The number of vehicles entering each of 15 junctions from a motorway during a 20-minute period on a Sunday morning is given below.
7 26 30 26 19 22 12 30 8 28 8 15 26 32 4
1 Choose the option that gives the median number of vehicles entering a junction.
Options for Question
A 4 B 7 C 19.53 D 22 E 22.33 F 22.50
2 Choose the TWO options that give the lower and upper quartiles for the numbers of vehicles entering a junction.
Options for Question
A 5 B 7 C 8 D 10 E 27 F 28 G 29 H 32.50
3 Choose the option that gives the range of the numbers of vehicles entering a junction.
Options for Question
A 26 B 28 C 29 D 30 E 32 F 36
Arrange scores in order of value.
Median = 50% percentile (50% score below that point)
Lower quartile = 25% score below, 25th percentile
Upper Quartile = 75% score below, 75th percentile
Range = highest score - lowest score.
I'll let you do the calculations.
To find the answers to these questions, we need to first sort the given numbers in ascending order:
4 7 8 8 12 15 19 22 26 26 28 30 30 32
1. To find the median, we need to determine the middle value. Since there are 14 numbers, the middle two numbers will be averaged. So, the median is (15 + 19) / 2 = 17.
2. To find the lower and upper quartiles, we need to determine the 25th and 75th percentiles, respectively.
- The lower quartile (Q1) is the median of the lower half of the data set. Since there are 14 numbers, the lower half consists of the first 7 numbers. The median of these numbers is (8 + 8) / 2 = 8.
- The upper quartile (Q3) is the median of the upper half of the data set. Since there are 14 numbers, the upper half consists of the last 7 numbers. The median of these numbers is (28 + 30) / 2 = 29.
So, the lower quartile is 8, and the upper quartile is 29.
3. To find the range, we subtract the smallest value from the largest value of the data set. In this case, the range is 32 - 4 = 28.
Therefore, the answers to the questions are:
1. Option C: 19.53 (median)
2. Options C (8) and G (29) (lower and upper quartiles)
3. Option B: 28 (range)