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Let's break down the problem step by step to calculate the change in the mean when a new race time of 26.1 seconds is included.

### Step 1: Extract the race times
From the information given:

- **Minimum race time**: 18.4 seconds
- **Range**: 5.8 seconds (This means the difference between the maximum and minimum race times is 5.8 seconds. Therefore, the maximum time is \(18.4 + 5.8 = 24.2 \) seconds.)
- **Median**: 22.9 seconds
- **Mode**: 24.2 seconds

We know the minimum and maximum times, and since the median is 22.9 and the mode is 24.2, we can assume the race times are likely:
1. 18.4 seconds (minimum)
2. 22.9 seconds (median)
3. 24.2 seconds (mode)
4. 24.2 seconds (because the mode appears twice)

So, her last 4 race times are:
\[
18.4, 22.9, 24.2, 24.2
\]

### Step 2: Calculate the current mean
The mean of her current 4 race times is:
\[
\text{Mean} = \frac{18.4 + 22.9 + 24.2 + 24.2}{4} = \frac{89.7}{4} = 22.425 \text{ seconds}
\]

### Step 3: Add the new race time of 26.1 seconds
Now, we include the new race time of 26.1 seconds. The total sum of all 5 race times is:
\[
18.4 + 22.9 + 24.2 + 24.2 + 26.1 = 115.8 \text{ seconds}
\]
Now, the new mean with 5 race times is:
\[
\text{New Mean} = \frac{115.8}{5} = 23.16 \text{ seconds}
\]

### Step 4: Calculate the change in the mean
The original mean was 22.425 seconds, and the new mean is 23.16 seconds. The change in the mean is:
\[
23.16 - 22.425 = 0.735 \text{ seconds}
\]

### Final Answer:
The mean will **increase by 0.735 seconds**.

Would you like more details or have any questions? 

Here are some related questions:
1. What would happen to the mean if she had added a race time lower than the current minimum?
2. How would the range change after adding this new time?
3. How can we calculate the variance of the original 4 times and the new 5 times?
4. What is the effect of adding the new time on the median?
5. How would the mode be affected if the new time was identical to the current mode?

**Tip**: When calculating averages, adding a number higher than the current mean will always increase the mean, and vice versa.

May competes in 100m wheelchair races. She calculates her race times as follows: Minimum race time: 18.4 s, Range: 5.8 s, Median: 22.9 s, Mode: 24.2 s. If May includes a new race time of 26.1 s, how much will the mean change by?

Discover how adding a new race time of 26.1 seconds affects the mean race time in May's 100m wheelchair race analysis. This problem covers essential statistical concepts like the mean and provides a step-by-step solution for calculating the new average.

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