Question

1. a sample of 15 college students was asked to indicate the number of hours they spend studying during a typical week. the responses given by this sample are included in the table below. which one of the following statements is a correct interpretation of this data? 14 28 7 4 25 3 21 19 14 1 12 35 9 17 8 a. the 25th percentile is 21 because about 25% of the observations in the data set lie above 21. b. the 25th percentile is 14.5 because this is the midpoint of the lower 50% of the distribution. c. the 25th percentile is 8 because roughly 25% of the observations in the data set are less than 8. d. the 25th percentile is 7.5 because this is the number we get when we order the data and average the values in the 4th and 5th positions. e. the 25th percentile is 7 because this is the 4th value when we order the data from smallest to largest.

Explanation:

Step1: Sort the data

1, 3, 4, 7, 8, 9, 12, 14, 14, 17, 19, 21, 25, 28, 35

Step2: Calculate the position of the 25th percentile

The formula for the position of the $p$th percentile ($L_p$) in a data - set of size $n$ is $L_p=\frac{p}{100}\times n$. Here, $p = 25$ and $n=15$. So $L_{25}=\frac{25}{100}\times15 = 3.75$.

Step3: Determine the 25th percentile

Since the position is not an integer, we interpolate. The 3rd value is 4 and the 4th value is 7. The 25th percentile is $4+(0.75)\times(7 - 4)=4 + 2.25=7.5$.

Answer:

D. The 25th percentile is 7.5 because this is the number we get when we order the data and average the values in the 4th and 5th positions.