A popular soft drink company has made headlines in recent months after the relaunch of one of their iconic brands. They claim that it has been reformulated and now has less than 11 grams of sugar per 355ml can. Sales have soared and consumer feedback about the taste has been exceptional. However, the process they use to reduce the sugar has recently been criticized by a health advocate group as being relatively ineffective. Furthermore, the same health advocate group has suggested that the actual sugar content advertised as 11g/355ml can is not true, and is probably much higher.
You have been hired as an independent party to test their suspected claim that the amount of sugar per 355ml can exceeds 11g. They have provided you with the resources to randomly sample 50 cans from various vendors and test each can for the amount of sugar content.
The data in the table (see appendix) gives the sugar content in grams for the random sample of the fifty 355ml cans.
Values> 14.101, 11.809, 11.963,12.504 ,11.389 ,10.584 ,11.449 ,12.710 ,12.504 ,13.034 ,12.278 ,13.614 ,10.020 ,11.569 ,12.044 ,10.951 ,10.088 ,11.496 ,9.957 ,11.542 ,11.921 ,14.263 ,10.411 ,10.815 ,12.563 ,11.198 ,13.458 ,11.188 ,13.422 ,11.846 ,11.978 ,11.736 ,12.912 ,9.9183 ,11.756 ,8.428 ,11.828 ,11.282 ,14.318 ,14.183 ,10.810 ,9.054 ,12.595 ,14.092 ,11.227,9.668 ,11.735 ,11.594 ,10.932 ,12.350
Can someone help me get the Measure of position: z-score for a sample, percentil, queartil, decil, outlier data; and the exploration of data analysys: boxplots
To calculate the z-scores for each data point in the sample, you can use the formula:
z = (X - μ) / σ
Where:
- X is the value in the sample
- μ is the sample mean
- σ is the sample standard deviation
First, calculate the sample mean and standard deviation:
Mean (X̄) = ΣX / n
Standard Deviation (σ) = √(Σ(X - X̄)² / n)
Next, calculate the z-score for each data point using the mean and standard deviation.
To find the percentiles, quartiles, deciles, and outliers, you can use R or Excel to create a boxplot of the data. This will give you a visual representation of the distribution of the sugar content in the sample cans.
The boxplot will include:
- The median (Q2 or 50th percentile)
- The first quartile (Q1 or 25th percentile)
- The third quartile (Q3 or 75th percentile)
- Any outliers outside the upper and lower whiskers of the boxplot
Additionally, you can calculate the quartiles and percentiles directly from the data using R or Excel.
For quartiles:
- Q1 (25th percentile) is the value below which 25% of the data fall
- Q2 (50th percentile or median) is the value below which 50% of the data fall
- Q3 (75th percentile) is the value below which 75% of the data fall
For deciles:
- D1 (10th percentile) is the value below which 10% of the data fall
- D2 (20th percentile), D3 (30th percentile), ..., D9 (90th percentile)
Outliers can be identified as data points that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR, where IQR is the interquartile range (Q3 - Q1).
By examining the boxplot and calculating the quartiles, percentiles, and z-scores, you can determine if there are any outliers or if the sugar content in the cans exceeds the advertised 11g per 355ml.