Question

Calculate the 20th, 40th, and 70th percentiles for the following data set: (Use the methodology shown in Section 3.2 of the text to calculate the percentiles. Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your final answers to 1 decimal place.) -362 -327 -321 211 340 472 -271 xc 20th percentile 40th percentile 70th percentile

Answer 1

20_Percnt (Asc. Order) -472 362 340 327 -321 -271 211 Position 4 The next step is to compute the position of the 20% percentile. The following is obtained: Percentile PositionP+1 20 10016 100 頁)

Since the position found is not integer, the method of interpolation needs to be used. The 20% percentile is located between the values in the positions 1 and 2. Those values, based on the data organized in ascending order, are -472 and -362. The value of 1.6-1 0.6 corresponds to the proportion of the distance between -472 and -362 where the percentile we are looking for is located at. In fact, we compute P20472 0.6 x (-362 -472)406

Position 40_Percnt (Asc. Order) -472 362 340 327 321 -271 -211 4 The next step is to compute the position of the 40% percentile. The following is obtained Percentile Position (n+1)P 100 (7+1) x 40 100 Since the position found is not integer, the method of interpolation needs to be used. The 40% percentile is located between the values in the positions 3 and 4. Those values, based on the data organized in ascending order, are -340 and -327.

The value of 3.2-3- 0.2 corresponds to the proportion of the distance between 340 and -327 where the percentile we are looking for is located at. In fact, we compute P40--340+0.2 x (-327-340)337.4

Position 70_Percnt (Asc. Order) -472 362 340 327 -321 -271 -211 4 6 The next step is to compute the position of the 70% percentile. The following is obtained (n+1)P 100 (7+1) x 70 100 Percentile Position -5.6

Since the position found is not integer, the method of interpolation needs to be used. The 70% percentile is located between the values in the positions 5 and 6 Those values, based on the data organized in ascending order, are -321 and -271 The value of 5.6-5-0.6 corresponds to the proportion of the distance between -321 and-271 where the percentile we are looking for is located at. In fact, we compute Pro321 0.6 x (-271 --321)291