To find the 61st percentile of the height of 8 boys in a class, follow the steps below:

Step 1: Arrange the data in ascending order
135, 138, 141, 146, 149, 155, 158, 160

Step 2: Calculate the total number of observations (n)
n = 8

Step 3: Calculate the rank of the 61st percentile
Rank of the 61st percentile = (61/100) x n
Rank of the 61st percentile = (61/100) x 8
Rank of the 61st percentile = 4.88
Round up to the nearest whole number: 5

Step 4: Find the value corresponding to the 5th rank
The value corresponding to the 5th rank is 141 (since the first four observations are less than 141)

Therefore, the 61st percentile of the height of 8 boys in a class is 141 cm.

Explanation:

Percentile is a measure that indicates the value below which a given percentage of observations in a group falls. In this case, we are asked to find the 61st percentile of the height of 8 boys in a class.

To find the percentile, we first arrange the data in ascending order. This helps us to easily identify the rank of each observation. In this case, the data is already in ascending order.

Next, we calculate the rank of the 61st percentile. This is done by multiplying the percentage (61%) by the total number of observations (8). The result is then rounded up to the nearest whole number.

Once we have the rank, we find the value corresponding to that rank in the data set. This value represents the 61st percentile of the data.

In this case, the 61st percentile corresponds to the 5th rank, which is 141 cm. This means that 61% of the boys in the class have a height less than or equal to 141 cm.