Mathematics
Minitab Statistics Questions Discussions

Question Description

I don’t know how to handle this Statistics question and need guidance.

You will need to be familiar with using the MINITAB. There are 6 simple questions, some questions must use minitab to answer.


Unformatted Attachment Preview

Question 1 The Minitab file that you require for this question should be downloaded from the ‘Assessment’ area on the module website. The data used in this question are about the numbers of students on three of the five most popular modules at the OU. The variable ModuleName contains the name of the module, and the variables 2015/16, 2016/17, 2017/18, 2018/19 contain the number of students at the start of each of the modules in each of the academic years 2015/16 to 2018/19. The variable MedianNumber contains the median of the number of students on each module. These data are given in the Minitab worksheet popular modules.mtw. Run Minitab and open this worksheet. The mean number of students on a module over the four years is mean number = (2015/16 + 2016/17 + 2017/18 + 2018/19)/4. (a) Calculate by hand the median number of students on AA100 and show all your working in your answer. (You can check that you have the same answer as in the Minitab worksheet.) (b) Use Minitab to produce a column of values, headed MeanNumber, containing the mean numbers of students on each module. Include this column of values in your answer. (c) Use Minitab to calculate a column of values, headed Diff, containing the differences between the mean and the median numbers of students on each module. Use Minitab to round the differences to the nearest whole number, i.e. zero decimal places, and include this column of values in your answer. (d) The range of the number of students on MST124 over the period is 1209. Using Minitab, or by hand, calculate the corresponding ranges for AA100 and for B100. What does the comparison of the ranges tell you about the numbers of students on MST124? Question 2 The Minitab file that you require for this question should be downloaded from the ‘Assessment’ area on the module website. The data used in this question relate to a measure of UK biodiversity. Insects are important pollinators and each year the number of 1km grid squares in which insect pollinators are found is recorded. An ‘occupancy index’ is calculated from these data and scaled so that for the first year (1980) the index is 100. (Data source: jncc.defra.gov.uk/page-6851.) These data are given in the Minitab worksheet pollinators.mtw. In the worksheet, for each year, the variable All Index contains the occupancy index for all insect pollinators and the variable Bees Index contains the corresponding indicator for wild bees only. Run Minitab and open this worksheet. Figure 1 shows a scatterplot of Bees Index (wild bee pollinators) against Year from 1980 to 2016, with a straight-line model fitted through the points. Figure 1 (a) By looking at the data file in the Minitab worksheet pollinators.mtw, in which year was the Bees Index highest and what was the value of Bees Index in that year? Describe two main features of the scatterplot for the Bees Index data against Year over this period. (b) Comment in general terms on whether the scatter of points around the straight-line model has changed over the period, and whether the straightline model provides an adequate representation of the data over this period. Give a reason for your answer to the latter part of the question. (c) Use Minitab to produce a scatterplot of All Index on the vertical axis against Year on the horizontal axis. Do not attempt to add a straight line to these data. Include a copy of your scatterplot in your answer. Describe briefly what the plot tells you, including whether or not you think that a straight-line model would be an appropriate thing to contemplate for these data. page 2 of 7 Question 3 The Minitab file that you require for this question should be downloaded from the ‘Assessment’ area on the module website. The National Survey of Young People’s Well-Being, 2010 collected information on how happy young people reported they felt. The data are available at beta.ukdataservice.ac.uk/datacatalogue/studies/study?id=7899. The Minitab worksheet well being secondary.mtw is an extract of the data and contains the (modified) school identifier and the average score of pupils, at 82 secondary schools, on an overall happiness scale. The happiness scale runs from 0, which represents very unhappy, through to 10, which is very happy. Open this worksheet in Minitab. (a) Produce the default stemplot of the average happiness score of pupils using Minitab (i.e. the stemplot produced when the Increment field is left blank and the Trim outliers option is not selected). Include a copy of your plot as your answer. (b) Briefly describe the shape of the stemplot that you produced in part (a). Your answer should consider whether the distribution is unimodal, bimodal or multimodal, whether it is symmetric, right-skew or left-skew, and whether or not there are outliers. Justify your conclusions. (c) Use the stemplot that you obtained in part (a) to find the median average happiness score of pupils. Remember to show your working. page 3 of 7 Question 4 Do not use Minitab to answer this question. The Higher Education Statistics Authority (HESA) publishes the median salaries of full-time first degree leavers who were employed in the UK in a professional job (www.hesa.ac.uk/news/28-06-2018/sfr250-higher-education -leaver-statistics). The stemplot in Figure 2 was obtained from the data for 2016/17. Stem-and-Leaf Display: Salary Stem-and-leaf of Salary N = 18 Leaf Unit = 100 2 19 00 5 20 000 7 21 00 (5) 22 00555 6 23 6 24 00 4 25 0 3 26 5 2 27 2 28 2 29 2 30 0 1 31 0 n = 18 19|0 