To find the interquartile range (IQR), we first need to find the 1st quartile (Q1) and the 3rd quartile (Q3).
Original dataset: {0, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 18, 20, 30}
1. Arrange the data in ascending order: {0, 7, 8, 8, 10, 11, 14, 15, 17, 17.5, 18, 18, 18, 20, 30}
2. Find Q1: Since there are 15 data points, Q1 is the average of the 8th and 9th values, which are 14 and 15.
Q1 = (14 + 15) / 2 = 14.5
3. Find Q3: Q3 is the average of the 13th and 14th values, which are 18 and 20.
Q3 = (18 + 20) / 2 = 19
4. Calculate the IQR:
IQR = Q3 - Q1
IQR = 19 - 14.5
IQR = 4.5 hours
Now, add the missing data value "15" to the dataset:
New dataset: {0, 7, 8, 8, 10, 11, 14, 15, 15, 17, 17.5, 18, 18, 18, 20, 30}
Repeat the steps to find the IQR for the new dataset:
Q1 = (14 + 15) / 2 = 14.5
Q3 = (18 + 20) / 2 = 19
IQR = 19 - 14.5 = 4.5 hours
Therefore, the interquartile range of the original dataset is 4.5 hours, and the interquartile range of the new dataset after "15" is added is also 4.5 hours.
The director of a local summer camp is interested in the number of hours kids spend on screens each week. He surveys a group of 15 kids at his camp and asks them how many hours they spent on screens last week. A list of his results follows.
{0,7,8,8,10,11,14,15,17,17.5,18,18,18,20,30}
The director realizes he forgot to include the data value “15” in his dataset. Calculate the interquartile range of the original dataset and the interquartile range of the new dataset after “15” is added.
The interquartile range of the original dataset is ___ hours. The interquartile range of the new dataset after “15" is ___ added is hours.
3 answers
are you positive
Apologies for the oversight in my response. Let's recalculate the IQR for the new dataset after adding the missing data value "15".
New dataset: {0, 7, 8, 8, 10, 11, 14, 15, 15, 17, 17.5, 18, 18, 18, 20, 30}
1. Arrange the data in ascending order: {0, 7, 8, 8, 10, 11, 14, 15, 15, 17, 17.5, 18, 18, 18, 20, 30}
2. Find Q1: Since there are 16 data points, Q1 is the average of the 8th and 9th values, which are 14 and 15.
Q1 = (14 + 15) / 2 = 14.5
3. Find Q3: Q3 is the average of the 12th and 13th values, which are 18 and 18.
Q3 = (18 + 18) / 2 = 18
4. Calculate the IQR:
IQR = Q3 - Q1
IQR = 18 - 14.5
IQR = 3.5 hours
Therefore, the interquartile range (IQR) of the new dataset after "15" is added is 3.5 hours. Thank you for pointing out the error.
New dataset: {0, 7, 8, 8, 10, 11, 14, 15, 15, 17, 17.5, 18, 18, 18, 20, 30}
1. Arrange the data in ascending order: {0, 7, 8, 8, 10, 11, 14, 15, 15, 17, 17.5, 18, 18, 18, 20, 30}
2. Find Q1: Since there are 16 data points, Q1 is the average of the 8th and 9th values, which are 14 and 15.
Q1 = (14 + 15) / 2 = 14.5
3. Find Q3: Q3 is the average of the 12th and 13th values, which are 18 and 18.
Q3 = (18 + 18) / 2 = 18
4. Calculate the IQR:
IQR = Q3 - Q1
IQR = 18 - 14.5
IQR = 3.5 hours
Therefore, the interquartile range (IQR) of the new dataset after "15" is added is 3.5 hours. Thank you for pointing out the error.
3 answers