Question

Lead is a heavy metal which is not good for human health. Lipsticks and lip gloss however contains lead in small amounts. Therefore, the U.S. Food and Drug Administration (FDA) set safety limit for lead in lip products at 10 parts per million (ppm). Below are the mean lead content (mg/kg) in randomly selected 14 lip products produced in USA. Source: European Survey of the Content in Lead in Lip Products by P. Piccinini, M. Piecha, S.F. Torrent (2013).

0.27, 1.37,1.02, 0.47, 0.25,2.11,0.98 1.04, 0.32, 0.09, 0.06, 0.39, 0.27,0.33 Note: 1ppm-lmg/kg. (a) Construct a frequency distribution for the above data. b) Find the sample mean , median, range. (c) Create a stem-and-leaf diagram of the data pertaining to the lead content in lip products. Discuss the main findings from these figures; e.g., does the data appear to by symmetric/left-skewed/ right-skewed, does there appear to be any outliers, etc. (d) Using the calculated statistics in parts (a)-(c), comment on the quality of the lip products.

Answer 1

Answer Date: 14/01/2019 a) The frequency distribution table for the lead in lip product is, By using Excel software, draw the frequency distribution with the help of following steps: 1) Import the data. 2) Select MegaStat option from Add-Ins menu. 3) Selct Quantitative from Frequency Distributions 4) Select Input range. 5) Enter lower boundaiy of first interval and interval width. 6) ClickOk

Frequency Distribution- Quantitative Lead cumulative frequenc midooint width 0.25 0.50 0.75 0.50 1.25 0.50 1.75 0.50 2.25 0.50 uenc rcent lower 0.00 < 0.50 0.50 <1.00 1.00 <1.50 1.50 < 2.00 2.00 <2.50 64.3 7.1 21.4 0.0 7.1 14 100.0 9 64.3 10 71.4 13 92.9 13 92.9 14 100.0 b) The sample mean, median andrange lead in lip product is, By using Excel software, find summary statistics with the help of following steps 1)Import the data 2) Select Data Analysis option from Data menu. 3)Select Descriptive Statistics from Data Analysis 4)Choose Input Range and Suunmary Statistics from Descriptive Statistics 5) Click Ok.

Lead Mean Median Range Count 0.64071429 0.36 2.05 14 From Excel output, the sample mean is 0.64. median is 0.36] and range is l2.05] lead in lip product. c) A stem-and-leafdiagram of lead content in lip product is, By using Excel software, draw stem-and-leafhelp with the following steps: 1) Import the data. 2) Select MegaStat option from Add-Ins menu. 3) Select Stem-and-Leaf from Descriptive Statistics 4) ClickOk

Stem and Leaf plot for Lead stem unit 1 leaf unit = 0.1 Frequency Stem Leaf 10 0 00 222 3334 9 1 003 2' 1 14 From Excel output, a stem-and-leaf diagram of lead content in lip product concludes the data does appear skewed to the right and there does not outliers in the data. d) Using calculated statistics in parts (a)-(c), the quality of lip product is not good due to it is skewed to the right-sided lead amount is higher.