Question

The number of cars at a given campus intersection at 9 am was counted for 4 consecutive days with the following results: 13, 7, 10, 18. The sample inter-quartile range for these data is:

a) 6.5
b) 5.5
c) 4.5
d) 3.5

Answer 1

The inter-quartile range (IQR) is calculated by ordering the data, finding the quartiles, and then subtracting Q1 from Q3. Using the provided data (13, 7, 10, 18), the calculated IQR is 7, which does not match any of the provided options. However, this assumes a more traditional approach to IQR calculation that may not be suitable for a small sample size of 4 data points.

Step-by-step explanation:

The question asks for the sample inter-quartile range (IQR) of the number of cars at a campus intersection at 9 am for 4 consecutive days. The data given are: 13, 7, 10, 18. To calculate the IQR, we need to follow these steps:

1. Order the data from smallest to largest: 7, 10, 13, 18.
2. Find the median (Q2), which is the average of the two middle numbers in our ordered list when the number of data points is even. So, Q2 = (10 + 13)/2 = 11.5.
3. The lower quartile (Q1) is the median of the lower half of the data. In this case, the lower half is 7 and 10, so Q1 = (7 + 10)/2 = 8.5.
4. The upper quartile (Q3) is the median of the upper half of the data. The upper half is 13 and 18, so Q3 = (13 + 18)/2 = 15.5.
5. Subtract the lower quartile from the upper quartile to find the IQR: IQR = Q3 - Q1 = 15.5 - 8.5 = 7.

Based on the choices given, none match the calculated IQR of 7. Therefore, it seems there may be a mistake in the provided options or in the calculations, considering that the number of data points is very limited (only 4), which does not allow for proper quartile calculation as typically defined for larger datasets.