Does age affect the number of cups of coffee one drinks in ...



5618582-447716MAY 2016MAY 20164768854041508Does age affect the number of cups of coffee one drinks in a working week at North London Collegiate School?Mathematical studies standard levelMira Trenner7900035000Does age affect the number of cups of coffee one drinks in a working week at North London Collegiate School?Mathematical studies standard levelMira Trennerright23002457450014820022760098000014820022Maths Studies Coursework Plan:Does age affect the number of cups of coffee one drinks in a working week at North London Collegiate School?I will be investigating whether there is any correlation between a person’s age and the number of cups of coffee they drink per day. I chose this topic as I have been drinking coffee since a reasonably young age and as I have gotten older I’ve noticed more of my peers drinking it.I intend to collect data from 10 people at random in each year group, from year 7 to year 13 at North London Collegiate School. This will give me a range of data from each year group, allowing me to establish a mean for the number of cups of coffee individuals of a given age drink. The size per year group is large enough that I will be able to see trends within age groups but small enough that I will be able to collect it easily. By using a large range of years I will be able to see more clearly any correlation. I am only looking at pupils because by Year 13 most people have reached a certain stage of maturity in their tastes. While not collecting data for staff member limits my range of ages, it would be impractical since they are less willing to disclose age. Furthermore, the range of ages would be dramatically increased but with a smaller sample for larger ages. In total I will be asking 70 people which will give me a large spread of data, hopefully minimising the effect of any anomalies. The list of people in each year group is numbered and so to select the individuals I will survey I will use a random number generator so that there is no human bias in the selection which could skew the results. To carry out the survey I will create an online survey using Surveymonkey, and then email it to my randomly selected individuals, as it will allow me to keep track of people’s responses and organise the responses for me. This will be especially useful as if someone does not reply to the survey I will be able to see who they are and follow them up by email and at school. Figure 1: screenshot of my survey with example responsesOn my survey I will ask 2 questions: “what is your date of birth?” and “how many cups of coffee did you drink over the course of the week?” By asking for individuals’ date of birth I will obtain continuous data which will give me a spread of data as age is continuous, and I will therefore be able to convert the ages into days. I will ask for the number of cups of coffee drunk in a week as the number may vary from day to day and therefore a longer period of time gives a better overall view. While different cups of coffee, such as espressos or filter coffees, may vary in strength and therefore affect the number an individual might drink, using the number of cups provides quantitative data and while different cups of coffee are not comparable in strength, it would not be possible to measure strength so I am therefore investigating the frequency of drinking a cup of coffee. This limitation is not possible to overcome since I do not have the equipment to measure the caffeine content of drinks. Let x = the agex= the mean age = the sumn = the total number of the sampleLet S = the variancey = the number of coffees drunk in the weeky= the mean number of cups of coffeeOnce I have collected the data I will begin by calculating the mean (x) and the standard deviation (σ) of the number of cups of coffee drunk per week by each year group. By separating my data in this way I will be able to see if individuals in different age brackets drink a similar number of cups of coffee and if the mean number varies from year group to year group.x=xnσ= (x-x)2n I will then plot a scatter graph with it to see if there is any visible correlation and then work out the Product Moment Correlation Coefficient (PMCC). From this I will be able to infer whether or not age and coffee consumption are correlated. If