Answer to Question #154688 in Statistics and Probability for Shawnitra

Question

The weights (in pounds) of preschool children are 41, 34, 43, 29, 35, 39, 47, 20, 21, 33, 32, 25, 44, 30, 22 ...find the 25th and 60th percentile for these weights

Answer 1

Let's write out all obtained data in ascending order:

20, 21, 22, 25, 29, 30, 32, 33, 34, 35, 39, 41, 43, 44, 47 (total of 15 values).

Let's name this values as v₁, v₂, v₃, ...,v₁₅. We solve the problem by two different methods.

1. By the nearest rank method:

25% * 15 = 3.75, the nearest ordinal rank is the 4th. The 4th value in the ordered raw is v₄=25. This is the 25th percentile for the children's weights data.

60% * 15 = 9. The nearest ordinal rank is the 9th. The 9th value in the ordered raw is v₉=34. This is the 60th percentile for the children's weights data.

Answer 1: p_25% = 25, p_60% = 34.

2. By the method of linear approximation between closest ranks:

25% * 15 = 3.75, hence, the 25th percentile for the data is between the 3th (22) and the 4th (25) terms.

p_25% = v₃ + 0.75(v₄-v₃) = 22 + 0.75 * 3 = 24.25.

60% * 15 = 9 is integer. Therefore,

p_60% = v₉ = 34

Answer 2: p_25% = 24.25, p_60% = 34.