts, including mean calculation, median position determination, and identifying the mode. Suitable for students in Grades 6-8.

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