Marks: --/20 What percentage of the general US population have bachelor's degrees? The Statistical Abstract of the United States (120th edition), gives the percentage of bachelor's degrees by state. For convenience, the data are sorted in increasing order.

17, 18, 18, 18, 19, 20, 20, 20, 21, 21
21, 21, 22, 22, 22, 22, 22, 22, 23, 23
24, 24, 24, 24, 24, 24, 24, 24, 25, 26
26, 26, 26, 26, 26, 27, 27, 27, 27, 27
28, 28, 29, 31, 31, 32, 32, 34, 35, 38

Find the interquartile range

Interquartile range = middle 50%

You have 50 scores arranged in order of value. 25th percentile is between 12th and 13th score, and the 75th percentile is between 37th and 38th score. What is the range for these two points?

20

50%

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To find the interquartile range, we first need to understand what quartiles are. Quartiles divide a data set into four equal parts, each containing 25% of the data.

To calculate the interquartile range, we'll first need to find the values for the first quartile (Q1) and the third quartile (Q3). Q1 represents the value below which 25% of the data falls and Q3 represents the value below which 75% of the data falls.

First, let's organize the data in ascending order:
17, 18, 18, 18, 19, 20, 20, 20, 21, 21,
21, 21, 22, 22, 22, 22, 22, 22, 23, 23,
24, 24, 24, 24, 24, 24, 24, 24, 25, 26,
26, 26, 26, 26, 26, 27, 27, 27, 27, 27,
28, 28, 29, 31, 31, 32, 32, 34, 35, 38

Next, we'll find the position of the first quartile:
Q1 = (25% * (N+1))th term, where N is the number of observations.
Since we have 50 observations, Q1 = 0.25 * (50 + 1) = 0.25 * 51 = 12.75.

To find the value of the first quartile (Q1), we need to check the values surrounding the position of 12.75. The values at positions 12 and 13 are both 22. So, Q1 = (22 + 22) / 2 = 22.

Next, we'll find the position of the third quartile:
Q3 = (75% * (N+1))th term.
Using the same formula, Q3 = 0.75 * (50 + 1) = 0.75 * 51 = 38.25.

To find the value of the third quartile (Q3), we need to check the values surrounding the position of 38.25. The value at position 39 is 38, and there is no value at position 38. So, Q3 = 38.

The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1).
Therefore, IQR = Q3 - Q1 = 38 - 22 = 16.

So, the interquartile range for the given data is 16.