Jennifer 229 Samantha 425 Phillip 565 Erin 246 Stanley 348 Dominic 315 Luke 278 Charlie 198 Lexie 189 Amol 205 Margaret 364 Lenisa 425 a. Compute the mean (in $1000), variance (in $10002), and standard deviation (in $1000) for these annual sales values. Round your answers to the nearest whole number. Mean thousand Variance thousand2 Standard deviation thousand b. In the previous fiscal year, the average annual sales amount was $298 thousand with a standard deviation of $85 thousand. Discuss any differences you observe between the annual sales amount in the most recent and previous fiscal years. (i) The difference in the
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Varatta Enterprises sells industrial plumbing valves. The following table lists the annual sales amounts for a portion of the salespeople in the organization for the most recent fiscal year.
Salesperson | Sales Amount ($1000) | Salesperson | Sales Amount ($1000) |
Joseph | 153 | Wei | 471 |
Jennifer | 229 | Samantha | 425 |
Phillip | 565 | Erin | 246 |
Stanley | 348 | Dominic | 315 |
Luke | 278 | Charlie | 198 |
Lexie | 189 | Amol | 205 |
Margaret | 364 | Lenisa | 425 |
a. Compute the mean (in $1000), variance (in $10002), and standard deviation (in $1000) for these annual sales values. Round your answers to the nearest whole number.
Mean | thousand |
Variance | thousand2 |
Standard deviation | thousand |
b. In the previous fiscal year, the average annual sales amount was $298 thousand with a standard deviation of $85 thousand. Discuss any differences you observe between the annual sales amount in the most recent and previous fiscal years.
(i) The difference in the mean annual sales amount is very small and is most likely due to random change in demand for these products.
(ii) The sample mean annual sales amount and standard deviation for the previous fiscal year were significantly higher.
(iii) The sample mean annual sales amount and standard deviation for the previous fiscal year were significantly lower.
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