Question

The accompanying data represent the wait time​ (in minutes) for a random sample of forty visitors to an amusement park ride. Complete parts​ (a) and​ (b).

Answer 1

The quartiles for the given dataset are as follows:

Q1 = 6 (25% of wait times are less than or equal to 6 minutes)

Q2 = 9 (50% of wait times are less than or equal to 9 minutes)

Q3 = 22 (75% of wait times are less than or equal to 22 minutes)

How to determine the quartiles from the data

To determine the quartiles, arrange the data in ascending order:

0, 0, 3, 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 12, 13, 14, 16, 16, 22, 22, 22, 26, 29, 30, 30, 32, 47, 54

There are 40 data points in the sample, so calculate the values of the quartiles:

Lower Quartile (Q₁):

Q₁ = (n + 1) / 4 = (40 + 1) / 4 = 10.25

Since Q₁ is not an integer, we can interpolate using the position formula:

Q₁ = Data[10] + 0.25 * (Data[11] - Data[10])

= 6 + 0.25 * (6 - 6)

= 6

Interpretation: The lower quartile (Q₁) is 6, which means that 25% of the wait times are less than or equal to 6 minutes.

Median (Q₂ / 50th percentile):

Since the data is already arranged in ascending order, the median is the middle value of the dataset.

Q₂ = Data[(n + 1) / 2] = Data[(40 + 1) / 2] = Data[20]

= 9

Interpretation: The median (Q₂) is 9, which means that 50% of the wait times are less than or equal to 9 minutes.

Upper Quartile (Q₃):

Q₃ = 3 * (n + 1) / 4 = 3 * (40 + 1) / 4 = 30.75

Since Q₃ is not an integer, interpolate using the position formula:

Q₃ = Data[30] + 0.75 * (Data[31] - Data[30])

= 22 + 0.75 * (22 - 22)

= 22

Interpretation: The upper quartile (Q₃) is 22, which means that 75% of the wait times are less than or equal to 22 minutes.

The accompanying data represent the wait time (in minutes) for a random sample of forty visitors to an amusement park ride. Complete parts (a) and (b). 7 14 4 6 5 30 6 6 22 9 7 47 10 10 30 0 26 6 9 5 22 8 22 9 29 16 54 3 10 32 0 4 7 13 3 7 5 12 8 16 (a) Determine and interpret the quartiles.

Answer 2

Explanation:

So basically when you have to calculate the quarters you need to first of all the data. So this modern number first and then so in this case will be 000 and so on. Then you have to find the position. So in this case you have Around 40 value. So In this case for example the first one will be the 10th value in this case. Day 20th In this case the 30th. So for example 25% of the data of the first party will be until six. So you know 25% of the others will be six or below six. 50% of the data will be in the 20th position. So it will be below nine Or nine and 75% of data will be below or equal to 16. 16. Anything couple of 16 will be in the top 25% and those are dancers. So this is a quick summary. Remember that you find these values When you calculate the 75% position. That in this case because you have 40 values that will be 30%. For the second quarter will be the 50% and for the first quarter will be the 25%. How do you know that? 1st? You need to sort all the data. So the first smallest bodies will be here from smaller to larger and then you find the relative position paid on this percentage.