represents £19000 Figure 2 (a) Use Figure 2 to calculate the median, upper quartile and lower quartile of the data. Show all your working.What other values, in addition to those that you have calculated in part (a), would you include in a five-figure summary? Give their values as part of your answer. (b) Calculate the range and the interquartile range for the data shown in Figure 2. Explain which you think is the most suitable measure of spread. (c) Why do you think HESA publish median salaries and not mean salaries? (You might draw on evidence from the stemplot to support your answer.) page 4 of 7 Question 5 The University has developed some statistical models that can generate information on how likely registered students are to complete all the assignments for a given module. This information is usually summarised as a number somewhere on a scale from 0 to 1 – which in this question will be called the ‘likelihood’ – with 0 meaning very unlikely to complete, and 1 meaning very likely to complete. Figure 3 is a boxplot showing this information for all the students registered in a geographical area for M140 in a previous year. Figure 3 (a) What does the boxplot tell us about the distribution of this batch of data? Justify your answer. (b) The mean value of the likelihood in Figure 3 was correctly calculated as 0.69 and the median value correctly calculated as 0.74. It was realised that the data for two students had been included in error and, after excluding their data, the mean and median were both correctly recalculated. The new value of the mean was 0.70 and the median remained 0.74. How could the mean value have changed but not the median? Make two valid points to answer this part of the question. (c) The statistical model that generates the likelihood of completing all assignments on M140 for each student uses data available at the start of the module that reflect each student’s motivation, opportunity, determination, resilience and interest in study. Where would you place yourself – in terms of the median, quartiles and whiskers – on the boxplot? Briefly justify your answer. page 5 of 7 Question 6 The Office for National Statistics publishes the Consumer Prices Index (CPI) (www.ons.gov.uk/economy/inflationandpriceindices). The monthly values of the CPI, for the last four months of 2018, 2017 and 2016, are listed in Table 1. Table 1 CPI values CPI 2018 CPI 2017 CPI 2016 September 106.6 104.1 101.1 October November 106.7 107.0 104.2 104.6 101.2 101.4 December 107.1 104.9 101.9 (a) Use the values of the CPI in Table 1 to calculate the annual inflation rates, based on the CPI, for each of the months September 2018, September 2017, December 2018 and December 2017, as a percentage rounded to two decimal places. (The base date is January 2015.) (b) Comment briefly on • the September 2018 inflation rate compared to the September 2017 rate • the December 2018 inflation rate compared to the December 2017 rate • how the inflation rate in September 2018 compared with that in December 2018, relative to the same comparison in 2017. (There is no need to try to justify any changes that you observe.) (c) A CPI index-linked pension was £600 per month in October 2017. How much should the pension be per month in October 2018? (d) Based on the CPI, calculate the purchasing power (in pence) of the pound in November 2018 compared to two years earlier. page 6 of 7 Figure descriptions Figure 1 in Question 2 A scatterplot showing the occupancy index of the wild bees as pollinators for each year from 1980 to 2016. The horizontal axis is labelled ‘Year’. The intervals are given in steps of 10 years, from 1980 to 2020. The vertical axis is labelled ‘Bees Index’. The intervals are given in steps of 5, from 70 to 105. The plot consists of a straight-line model, which decreases from about (1980, 105) to (2016, 83), and 37 points at (1980, 100.00), (1981, 99.32), (1982, 99.25), (1983, 100.88), (1984, 102.57), (1985, 102.06), (1986, 100.44), (1987, 98.85), (1988, 96.27), (1989, 94.84), (1990, 94.09), (1991, 95.44), (1992, 97.45), (1993, 99.91), (1994, 103.53), (1995, 103.78), (1996, 102.51), (1997, 100.65), (1998, 99.15), (1999, 97.68), (2000, 98.71), (2001, 95.48), (2002, 93.95), (2003, 95.51), (2004, 96.19), (2005, 97.12), (2006, 97.59), (2007, 94.30), (2008, 89.85), (2009, 84.37), (2010, 81.51), (2011, 80.65), (2012, 77.65), (2013, 74.14), (2014, 74.82), (2015, 79.55), (2016, 82.73). Figure 2 in Question 4 Above the stemplot is written: ‘Stem-and-Leaf Display: Salary Stem and leaf of Salary N = 18 Leaf Unit = 100’ There is then a stemplot with 13 levels and the numbers in the stem are: 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 and 31. Level 19 has 2 leaves 0. Level 20 has 3 leaves 0. Level 21 has 2 leaves 0. Level 22 has 2 leaves 0 and 3 leaves 5. Level 23 has no leaves. Level 24 has 2 leaves 0. Level 25 has a single leaf 0. Level 26 has a single leaf 5. Levels 27, 28 and 29 have no leaves. Level 30 has a single leaf 0. Level 31 has a single leaf 0. Beneath the stemplot is written ‘n = 18’ then ‘19 vertical line 0 represents £19 000’. Figure 3 in Question 5 A horizontal boxplot showing the likelihood of completing all assignments for M140. The horizontal axis is labelled ‘Likelihood’. The intervals are given in steps of 0.1, from 0.0 to 1.0. The plot consists of two isolated stars near 0.0, a group of stars at about 0.17 to 0.22, a horizontal line commencing at about 0.22 and ending at about 0.6, a horizontal box commencing at about 0.6 and ending at about 0.85, with a vertical line through the box at about 0.74, and another horizontal line commencing at about 0.85 and ending at about 0.96. page 7 of 7 ...
Purchase answer to see full attachment
Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service.

