Lead in Medicine Listed below are the lead concentrations (in μ g / g ) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations listed here are from medicines manufactured in the United States. The data are based on the article “Lead, Mercury, and Arsenic in US and Indian Manufactured Ayurvedic Medicines Sold via the Internet,” by Saper et al., Journal of the American Medical Association, Vol. 300, No. 8. What do the results suggest about the safety of these medicines? What do the decimal values of the listed amounts suggest about the precision of the measurements?

Problem 13BSC

Answer:

Step1 of 3:

We have Listed below are the lead concentrations (in μ-g/g) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations listed here are from medicines manufactured in the United States. The data are based on the article “Lead, Mercury, and Arsenic in US and Indian Manufactured Ayurvedic Medicines Sold via the Internet, “ by Saper et al., Journal of the American Medical Association, Vol. 300, No. 8.

3 |
6.5 |
6 |
5.5 |
20.5 |
7.5 |
12 |
20.5 |
11.5 |

Step2 of 3:

We need to find the (a)mean, (b) median, (c) mode, and (d) midrange for the given sample data. Express answers with the appropriate units of measurement. Then answer the given questions.

Step3 of 3:

a)Mean:mean is the average of the numbers and it is given by

Mean() =

=

=

= 11.05

Therefore,the mean of the given data is 11.05

b).Median:The median is a simple measure of central tendency. To find the median, we arrange the observations in order from smallest to largest value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

Write the given data in Ascending order

3 |
5.5 |
6 |
6.5 |
7.5 |
11.5 |
12 |
17.5 |
20.5 |
20.5 |

Median = , if the given data is even

=

=

= 9.5

Therefore,the median of the given data is 9.5

c)Mode:The mode is the value that appears most often in a set of data. The mode of a discrete probability distribution is the value x at which its probability mass function takes its maximum value. In other words, it is the value that is most likely to be sampled.

Here, 20.5 is repeated two times hence the mode value is 20.5

Therefore, Mode = 20.5

d).Midrange:the midrange or mid-extreme of a set of statistical data values is the arithmetic mean of the maximum and minimum values in a data set, defined as: The mid-range is the midpoint of the range

Mid-range =

=

=

= 11.75.

Therefore,midrange of the given data is 11.75.

There is not enough information given here to assess the true danger of these drugs, but ingestion of any lead is generally detrimental to good health. All of the decimal values are either 0 or 5, so it appears that the lead concentrations were rounded to the nearest one-half unit of measurement.