Make a box and whisker plot of the data. 13,13,20,21,21,22,24,27.
I know the median is 21. The 3Q is 23
Min is 4 and the max is 27. But I can't figure what number is the Q1 because I don't know what number comes between 13 and 20. Is it 15 or 16.5?
Please help me understand. Thank you.
To find the value of the first quartile (Q1), you need to determine the median of the lower half of the data set. In your case, the data set is: 13, 13, 20, 21, 21, 22, 24, 27.
To find the median of the lower half, you need to order the data set from least to greatest:
13, 13, 20, 21, 21, 22, 24, 27
The lower half consists of the first four values:
13, 13, 20, 21
To find the median of this lower half, you need to find the middle value. Since there is an even number of values (4), you need to find the average of the two middle values, which in this case are 13 and 20.
(13 + 20) / 2 = 16.5
Therefore, the value of the first quartile (Q1) in this data set is 16.5.
To make a box and whisker plot, you need to follow these steps:
1. Determine the minimum and maximum values in the data set. In this case, the minimum is 13 and the maximum is 27.
2. Determine the first quartile (Q1), the median, and the third quartile (Q3). In this case, Q1 is 16.5, the median is 21, and Q3 is 23.
3. Draw a number line and mark the minimum, Q1, median, Q3, and maximum values accordingly.
4. Draw a box between Q1 and Q3, and draw a vertical line through the box to represent the median.
5. Extend two lines (whiskers) from the box to the minimum and maximum values.
The final box and whisker plot for this data set would look like this:
--------------
| |
-------. .-------
13 16.5 21 23 27
"Min is 4 "
I do not find a 4 in the data. Is there a typo in the answer or the question?
Q1 is the median of the left half of data, which is 13,13|20,21
For the given data, Q1 equals the mean of 13 and 20, which makes 16.5.
Good work!