PHC 4069 Lecture Notes - Lecture 3: Unimodality, Quartile, Squared Deviations From The Mean

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22 Jul 2018

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Use two types of measures when describing data. If the data are from a sample, the mean is denoted by. N = total number of observations in the data. If the data is from a population, the mean is denoted by. Summation = sum of a set of numbers. X = each observation in the data set. N = total number of observations in the population. Value in the middle when the data are arranged in ascending order. Odd number of observations, the median is the exact middle value. Value that occurs with the greatest frequency. Can occur at 2 or more values. If the data have exactly two modes, the data are bimodal. If the data have >2 model, the data are multimodal. If the data have one mode, the data are unimodal. Provide information about how the data are spread over the interval from the smallest value to the largest value.

Related Questions

Module 2 Minitab Assignment

Instructions:
Below you will find questions and a sample dataset. Please use the provided dataset to complete the tasks and to answer the questions.

As reported by the U.S. Census Bureau in Current Population Reports, the percentage of adults in each state and the District of Columbia who have completed high school is provided below.
Find the mean, median, and mode for this data set. Be aware that the mode does not always exist.
Find the range and standard deviation of this data set.
Write a sentence interpreting the mean and standard deviation.
Write a sentence interpreting the median.
Dataset:
State Percent - Dataset
Alabama 95
Alaska 89
Arizona 95
California 84
Delaware 80
Georgia 81
Illinois 88
Kansas 83
Louisiana 85
Massachusetts 85
New Mexico 91
New York 93
North Carolina 88
Oklahoma 85
Texas 88
Utah 91
Vermont 86
Washington 80
Wisconsin 81
Wyoming 95

(continued on next page)
Based on the following data,
Determine and interpret the first, second, and third quartiles.
Determine and interpret the interquartile range.
Construct a box-plot and describe the shape of the distribution.
Identify any outliers, if any.
Dataset:
96
59
55
111
76
91
60
57
84
123
56
89
61
72
89
72
81
88
75
79

(continued on next page)
This is a set of data from a sample of n = 11 items:
Produce a scatterplot of the data.
What does the plot suggest about the relationship between the variables?
Find and interpret the correlation coefficient.
Find and interpret the coefficient of determination.
Predict the value of y when x = 65. How much faith do you have in this prediction? Explain.
Dataset:
x y
46.1 150.8
47.6 150.2
45.5 141.3
43.1 167.4
44.5 166.7
36.9 121.7
47.4 143.6
44.8 186.1
41.3 166.2
33.5 140.4
34.4 132.9

sbmrgd

A scientist wanted to determine if two newly discovered populations of insects exchanged information with other members of the same population about the location of a food source. The scientist set up a systematic observation in which food was placed for the insects to find. Over a period of time, the scientist recorded how many insects were found at the food source. The scientist collected the following data: A graph showing the number of insects recorded at a food source over a period of time. On the horizontal x-axis is time. On the vertical y-axis is the number of insects. Both populations start at 1 insect. At 2 minutes, both are at 2 insects. At three minutes, population 1 drops to 1 and population 2 increases to 4. At 4 minutes, population 1 increases to 4 and population 2 increases to 10. At 5 minutes population 1 increases to 5 and population 2 increases to 15. At 6 minutes, population 1 peaks at 6 and population 2 increases to 17. At 7 minutes, population 1 drops to 5 insects and population 2 rises to 18. At 8 minutes population 1 drops to 4 and population 2 increases to 19. Â© 2012 FLVS The scientist concludes that population 2 has a greater chance of survival than population 1. What is the correct response to the scientist's conclusion? (2 points)

Invalid because it can be deduced that population 2 will run out of food before population 1.

Invalid because survival is not dependent on the data found in the observation.

Valid because the data shows population 2 is able to communicate with one another.

Valid because the data reveals population 1 is found in lower numbers than population 2.

1. You are given only three quarterly seasonal indices and quarterly seasonally adjusted data for the entire year. What is the raw data value for Q4? Raw data is not adjusted for seasonality.

Quarter Seasonal Index Seasonally Adjusted Data

Q1 .80 295

Q2 .85 299

Q3 1.15 270

Q4 --- 271

2. One model of exponential smoothing will provide almost the same forecast as a liner trend method. What are linear trend intercept and slope counterparts for exponential smoothing?

