Given the following dataset, identify the third quartile: 9, 4, 6, 9, 5, 8, 7, 6, 4, 2, 6, 2, 5, 7, 5

Answer 1

To find the third quartile (Q3), we first need to sort the data in ascending order: 2, 2, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 8, 9, 9.

The dataset has 15 numbers, so Q3 is at the position (3/4) * 15 = 11.25. Since this is not a whole number, we take the average of the 11th and 12th numbers to find Q3: (6 + 7) / 2 = 6.5.

Therefore, the third quartile in this dataset is 6.5.

Answer 2

The scores of 14 students on a weekly assignment for Mrs. Brown’s math class are shown here.

10, 9, 6, 8, 9, 10, 8, 2, 6, 5, 7, 4, 5, 9

Find the interquartile range of this dataset

Answer 3

To find the interquartile range (IQR) of a dataset, we first need to find Q1 (the first quartile) and Q3 (the third quartile).

To calculate Q1 and Q3 for the given dataset:

Sorted data: 2, 4, 5, 5, 6, 6, 7, 8, 9, 9, 9, 10, 10

There are 14 numbers in the dataset.

Median of the entire dataset (Q2): (7th value + 8th value) / 2 = (7 + 8) / 2 = 7.5

Q1 is the median of the lower half of the dataset: 2, 4, 5, 5, 6, 6, 7
Median of the lower half (Q1): (4th value + 5th value) / 2 = (5 + 5) / 2 = 5

Q3 is the median of the upper half of the dataset: 9, 9, 9, 10, 10
Median of the upper half (Q3): (3rd value + 4th value) / 2 = (9 + 9) / 2 = 9

Now, calculate the IQR:

IQR = Q3 - Q1
IQR = 9 - 5
IQR = 4

Therefore, the interquartile range of the dataset is 4.