Determine who is the best seller

Question

The numbers below show the number of lollipops Betty and Sharon each month for a total of 12 months or a year.

Using the data and plot below, can you determine who is the bestseller? Would it be correct to say one person is a better seller than the other? Explain

Betty: $30,34,28,29,50,32,49,31,35,37$

Sample size: 10 Median: 33 Minimum: 28 Maximum: 50 First quartile: 29.75 Third quartile: 40 Interquartile Range: 10.25 Outliers: none

Sharon: $34,45,50,56,67,75,76,78,89,89$

Sample size: 10 Median: 71 Minimum: 34 Maximum: 89 First quartile: 48.75 Third quartile: 80.75 Interquartile Range: 32 Outliers: none

I'm not sure but what does skewness tell us. Looking at the numbers I can see sharon is the best-seller.

Answer 1

In addition to mixing up the plots, there are several difficulties here. On the chance that this Question has resulted from serious confusion (as opposed to maybe being spam), I'll address one difficulty at a time.

First, there are 10 observations for each person not 12.

Considered as independent samples. Second, if we had 10 $randomly\; chosen$ months for each person, then it would be best to put the two boxplots side-by-side for easier comparison. In R software this can be done as follows:

 b = Betty = c(30,34,28,29,50,32,49,31,35,37)
 s  = Sharon = c(34,45,50,56,67,75,76,78,89,89)
 sales = c(b, s); 
 person = as.factor( rep(c("Betty","Sharon"), each=10) )
 boxplot(sales ~ person)

So it seems Sharon is the better salesperson. Most software has the capability to put 'notches' in the sides of boxplots. The notches show nonparametric confidence intervals for the median of each plot. They are scaled so that two boxplots with nonoverlapping notches (as here) have significantly different medians.

 boxplot(sales ~ person, notch=T, col="skyblue")

Perhaps you know about two-sample t tests (or will soon learn about them). Treating the two samples of sales performance as independent, a two-sample t test would certainly show a significant difference in sales.

Considered as paired samples. Third, the wording of your problem suggests that the 10 months for Betty are the same as the 10 months for Sharon. (The statement says 12, but there are only 10 observations for each person.) If this is a month-by-month comparison of sales performance, then we should be looking at month-by-month differences.

 d = Dif.by.Mo = s - b;  d
 ##  4 11 22 27 17 43 27 47 54 52

So it seems that Sharon sold more lollipops in $every\; one$ of the 10 months. The chances of this for equally matched sales performances are like getting 10 Heads of 10 Tails in a row tossing a fair coin: $1/2^9 \approx 0.002$ or about 2 chances in a thousand. So either a lollipop selling miracle has occurred, or there is strong evidence that Sharon is the better lollipop salesperson.

Answer 2

First of all, I think the sample size 10 is different from what you described as the monthly sales.

From the data distribution, we can say that Sharon is a better seller than Betty. From the data of sale, Sharon has a higher median, minimum and maximum. And also a higher quartiles.

What I would suggest is that you should also calculate the mean and variance which would give you more insight about the data.

You should also plot these two sets of data together in one graph. I believe you can see Sharon does better from this graph.