Statistics of the Minimum Value Set Order Instructions**: P**lease , you have to write the questions, just answer the 5 problems.

just one page. is actually due by the 12, so I will make a payment on that pretty soon.

# Statistics of the Minimum Value Set Sample Answer

The minimum value is the least observation in a set (Larson, 2012). For instance, the minimum value list is 2.

The **lower quartile** or **first quartile**, in this case, will be computed as follows:

N = number of observations = 15

1^{st} quartile = 0.25*15 = the 3.75 observations

The first quartile will be the average of the 3^{rd} and the 4^{th} observation.

1^{st} quartile = (3 + 4) /2 = 7/2 = 3.5

**The median** is defined simply as the central or middle observation when all values are arranged in descending or ascending order (Larson, 2012). In this case, when the observations are arranged in ascending order, and the middle value considered the median is 5.

The **upper quartile **or 3^{rd} quartile is calculated as follows;

3^{rd} quartile = 0.75*15 = 11.25 observations

This implies that the 3^{rd} quartile is the average of the 10^{th} and 11^{th} observations.

3^{rd} quartile = (11 + 11) /2 = 22/2 = 11

**Maximum value **is the largest observed value = 20

Inter-quartile range = 3^{rd} quartile – 1^{st} quartile

= 11 – 3.5

= 7.5

Standard deviation =

= =

=

=

= 14.14213562373095

= 14.14

Z-score = = = 1.2

The sample standard deviation can be derived from the population standard deviation using the following formulae (Larson, 2012).

= = 5 / √25 = 5 / 5

= 1

Thus, the sample standard deviation is 1.00.

:

:

n = 30, NY mean = 2.00 and NY sd. Dev. = 0.05

n = 30 NJ mean = 2.02, and NJ Sd. Dev. = 0.05

t =

=

=

=

DF =

=

= 58

t _{(.05, 58)} = T.INV.2T(0.05,58) = 2.0017

Since the |t_{ calculated}| = 3.8730 > t _{(.05, 58)} = 2.0017 reject (Larson, 2012). This means that the two means are not equal, NJ and NY gas prices is not equal.

## Statistics of the Minimum Value Set References

Larson, R., & Farber, E. (2012). *Elementary statistics*. Pearson Prentice Hall. From http://dl.ilam.ac.ir/handle/Hannan/58573