Answer :
Answer: D. 112
Step-by-step explanation:
Given : The times recorded were as follows (in minutes):-
118, 124, 108, 116, 99, 120, 148, 118, 119, 121, 45, 130,118
First arrange the above data set in ascending order , we get
45, 99,108, 116,118,118,118,119, 120, 121,124, 130, 148
Median = center-most value = 118
Lower-half of data : 45, 99,108, 116,118,118
First Quartile = Median of lower half=[tex]\dfrac{108+116}{2}=112[/tex]
Hence, the first quartile = 112
Final answer:
The first quartile of the recorded wait times at an amusement park is 112 minutes, calculated by organizing the data in ascending order and averaging the 3rd and 4th data points.
Explanation:
To calculate the first quartile of the wait times, we first need to organize the data in ascending order. The wait times in minutes are: 45, 99, 108, 116, 118, 118, 118, 119, 120, 121, 124, 130, 148. Since there are 13 data points, the first quartile (Q1) is the data point that separates the lowest 25% of the data from the rest.
To find Q1, we calculate the position using the formula for the quartile position (P) in a dataset sorted in ascending order: P = (n + 1) * (1/4). Substituting 13 for n, we get P = (13 + 1) * (1/4) = 14/4 = 3.5. This means that Q1 is the average of the 3rd and 4th data points after the dataset is sorted. These points are 108 and 116.
Calculating the average of these two points, we get: Q1 = (108 + 116) / 2 = 224 / 2 = 112 minutes. Therefore, the first quartile of the wait times at the amusement park is 112 minutes.
