In a large data set the 40th percentile is 125 and the 82nd percentile is 158. Approximately what percentage of observations lie between 125 and 158

42% of observations lie between 125 and 158.

Step-by-step explanation:

Interpretation of a percentile

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x) % of the values in the set are higher than V.

Two values have a percentile, how many are between then?

In this example, y is larger than x.

When a value V is said to be in the xth percentile of a set, x% of the values in the set are lower than V and (100-x) % of the values in the set are higher than V.

When a value Z is said to be in the yth percentile of a set, y% of the values in the set are lower than V and (100-y) % of the values in the set are higher than V.

Also, (y-x) % of the values are between V and Z.

In this problem, we have that:

125 is the 40th percentile

158 is the 82nd percentile

Approximately what percentage of observations lie between 125 and 158

82 - 40 = 42% of observations lie between 125 and 158.