An important quality characteristic of water is the concentration of suspended solid material. Following are 60 measurements on suspended solids from a certain lake. Construct a box plot of the concentrations.

44.4, 64.8, 31.7, 55.1, 53.0, 59.1, 58.7, 68.9, 66.9, 63.4, 51.6, 52.4, 75.8, 85.2

57.5, 56.6, 60.0, 71.7, 69.9, 62.6, 56.4, 47.8, 60.7, 41.5, 83.9, 50.8, 38.6, 37.4

56.1, 61.5, 61.3, 60.0, 68.4, 74.5, 69.4, 41.1, 50.0, 54.6, 66.8, 75.2, 44.4, 80.7

49.7, 57.7, 72.3, 37.2, 77.2, 57.2, 52.7, 74.9, 61.1, 78.1, 72.9, 52.6, 93.8, 53.9

55.7, 61.1, 64.0, 26.8

To create a box plot, arrange the data ascendingly, and identify the minimum, maximum, and quartile values. Plot these values on a number line, with a box spanning from the first to the third quartile and the median displayed as a vertical line inside the box.

Explanation:

To construct a box plot of the concentrations of suspended solids in the lake, we first need to arrange the data in increasing order and find out the minimum, first quartile (Q1), median (Q2), third quartile (Q3), and maximum values.

Once we've determined these values, we can then plot them on a number line. The box will extend from Q1 to Q3, and the median will be represented by a vertical line inside the box. The minimum and maximum values will be represented by lines (or whiskers) drawn from the box to the respective data values. Any value 1.5 times the interquartile range above Q3 or below Q1 is considered an outlier, and should be marked with a dot.

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muskangiri9405 muskangiri9405 · Answer 2 · 2024-08-07T00:34:42-04:00

Final answer:

To construct a box plot for the given measurements of suspended solid material concentrations, arrange the measurements in ascending order and find the minimum, first quartile, median, third quartile, and maximum values. Use these five summary statistics to construct the box plot.

Explanation:

A box plot is a graphical representation of the distribution of a dataset, showing the minimum, first quartile, median, third quartile, and maximum values. To construct a box plot for the given measurements of suspended solid material concentrations, we need to find these five summary statistics.

1. Arrange the measurements in ascending order:
26.8, 31.7, 37.2, 37.4, 38.6, ..., 93.8

2. Find the minimum value (26.8) and maximum value (93.8).

3. Find the first quartile (Q1), which is the median of the lower half of the dataset. In this case, it is the median of the first 30 values (from 26.8 to 55.1). The first quartile is 44.4.

4. Find the median (Q2), which is the middle value of the dataset. In this case, it is the average of the two middle values (60.7 and 61.1). The median is 60.9.

5. Find the third quartile (Q3), which is the median of the upper half of the dataset. In this case, it is the median of the last 30 values (from 61.1 to 93.8). The third quartile is 69.4.

6. Construct the box plot using these five summary statistics: minimum (26.8), first quartile (44.4), median (60.9), third quartile (69.4), and maximum (93.8). The box represents the interquartile range (Q3 - Q1) and the lines extending from the box represent the range of the dataset excluding outliers. v