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The following data are the number of pages in 40 books on a shelf. Construct a box plot using a graphing calculator, and state the interquartile range.
IQR = 158
For some sets of data, some of the largest value, smallest value, first quartile, median, and third quartile may be the same. For instance, you might have a data set in which the median and the third quartile are the same. In this case, the diagram would not have a dotted line inside the box displaying the median. The right side of the box would display both the third quartile and the median. For example, if the smallest value and the first quartile were both one, the median and the third quartile were both five, and the largest value was seven, the box plot would look like:
In this case, at least 25% of the values are equal to one. Twenty-five percent of the values are between one and five, inclusive. At least 25% of the values are equal to five. The top 25% of the values fall between five and seven, inclusive.
Test scores for a college statistics class held during the day are:
Test scores for a college statistics class held during the evening are:
The following data set shows the heights in inches for the boys in a class of 40 students.
66; 66; 67; 67; 68; 68; 68; 68; 68; 69; 69; 69; 70; 71; 72; 72; 72; 73; 73; 74
The following data set shows the heights in inches for the girls in a class of 40 students.
61; 61; 62; 62; 63; 63; 63; 65; 65; 65; 66; 66; 66; 67; 68; 68; 68; 69; 69; 69
Construct a box plot using a graphing calculator for each data set, and state which box plot has the wider spread for the middle 50% of the data.
IQR for the boys = 4
IQR for the girls = 5
The box plot for the heights of the girls has the wider spread for the middle 50% of the data.
Graph a box-and-whisker plot for the data values shown.
The five numbers used to create a box-and-whisker plot are:
The following graph shows the box-and-whisker plot.
Follow the steps you used to graph a box-and-whisker plot for the data values shown.
The data are in order from least to greatest. There are 15 values, so the eighth number in order is the median: 50. There are seven data values written to the left of the median and 7 values to the right. The five values that are used to create the boxplot are:
Data from West Magazine .
Box plots are a type of graph that can help visually organize data. To graph a box plot the following data points must be calculated: the minimum value, the first quartile, the median, the third quartile, and the maximum value. Once the box plot is graphed, you can display and compare distributions of data.
Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell three cars; nineteen generally sell four cars; twelve generally sell five cars; nine generally sell six cars; eleven generally sell seven cars.
Construct a box plot below. Use a ruler to measure and scale accurately.
Looking at your box plot, does it appear that the data are concentrated together, spread out evenly, or concentrated in some areas, but not in others? How can you tell?
More than 25% of salespersons sell four cars in a typical week. You can see this concentration in the box plot because the first quartile is equal to the median. The top 25% and the bottom 25% are spread out evenly; the whiskers have the same length.
Santa Clara County, CA, has approximately 27,873 Japanese-Americans. Their ages are as follows:
| Age Group | Percent of Community |
|---|---|
| 0–17 | 18.9 |
| 18–24 | 8.0 |
| 25–34 | 22.8 |
| 35–44 | 15.0 |
| 45–54 | 13.1 |
| 55–64 | 11.9 |
| 65+ | 10.3 |
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