Given Information
- Runs scored by a batsman in five one-day matches are 55, 75, 67, 88, and 15.

To find
- The standard deviation of the runs scored.

Formula for Standard Deviation
- The standard deviation is a measure of how spread out the values in a data set are from the mean. It is calculated using the following formula:

σ = √(Σ(x - μ)² / N)

where σ is the standard deviation, Σ is the sum of the squared differences between each value (x) and the mean (μ), and N is the total number of values.

Step 1: Calculate the Mean
- The first step is to calculate the mean of the runs scored. The mean is calculated by summing up all the values and dividing by the total number of values.

Mean (μ) = (55 + 75 + 67 + 88 + 15) / 5
= 300 / 5
= 60

Step 2: Calculate the Deviations from the Mean
- Next, we need to calculate the deviations of each value from the mean. This is done by subtracting the mean from each value.

Deviation (x - μ) = (55 - 60), (75 - 60), (67 - 60), (88 - 60), (15 - 60)
= -5, 15, 7, 28, -45

Step 3: Square the Deviations
- After calculating the deviations, we square each deviation to remove the negative signs and to emphasize the differences from the mean.

Square of Deviation (x - μ)² = (-5)², 15², 7², 28², (-45)²
= 25, 225, 49, 784, 2025

Step 4: Calculate the Sum of the Squared Deviations
- Next, we sum up all the squared deviations.

Sum of Squared Deviations Σ(x - μ)² = 25 + 225 + 49 + 784 + 2025
= 3108

Step 5: Calculate the Variance
- The variance is obtained by dividing the sum of the squared deviations by the total number of values.

Variance (σ²) = Σ(x - μ)² / N
= 3108 / 5
= 621.6

Step 6: Calculate the Standard Deviation
- Finally, the standard deviation is calculated by taking the square root of the variance.

Standard Deviation (σ) = √(σ²)
= √(621.6)
≈ 24.93

Therefore, the standard deviation of the runs scored by the batsman in the five one-day matches is approximately 24.93.