The following activities and questions relate to material covered in Chapter 2.2 Measures of the Location of the Data in Introductory Business Statistics (OpenStax).

Questions

1. This is a table of monthly ticket sales at the Yukon Beringia Interpretive Centre in 2018.
   

   Monthly Ticket Sales at Yukon Beringia Interpretive Centre ^[1]

   Month	Beringia 2018 Ticket Sales	Relative Frequency	Cumulative Frequency
   January	673
   February	814
   March	1670
   April	1303
   May	1347
   June	3519
   July	4745
   August	4065
   September	1808
   October	1170
   November	1475
   December	1309

   1. Complete the table.
   2. What proportion of 2018 ticket sales were sold in July and August?
   3. What proportion of ticket sales in the first 8 months of 2018?
2. Use the 2020 Yukon population by age group table below to:
   

   Age Group (yrs.)	Frequency	Relative Frequency
   0-9	4692
   10-19	4355
   20-29	5435
   30-39	7266
   40-49	5938
   50-59	5913
   60-69	5459
   70-79	2574
   80+	875

   1. Create a bar chart.
   2. Complete the table.
   3. Which age category has the highest frequency and what proportion of the total population is that category?
   4. Use 2 sentences to describe features of the bar chart
3. Forty randomly selected people in Yellowknife, NWT were asked the number of nights they saw northern lights last year. The results are as follows:
   

   Number of Nights Northern Lights Viewed	Frequency	Relative Frequency	Cumulative Frequency
   0	0
   1	15
   2	10
   3	2
   4	2
   5	2

   1. Complete the columns of the chart.
   2. Use a bar chart to graph the frequencies.
   3. What is the probability someone chosen randomly viewed at least one night of northern lights?
4. In a survey collecting data about the salaries earned by recent Yukon University graduates, Christy found that her salary was in the 85^th percentile. Should Christy be pleased by this result? Explain.
5. Thirty part-time grocery clerks who work at grocery store in northern Canada were asked, “What is your average weekly salary?” The results are in the table below.
   

   Weekly Salary ($)	Frequency
   No response	7
   200-250	5
   350-300	6
   300-350	6
   350-400	3
   400-450	1
   450-500	2

   1. What percentage of the survey did not give an answer?
   2. What percentage says their weekly salary is from $200.00 to $350.00?
   3. Construct a bar graph of the data.
6. The annual precipitation in Atlin, BC between 2005 and 2014 is as follows:
   

   Annual Precipitation in Altlin, BC ^[2]

   Year	Annual Atlin Precip. (mm)
   2005	307.3
   2006	24.1
   2007	50.0
   2008	143.8
   2009	66.4
   2010	54.2
   2011	85.9
   2012	259.7
   2013	330.8
   2014	279.4

   1. Organize the data into a line graph.
   2. Construct a histogram of the data.
   3. Calculate the sample mean.
   4. Find the interquartile range.

Solutions

1. 1. Monthly Ticket Sales at Yukon Beringia Interpretive Centre

      Month	Beringia 2018 Ticket Sales	Relative Frequency	Cumulative Frequency
      January	673	2.82%	2.82%
      February	814	3.41%	6.22%
      March	1670	6.99%	13.21%
      April	1303	5.45%	18.66%
      May	1347	5.64%	24.30%
      June	3519	14.73%	39.02%
      July	4745	19.86%	58.88%
      August	4065	17.01%	75.89%
      September	1808	7.57%	83.45%
      October	1170	4.90%	88.35%
      November	1475	6.17%	94.52%
      December	1309	5.48%	100%

   2. In July and August of 2018, (19.86%+17.01% =) 36.87% of 2018’s tickets were sold.
   3. In 2018, 75.89% of 2018’s tickets were sold in the first 8 months of the year.
2. 1. Bar chart of 2020 Yukon population by age group
      

   2. Age Group (yrs.)	Frequency	Relative Frequency
      0-9	4692	11.04%
      10-19	4355	10.25%
      20-29	5435	12.79%
      30-39	7266	17.09%
      40-49	5938	13.97%
      50-59	5913	13.91%
      60-69	5459	12.84%
      70-79	2574	6.06%
      80+	875	2.06%

   3. The age category with the highest frequency is Yukoners between 30-39 years of age occupying 17.09% of the total Yukon population.
   4. There is a lower probability of choosing a random Yukoner between 10 and 19 years of age than any other age group. There are almost as many Yukoners between the ages of 0 and 39 as there are Yukoners older than 40 yrs. old.

3. 1. Number of Nights Northern Lights Viewed	Frequency	Relative Frequency	Cumulative Frequency
      0	0	22.50%	22.50%
      1	15	37.50%	60.00%
      2	10	25.00%	85.00%
      3	2	5.00%	90.00%
      4	2	5.00%	95.00%
      5	2	5.00%	100.00%

   2. Bar chart of the frequency of viewing northern lights.
      
   3. The probability a randomly chosen person in Yellowknife viewed northern lights last year is 77.5%.
4. Christy should be pleased considering this means her salary is higher than 85% of people surveyed, or rather it is in the top 15% of people surveyed.
5. 1. The percentage of people who did not provide a response 7/30 = 0.2333 = 23.33%. 23.37% of grocery clerk refused to give answers.
   2. 16.67% + 20% + 20% = 56.67%. 56.67% of the grocery clerks says their weekly salary is from $200.00 to $350.00.
   3. Bar graph of part-time grocery employee weekly salary frequency.
      
6. 1. Line graph of annual precipitation in Atlin, BC.
      
   2. [latex]\text{Width of bins}= \dfrac{(\text{max }−\text{ min})}{\text{No. of bins}}= \dfrac{(330.80−24.10)}{6} = 51.12[/latex], use 50 mm for the width.
   3. Sample mean = 160.15 mm
   4. Interquartile Range = Q₃ − Q₁ = 286.375mm − 53.075 mm = 233.3 mm