Finishing Times
Number of classes: 8
Data set: Finishing times (in seconds) of 21 participants in a 10K race
3449
2645
3255
3712
4183
3896
3760
5008
3983
2855
3789
3176
2923
2281
2574
2252
4223
2588
2243
2837
3292

To analyze the given finishing times for the 10K race participants, let's start by organizing the data into classes and calculating basic statistics like class intervals, frequencies, and other relevant statistics.

### Step 1: Sorting the Data
First, let's sort the finishing times (in seconds):

- Sorted dataTo analyze the given finishing times for the 10K race participants, let's start by organizing the data into classes and calculating basic statistics like class intervals, frequencies, and other relevant statistics.

### Step 1: Sorting the Data
First, let's sort the finishing times (in seconds):

- Sorted  
  2243, 2252, 2281, 2574, 2588, 2645, 2837, 2855, 2923, 3176, 3255, 3292, 3449, 3712, 3760, 3789, 3896, 3983, 4183, 4223, 5008

### Step 2: Define the Number of Classes
Given:
- Number of classes = 8

We can calculate the range and the class interval to group the data.

### Step 3: Range of the Data
- Range = Max value - Min value
- Max value = 5008
- Min value = 2243
- Range = 5008 - 2243 = 2765 seconds

### Step 4: Class Interval Calculation
The class interval (width of each class) is determined by dividing the range by the number of classes:

\[
\text{Class Interval} = \frac{\text{Range}}{\text{Number of Classes}} = \frac{2765}{8} \approx 346 \text{ seconds}
\]

So, each class will have a width of 346 seconds.

### Step 5: Defining the Class Intervals
Starting from the minimum value (2243), we can define the 8 class intervals as follows:

1. 2243 – 2589
2. 2590 – 2936
3. 2937 – 3283
4. 3284 – 3630
5. 3631 – 3977
6. 3978 – 4324
7. 4325 – 4671
8. 4672 – 5018

### Step 6: Tally the Frequencies
Now we can count how many finishing times fall into each class interval:

1. **2243 – 2589**: 2243, 2252, 2281, 2574, 2588 (5 values)
2. **2590 – 2936**: 2645, 2837, 2855, 2923 (4 values)
3. **2937 – 3283**: 3176, 3255, 3292 (3 values)
4. **3284 – 3630**: 3449 (1 value)
5. **3631 – 3977**: 3712, 3760, 3789, 3896 (4 values)
6. **3978 – 4324**: 3983, 4183, 4223 (3 values)
7. **4325 – 4671**: No values
8. **4672 – 5018**: 5008 (1 value)

### Step 7: Frequency Table

| Class Interval | Frequency |
|----------------|-----------|
| 2243 – 2589    | 5         |
| 2590 – 2936    | 4         |
| 2937 – 3283    | 3         |
| 3284 – 3630    | 1         |
| 3631 – 3977    | 4         |
| 3978 – 4324    | 3         |
| 4325 – 4671    | 0         |
| 4672 – 5018    | 1         |

This is the frequency distribution of the finishing times.

Would you like to explore further analysis, like calculating the mean, median, or constructing a histogram?

### 5 Related Questions:
1. How do we calculate the mean finishing time for this dataset?
2. What is the median of these finishing times?
3. How do we create a histogram to visually represent the frequency distribution?
4. How can we calculate the standard deviation of the finishing times?
5. Can we use this data to calculate percentiles or quartiles?

### Tip:
When grouping data into classes, make sure the class intervals are non-overlapping and cover the entire range of data. This ensures accurate and clear analysis.

Finishing Times Number of classes: 8 Data set: Finishing times (in seconds) of 21 participants in a 10K race

Analyze the finishing times of 21 participants in a 10K race. Learn how to calculate the range, define class intervals, and create a frequency distribution. This solution involves key concepts such as class intervals and frequency distribution, suitable for Grades 9-12.

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