Final Answer

Attached.

Question 1
The Minitab file that you require for this question should be downloaded from the
‘Assessment’ area on the module website.
The data used in this question are about the numbers of students on three of
the five most popular modules at the OU. The variable ModuleName contains
the name of the module, and the variables 2015/16, 2016/17, 2017/18,
2018/19 contain the number of students at the start of each of the modules
in each of the academic years 2015/16 to 2018/19. The variable
MedianNumber contains the median of the number of students on each
module. These data are given in the Minitab worksheet popular
modules.mtw. Run Minitab and open this worksheet.
The mean number of students on a module over the four years is mean
number = (2015/16 + 2016/17 + 2017/18 + 2018/19)/4.
(a) Calculate by hand the median number of students on AA100 and show all
your working in your answer. (You can check that you have the same
answer as in the Minitab worksheet.)

To get the median, we arrange values in ascending order. For count of data
that is odd, for example 5, then the median is the middle value but for an
even number count of data, the median is the average of the two middle
values.
For AA100 data;
AA100-The arts past and present

4960

4404

4504

4366

In ascending order; 4366, 4404, 4504,4960
The median = (4404+4504)/2 = 4454
(b) Use Minitab to produce a column of values, headed MeanNumber, containing
the mean numbers of students on each module. Include this
column of values in your answer.
ModuleName
AA100-The arts past and present
B100-An introduction to business and management
MST124-Essential mathematics 1

MeanNumber
4558.5
4138.25
3514.5

(c) Use Minitab to calculate a column of values, headed Diff, containing the
differences between the mean and the median numbers of students on
each module. Use Minitab to round the differences to the nearest whole
number, i.e. zero decimal places, and include this column of

values in your answer.
ModuleName
AA100-The arts past and present
B100-An introduction to business and management
MST124-Essential mathematics 1

Diff
105
93
111

(d) The range of the number of students on MST124 over the period is 1209.
Using Minitab, or by hand, calculate the corresponding ranges for
AA100 and for B100. What does the comparison of the ranges tell
you about the numbers of students on MST124?

ModuleName
AA100-The arts past and present
B100-An introduction to business and management
MST124-Essential mathematics 1

Range
594
1086
1209

The ranges for AA100 and B100 are 594 and 1086 respectively. This indicates
that the variability in MST124 is much greater than for the other courses.

Question 2
The Minitab file that you require for this question should be downloaded from the
‘Assessment’ area on the module website.
The data used in this question relate to a measure of UK biodiversity. Insects
are important pollinators and each year the number of 1km grid squares in
which insect pollinators are found is recorded. An ‘occupancy index’ is
calculated from these data and scaled so that for the first year (1980) the
index is 100. (Data source: jncc.defra.gov.uk/page-6851.) These data are given
in the Minitab worksheet pollinators.mtw. In the worksheet, for each year,
the variable All Index contains the occupancy index for all insect
pollinators and the variable Bees Index contains the corresponding
indicator for wild bees only. Run Minitab and open this wor...

mickeygabz (5205)
Cornell University

Anonymous
Solid work, thanks.

Anonymous
The tutor was great. I’m satisfied with the service.

Anonymous
Goes above and beyond expectations !

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4