Question 1 Mean Median Variance Standard Deviation A hypoth

Question 1. Mean, Median, Variance, & Standard Deviation A hypothetical population is represented by the following data 9.4 4.6 12.5 8.3 7.4 11.4 3.6 20.7 13.2 15.4 7.2 3.2 9.5 15.2 12.3 7.3 10.4 15.4 10.7 9.5 8.3

(a) Find the mean. (Equation & calculations, use 1 decimal digit for the whole question)

(b) Find the median. (Show steps)

(c) Find the variance. (Equation & calculations)

(d) Find the standard deviation. (Equation & calculations)

(e) From the original data, replace the max with 92.3. Again, find the median.

(f) Add 11.8 to the original data. Again, find the median. (Refer to the textbook)

2. Histogram File Question02Data.xlsx contains the necessary data for this question. You should use relevant functions in Excel to answer the question. Use 2 decimal digits in your answer.

(a) Based on the provided data, fill values in the following table

STATISTICS Count, Min, Max, Range, Mean, Median, Variance, Standard Deviation Value…??

Note: for Variance, use VAR.S(); for Standard Deviation, use STDEV.S()

(b) Based on the table in (a), define limits to divide data into classes (bins). You should define 21 bins. Fill the upper limits of those 21 bins in the following table:

BIN # 1 2 ... ... 20 21 UPPER LIMIT

(c) Draw a histogram based on the provided data and your defined bins. Format the histogram to make it look clear and good.

Binomial Distribution

A coin has the probability of turning head to be 0.6. The coin is tossed 15 times. Define x = number of heads after 15 tosses. Using a relevant Binomial table (at the end of the textbook) and crosschecking the initial results with BINOM.DIST() in Excel, find the following:

(a) Average of x. (Equation & calculations)

(b) Variance of x. (Equation & calculations)

(c) P(x = 8) (Elaboration & lookup results, use 5 decimal digits)

(d) P(x 5) (Elaboration & lookup results)

(e) P(x 10) (Elaboration & lookup results) (f) P(4 < x 7) (Elaboration & lookup results)

Normal Distribution

We have a normal probability distribution for variable x with = 42.79 and = 9.5. Determine the following (you may need to take averages between cells in the ztable):

(a) PDF(x = 32) (Equation, manual calculations in Excel, check with NORM.DIST(*,*,*,0) in Excel)

(b) P(x 21) (zscore, ztable, check with NORM.DIST(*,*,*,1) in Excel, use 5 decimal digits)

(c) P(37 x 60) (zscore, ztable, check with NORM.DIST(*,*,*,1) in Excel)

(e) P(x 57) (zscore, ztable, check with NORM.DIST(*,*,*,1) in Excel)

(f) x* so that P(x x*) = 0.9

Solution

mean = sum of values /total number of values

= 215.5/21

= 10.2619

median = 11th element when sorted

= 9.5

c)

variance

= (sum of squares of values ˆ2 / total number of values ) - meanˆ2

= 122.8157 - 10.2619ˆ2

= 17.5091

d)

standard deviation = sqrt(variance) = 4.1844