Use the data set to determine which statements are correct. Check the four that apply.

Question

23, 45, 39, 57, 31, 53, 28, 50, 42, 36(4 points)
Responses

The upper quartile is 50.
The upper quartile is 50.

The lower quartile is 31.
The lower quartile is 31.

The interquartile range is 19.
The interquartile range is 19.

The lower quartile is 36.
The lower quartile is 36.

The upper quartile is 53.
The upper quartile is 53.

The median is 40.5.
The median is 40.5.

The median is 41.

Answer 1

To determine which statements are correct, we need to analyze the given data set:

23, 45, 39, 57, 31, 53, 28, 50, 42, 36

First, we should sort the data:

Sorted data: 23, 28, 31, 36, 39, 42, 45, 50, 53, 57

Next, we can find the quartiles and median:

1. Median:

   • The median is the average of the 5th and 6th values (since there are 10 values, the median will be the average of the 5th and 6th values).
   • 5th value: 39
   • 6th value: 42
   • Median = (39 + 42) / 2 = 40.5

2. Lower Quartile (Q1):

   • The lower quartile is the median of the first half of the data (23, 28, 31, 36, 39).
   • 3rd value (the median of the first half): 31 (as it is the 3rd of 5 values).

3. Upper Quartile (Q3):

   • The upper quartile is the median of the second half of the data (42, 45, 50, 53, 57).
   • 3rd value of the second half: 50.

4. Interquartile Range (IQR):

   • IQR = Q3 - Q1
   • IQR = 50 - 31 = 19.

Now, let's check each of the statements:

1. The upper quartile is 50. (Correct)
2. The lower quartile is 31. (Correct)
3. The interquartile range is 19. (Correct)
4. The lower quartile is 36. (Incorrect, it is 31)
5. The upper quartile is 53. (Incorrect, it is 50)
6. The median is 40.5. (Correct)
7. The median is 41. (Incorrect, it is 40.5)

Thus, the four correct statements are:

1. The upper quartile is 50.
2. The lower quartile is 31.
3. The interquartile range is 19.
4. The median is 40.5.