the PMCC value (r) is between -1 and 0 then they are negatively correlated and if between 0 and 1 they are positively correlated. The further from 0 it is, the more strongly correlated they are. r=SxySxSy Sxy= (x- x)(y-y)n Sx=x2n- x2 Sy=y2n- y2Statistical TestsYear 13Figure 1: table showing date of birth, age and number of cups of coffee drunk in the past week for year 13Date of BirthAge in days(as of 29/09/15)Number of cups of coffee drunk in the past week07/11/19976535015/11/19976527608/07/199862922605/03/19986417010/12/199765022108/11/199765341302/07/19986298925/04/19986366110/01/19986471729/11/199765136Let x = the number of cups of coffee drunk in the past weekLet = the sumLet n = the number of pieces of dataMean (x) number of cups of coffee:x=xn x=0+6+26+0+21+13+9+1+7+610 x=8.9 Standard deviation (σ) of number of cups of coffee:σ= (x-x)2n σ = (0-8.9+6-8.9+26-8.9+0-8.9+21-8.9+13-8.9+9-8.9+1-8.9+7-8.9+(6-8.9))210 σ=8.799621 σ=8.80 (to 3 significant figures) Year 12Figure 2: table showing date of birth, age and number of cups of coffee drunk in the past week for year 12Date of BirthAge in days(as of 29/09/15)Number of cups of coffee drunk in the past week13/05/19995983630/09/199862081218/12/19986129122/02/19996063907/04/19996019712/11/19986165001/03/199959822810/06/19995955503/12/199861441428/01/199960880Let x = the number of cups of coffee drunk in the past weekLet = the sumLet n = the number of pieces of dataMean (x) number of cups of coffee:x=xn x=6+12+1+9+7+0+28+5+14+010 x=8.2 Standard deviation (σ) of number of cups of coffee:σ= (x-x)2n σ = (6-8.2+12-8.2+1-8.2+9-8.2+7-8.2+0-8.2+28-8.2+5-8.2+14-8.2+(0-8.2))210 σ=8.456424 σ=8.46 (to 3 significant figures) Year 11Figure 3: table showing date of birth, age and number of cups of coffee drunk in the past week for year 11Date of BirthAge in days(as of 29/09/15)Number of cups of coffee drunk in the past week24/12/19995758309/10/19995834931/07/20005538406/03/20005685116/02/20005704029/09/199958441514/12/19995768517/11/199957951805/05/200056252101/10/199958422Let x = the number of cups of coffee drunk in the past weekLet = the sumLet n = the number of pieces of dataMean (x) number of cups of coffee:x=xn x=3+9+4+1+0+15+5+18+21+210 x=7.8 Standard deviation (σ) of number of cups of coffee:σ= (x-x)2n σ = (3-7.8+9-7.8+4-7.8+1-7.8+0-7.8+15-7.8+5-7.8+18-7.8+21-7.8+(2-7.8))210 σ=7.58360805 σ=7.58 (to 3 significant figures) Year 10Figure 4: table showing date of birth, age and number of cups of coffee drunk in the past week for year 10Date of BirthAge in days(as of 29/09/15)Number of cups of coffee drunk in the past week27/09/20005480106/08/20015167019/11/20005427808/12/20005222515/04/200152801012/06/20015222023/04/200152721802/10/20005475329/01/20015356314/11/200054324Let x = the number of cups of coffee drunk in the past weekLet = the sumLet n = the number of pieces of dataMean (x) number of cups of coffee:x=xn x=1+0+8+5+10+0+18+3+3+410 x=5.2 Standard deviation (σ) of number of cups of coffee:σ= (x-x)2n σ = (1-5.2+0-5.2+8-5.2+5-5.2+10-5.2+0-5.2+18-5.2+3-5.2+3-5.2+(4-5.2))210 σ=5.55377749 σ=5.55 (to 3 significant figures) Year 9Figure 5: table showing date of birth, age and number of cups of coffee drunk in the past week for year 9Date of BirthAge in days(as of 29/09/15)Number of cups of coffee drunk in the past week24/11/200150571423/06/20024846006/11/20015075626/10/20015086213/03/20024948027/07/20024812308/09/20015134430/12/200150211215/02/20024974009/09/200151339Let x = the number of cups of coffee drunk in the past weekLet = the sumLet n = the number of pieces of dataMean (x) number of cups of coffee:x=xn x=14+0+6+2+0+3+4+12+0+910 x=5 Standard deviation (σ) of number of cups of coffee:σ= (x-x)2n σ = (14-5+0-5+6-5+2-5+0-5+3-5+4-5+12-5+0-5+(9-5))210 σ=5.12076383 σ=5.12 (to 3 significant figures) Year 8Figure 6: table showing date of birth, age and number of cups of coffee drunk in the past week for year 8Date of BirthAge in days(as of 29/09/15)Number of cups of coffee drunk in the past week23/04/20034542206/07/20034468014/10/20024733007/01/20034648502/12/20024684117/12/20024669030/09/20024747322/05/20034513701/11/20024715424/03/200345720Let x = the number of cups of coffee drunk in the past weekLet = the sumLet n = the number of pieces of dataMean (x) number of cups of coffee:x=xn x=2+0+0+5+1+0+3+7+4+010 x=2.2 Standard deviation (σ) of number of cups of coffee:σ= (x-x)2n σ = (2-2.2+0-2.2+0-2.2+5-2.2+1-2.2+0-2.2+3-2.2+7-2.2+4-2.2+(0-2.2))210 σ=2.48551358 σ=2.49 (to 3 significant figures) Year 7Figure 7: table showing date of birth, age and number of cups of coffee drunk in the past week for year 7Date of BirthAge in days(as of 29/09/15)Number of cups of coffee drunk in the past week06/04/20044193029/10/20034353012/09/20034400022/08/20044055326/02/20044233001/12/20034320709/03/20044221218/11/20034333004/11/20034347002/07/200441061Let x = the number of cups of coffee drunk in the past weekLet = the sumLet n = the number of pieces of dataMean (x) number of cups of coffee:x=xn x=0+0+0+3+0+7+2+0+0+110 x=1.3 Standard deviation (σ) of number of cups of coffee:σ= (x-x)2n σ = (0-1.3+0-1.3+0-1.3+3-1.3+0-1.3+7-1.3+2-1.3+0-1.3+0-1.3+(1-1.3))210 σ=2.26323269 σ=2.26 (to 3 significant figures) Figure 8: table showing the mean and standard deviation of number of cups of coffee drunk in the past week for each year groupYear groupMean number of coffees drunk in a weekStandard deviation of number of coffees drunk in a week (to 3 significant figures)Year 138.98.80Year 128.28.46Year 117.87.58Year 105.25.55Year 955.12Year 82.22.49Year 71.32.26There is a clear trend of both increasing mean numbers of coffee drunk in a week and increasing standard deviation as the year groups get older. There is a clear indication that older girls drink more cups of coffee on average. However, the standard deviation increasing shows that while for some individuals there is a dramatic increase in coffee consumption between years 7 and 13, some individuals continue to drink minimal numbers or no cups of coffee, or the number increases at a far slower rate. This is likely to be because while age increases some individuals develop a taste for coffee, not everyone enjoys the beverage, whereas some younger individuals might enjoy it but might be discouraged from drinking at as it is commonly said that coffee stunts growth.Figure 9: scatter graph showing age in days against number of cups of coffee drunk in the past weekThe scatter graph appears to suggest that there is a positive correlation between age and number of cups of coffee drunk in a week; however, it does not appear to be a strong correlation. This concurs with the mean which increased as year group increased, creating a positive correlation, and the standard deviation which also increased, which is why the correlation does not appear to be particularly strong.Pearson Product Moment CoefficientLet x = the agex= the mean age = the sumn = the total number of the sampleLet S = the variancey = the number of coffees drunk in the weeky= the mean number of cups of coffeer=SxySxSy Sxy= (x- x)(y-y)n Sx=x2n- x2 Sy=y2n- y2 -17145568071000xx2yy2x-xy-y(x-x)(y-y)(x-x)(y-y)n653542706225001179.929-5.51429-6506.46-92.94956527426017296361171.9290.485714569.22248.13174962923958926426676936.928620.4857119193.65274.195641741177889001061.929-5.51429-5855.78-83.654650242276004214411146.92915.4857117761.01253.7287653442693156131691178.9297.4857148825.122126.0732629839664804981942.92863.4857143286.7846.95399636640525956111010.929-4.51429-4563.62-65.19466471418738417491115.9291.4857141657.95123.685016513424191696361157.9290.485714562.42248.034606598335796289636627.92860.485714304.99394.35705562083853926412144852.92866.4857145531.85179.0264461293756464111773.9286-4.51429-3493.73-49.9105606336759969981707.92863.4857142467.63735.25195601936228361749663.92861.485714986.408214.0915561653800722500809.9286-5.51429-4466.18-63.802559823578432428784626.928622.4857114096.94201.3848595535462025525599.9286-0.51429-308.535-4.4076461443774873614196788.92868.4857146694.62295.6374660883706374400732.9286-5.51429-4041.58-57.736857583315456439402.9286-2.51429-1013.08-14.4725583434035556981478.92863.4857141669.40823.84869553830669444416182.9286-1.51429-277.006-3.9572356853231922511329.9286-4.51429-1489.39-21.27757043253561600348.9286-5.51429-1924.09-27.48758443415233615225488.92869.4857144637.83766.25481576833269824525412.9286-0.51429-212.363-3.0337657953358202518324439.928612.485715492.82278.4688956253164062521441269.928615.485714180.03759.7148158423412896424486.9286-3.51429-1711.21-24.445854803003040011124.9286-4.51429-563.963-8.0566251672669788900-188.071-5.514291037.0814.8154254272945232986471.928572.485714178.79392