Question

The following data give the speeds of 13 cars (in mph) measured by radar, traveling on I-84. 73 75 69 68 78 69 74 76 72 79 68 77 71 a) Find the values of the three quartiles and the interquartile range. b) Calculate the (approximate) value of the 35th percentile (round to two decimal places). c) Compute the percentile rank of 71 (round to two decimal places. Do not include the % symbol).

Answer 1

Question a)

To find the quartiles, first, we need to put the data in ascending order.

The value of Q₂ [Median] is on the 7th value, which is 73
The value of Q₁, the lower quartile, is the 3.5th value, which is 69
The value of Q₃, the upper quartile, is the 10.5th value, which is 76.5

Interquartile range = Q₃ - Q₁ = 76.5 - 69 = 7.5

Question b)

The 35th percentile is located at 0.35 × 13 = 4.55 ≈ 5th value
The 5th value is 71 ⇒ Need to read this when data is in ascending order

Question c)

Percentile rank of 71 is located at 0.71 × 13 = 9.23 ≈ 9th value
The 9th value is 75 ⇒ Need to read this when data is in ascending order