A. Alpha and Delta

B. Delta and Gamma

C. Alpha and Gamma

D. Standard Deviation and Mean

3. When performing correlation analysis what is the null hypothesis? What measure in Minitab is used to test it and to be 95% confident in the significance of correlation coefficient.

A. Ho: r = .05 p < .5

B. Ho: r = 0 p >.05

C. Ho: r ? 0 p?.05

D. Ho: r = 0 p?.05

In decomposition what does the cycle factor (CF) of .80 represent for a monthly forecast estimate of a Y variable?

A. The estimated value is 80% of the average monthly seasonal estimate.
B. The estimate is .80 of the forecasted Y trend value.
C. The estimated value is .80 of the historical average CMA values.
D. The estimated value has 20% more variation than the average historical Y data values.

5. A Wendy's franchise owner notes that the sales per store has fallen below the stated national Wendy's outlet average of $1,368,000. He asserts a change has occurred that reduced the fast food eating habits of Americans. What is his hypothesis (H1) and what type of test for significance must be applied?

A. H1: u ? $1,368,000 A one-tailed t-test to the left.
B. H1: u = $1,368,000 A two-tailed t-test.
C. H1: u < $1,368,000 A one-tailed t-test to the left.
D. H1: p < $1,368,000 A one-tailed test to the right

6. As the sample size from a population increases, for a given level of significance what happens to the null hypothesis rejection region and size of the t-table value?

A. The rejection region and the t-table value generally gets smaller for sample size below 31.
B. The rejection region gets larger and the t-table value generally gets smaller for sample sizes below 31.
C. The rejection region remains unchanged while the t-table value gets smaller for all sample sizes.
D. The zero mean hypothesis region gets larger and the t-table value gets larger as well for sample sizes below 31.

7. You obtained autocorrelation LBQ value of 18.58 for the 12^th lag from a data sample. Are the data significantly correlated at the lag examined or not? You want to be 95% confident in your answer.

A. Yes. The data are significantly correlated through the 12th lag.
B. No. The data are not significantly correlated through the 12^th lag.

C. No. Only the 12 lag period is not correlated.

D. You cannot tell since the number of sample observations is not provided.

E. The p-value is above .05 so the data is correlated.

8. Sometimes forecasters get lazy or forgetful and do not check the significance of XY data correlations and use the X variable to forecast Y. What is the result of this?

A. Type 2 error
B. Autocorrelation error
C. Type 3 error
D. Type 1 error

9. Do error measures indicate the statistical significance of forecast model variables?

A. Yes. They move in the same direction as statistical significance.
B. Yes. As error measures decrease the variable significance increases.
C. No They indicate only the magnitude of estimate error.
D. No. They indicate only the statistical significance of a forecast or fitted values.

10. In exponential smoothing what is the weight of the alpha coefficient for a time series data observation from the 3^rd previous period if the original alpha value is set at .8?

A. The weight cannot be calculated since the data observation is not given.
B. The weight is zero since the alpha value is set relatively high.
C. .548
D. .0064

11.Given the data series below for variables Y (Monthly Inventory Balance) and X (Monthly Sales) are they significantly correlated at the 95% confidence level and how can you tell?

Ending Inv. Bal. Y		Monthly Sales X
1544		5053
1913		5052
2028		7507
1178		2887
1554		3880
1910		4454
1208		3855
2467		8824
2101		5716

A. Yes. The correlation coefficient is .873 that is greater than .05.
B. Yes. The correlation p-value is .002 which is less than .05.
C. No. The correlation coefficient is above the p-value.
D.No. The correlation p-value is greater than the 95% confidence level.

12. You have forecast the sales for your company for the last 12 months and the forecast residuals are shown below. Are these residuals to be considered random?
Residuals

-24

-348

-892

-62

-378

-489

-342

490

578

198

A. Yes, since the residuals randomly vary in magnitude.
B. Yes since the residuals are positive and negative and vary in magnitude.
C. No, since the residuals are stationary and vary in magnitude.
D. No, since the residuals indicate positive slope.

13. Given the residuals in problem 12 above what is the RMSE for the forecast?

A. -101.0
B. 411.8
C. 169603
D. 220.1

14. Which form of exponential smoothing can result in a na

PHC 4069 Lecture Notes - Lecture 3: Unimodality, Quartile, Squared Deviations From The Mean

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