.554198522227269284525-133.071-0.5142968.436730.97766852802787840010100-75.07144.485714-336.749-4.810752222726928400-133.071-5.51429733.793910.4827752722779398418324-83.071412.48571-1037.21-14.817254752997562539119.9286-2.51429-301.535-4.30764535628686736390.928571-2.51429-2.33469-0.0333554322950662441676.92857-1.51429-116.492-1.6641750572557324914196-298.0718.485714-2529.35-36.133648462348371600-509.071-5.514292807.16540.10236507525755625636-280.0710.485714-136.035-1.9433550862586739624-269.071-3.51429945.593913.5084849482448270400-407.071-5.514292244.70832.0672648122315534439-543.071-2.514291365.43719.50624513426357956416-221.071-1.51429334.76534.78236250212521044112144-334.0716.485714-2166.69-30.952749742474067600-381.071-5.514292101.33730.0191513326347689981-222.0713.485714-774.078-11.058345422062976424-813.071-3.514292857.36540.819544681996302400-887.071-5.514294891.56569.879547332240128900-622.071-5.514293430.2849.00399464821603904525-707.071-0.51429363.63675.1948146842193985611-671.071-4.514293029.40843.2772646692179956100-686.071-5.514293783.19454.0456347472253400939-608.071-2.514291528.86521.84093451320367169749-842.0711.485714-1251.08-17.8725471522231225416-640.071-1.51429969.25113.8464445722090318400-783.071-5.514294318.0861.6868541931758124900-1162.07-5.514296407.99491.5427743531894860900-1002.07-5.514295525.70878.9386944001936000000-955.071-5.514295266.53775.2362440551644302539-1300.07-2.514293268.75146.6964442331791828900-1122.07-5.514296187.42288.39175432018662400749-1035.071.485714-1537.82-21.968942211781684124-1134.07-3.514293985.45156.9350143331877488900-1022.07-5.514295635.99480.514243471889640900-1008.07-5.514295558.79479.4113441061685923611-1249.07-4.514295638.66580.55236374855204514007738651321939.52Sx=x2n- x2 x2=2045140077 x2n=204514007770 x2n=29216286.8 x=37485570 x=5355.071 x2=28676790 Sx= 29216286.8- 28676790 Sx=539496.8 Sy=y2n- y2 y2=5132 y2n=513270 x2n=73.31429 y=38670 y=5.514286 y2=30.40735 Sy= 73.31429- 30.40735 Sy=42.9069 Sxy= (x- x)(y-y)n r=SxySxSy r=1939.52539496.8×42.9069 r=0.403122 r=0.403 (to 3 significant figures) A positive r value suggests positive correlation, while a negative one suggests negative correlation. A number from 0<±0.2 suggests very weak correlation; a number from ±0.2<±0.4 suggests weak correlation; a number from ±0.4<±0.6 suggests moderate correlation; a number from ±0.6<±0.8 suggests strong correlation; a number from ±0.8<±1 suggests very strong correlation. This number supports what can be inferred from the standard deviation in that a large standard deviation implies weaker correlation. Similarly, the increasing mean suggests positive correlation, which the r value confirms.Therefore, the r value of 0.403 indicates that there is a moderate positive correlation between age and the number of cups of coffee drunk in a week. It would appear that there is some relationship between the two sets of data, but the correlation is not strong enough to state for certain that age affects the number of cups of coffee drunk in a week. This might be due to not everyone enjoying the taste of coffee regardless of age, and while older girls might use caffeine stimulants to get through their heavy workload, not everyone requires it.ConclusionHaving found the mean and standard deviation of the number of cups of coffee drunk by my samples from each year group, it appears that both increase with age. This would suggest that many older pupils drink more coffee than younger pupils. However, since the standard deviation also increases significantly, evidently for some age does not affect the number of cups of coffee drunk in a week, and they do not drink any. For example, 2 girls in year 13 drank no coffee in the past week and should they have been asked in year 7 they likely would give the same answer since coffee intake is very much dependent on personal preference. The scatter graph of age against number of cups of coffee drank in the past week as well as the PMCC also show that while there is a correlation between the two variables, it is only moderate. Therefore, one can conclude that while age does affect the number of cups of coffee drunk in a week, it does not affect it strongly.Bibliography, 17/01/16, 12.12, 17/01/16, 12.14, 17/01/16, 12.17, 17/01/16, 12.19 ................
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