MAY
2016
001482
0022
Does age affect the
number of cups of coffee
one drinks in a working
week at North London
Collegiate School?
MATHEMATICAL STUDIES STANDARD LEVEL
MIRA TRENNER
Maths 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 responses
On 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
1
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 age
𝑥̅ = the mean age
∑ = the sum
𝑛 = the total number of the sample
Let 𝑆 = the variance
𝑦 = the number of coffees drunk in the week
𝑦̅= the mean number of cups of coffee
Once I have collected the data I will begin by calculating the mean (𝑥̅ ) 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
1
𝑥̅ =
𝑛
∑(𝑥−𝑥̅ )2 2
√
𝑛
𝜎=
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 3.
𝑟=
𝑆𝑥𝑦
√𝑆𝑥 𝑆𝑦
𝑆𝑥𝑦 = ∑
𝑆𝑥 =
∑ 𝑥2
𝑛
(𝑥− 𝑥̅ )(𝑦−𝑦̅)
− 𝑥̅
𝑛
2
𝑆𝑦 =
∑ 𝑦2
𝑛
− 𝑦̅ 2
1
http://www.fgse.nova.edu/edl/secure/stats/lesson1.htm, 17/01/16, 12.12
http://www.bbc.co.uk/bitesize/standard/maths_ii/statistics/standard_deviation/revision/2/, 17/01/16, 12.14
3
http://revisionmaths.com/advanced-level-maths-revision/statistics/product-moment-correlation-coefficient, 17/01/16,
12.17
2
2
Statistical Tests
Year 13
Figure 1: table showing date of birth, age and number of cups of coffee drunk in the past
week for year 13
Date of Birth
Age in days
Number of cups
(as of 29/09/15) of coffee drunk
in the past week
07/11/1997
15/11/1997
08/07/1998
05/03/1998
10/12/1997
08/11/1997
02/07/1998
25/04/1998
10/01/1998
29/11/1997
6535
6527
6292
6417
6502
6534
6298
6366
6471
6513
0
6
26
0
21
13
9
1
7
6
Let 𝑥 = the number of cups of coffee drunk in the past week
Let ∑ = the sum
Let 𝑛 = the number of pieces of data
̅) number of cups of coffee:
Mean (𝒙
𝑥̅ =
𝑥̅ =
∑𝑥
𝑛
0+6+26+0+21+13+9+1+7+6
10
𝑥̅ = 8.9
Standard deviation (𝝈) of number of cups of coffee:
2
∑(𝑥−𝑥̅ )
𝜎= √
𝑛
𝜎 =
2
√∑((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))
10
3
𝜎 = 8.799621
𝜎 = 8.80 (𝑡𝑜 3 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑓𝑖𝑔𝑢𝑟𝑒𝑠)
Year 12
Figure 2: table showing date of birth, age and number of cups of coffee drunk in the past
week for year 12
Date of Birth
Age in days
Number of cups
(as of 29/09/15)
of coffee drunk
in the past week
13/05/1999
30/09/1998
18/12/1998
22/02/1999
07/04/1999
12/11/1998
01/03/1999
10/06/1999
03/12/1998
28/01/1999
5983
6208
6129
6063
6019
6165
5982
5955
6144
6088
6
12
1
9
7
0
28
5
14
0
Let 𝑥 = the number of cups of coffee drunk in the past week
Let ∑ = the sum
Let 𝑛 = the number of pieces of data
̅) number of cups of coffee:
Mean (𝒙
𝑥̅ =
𝑥̅ =
∑𝑥
𝑛
6+12+1+9+7+0+28+5+14+0
10
𝑥̅ = 8.2
Standard deviation (𝝈) of number of cups of coffee:
2
∑(𝑥−𝑥̅ )
𝜎= √
𝑛
4
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))
2
10
𝜎 = 8.456424
𝜎 = 8.46 (𝑡𝑜 3 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑓𝑖𝑔𝑢𝑟𝑒𝑠)
Year 11
Figure 3: table showing date of birth, age and number of cups of coffee drunk in the past
week for year 11
Date of Birth
Age in days
Number of cups
(as of 29/09/15) of coffee drunk
in the past week
24/12/1999
09/10/1999
31/07/2000
06/03/2000
16/02/2000
29/09/1999
14/12/1999
17/11/1999
05/05/2000
01/10/1999
5758
5834
5538
5685
5704
5844
5768
5795
5625
5842
3
9
4
1
0
15
5
18
21
2
Let 𝑥 = the number of cups of coffee drunk in the past week
Let ∑ = the sum
Let 𝑛 = the number of pieces of data
̅) number of cups of coffee:
Mean (𝒙
𝑥̅ =
𝑥̅ =
∑𝑥
𝑛
3+9+4+1+0+15+5+18+21+2
10
𝑥̅ = 7.8
Standard deviation (𝝈) of number of cups of coffee:
2
∑(𝑥−𝑥̅ )
𝜎= √
𝑛
5
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))
2
10
𝜎 = 7.58360805
𝜎 = 7.58 (𝑡𝑜 3 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑓𝑖𝑔𝑢𝑟𝑒𝑠)
Year 10
Figure 4: table showing date of birth, age and number of cups of coffee drunk in the past
week for year 10
Date of Birth
Age in days
Number of cups
(as of 29/09/15) of coffee drunk
in the past week
27/09/2000
06/08/2001
19/11/2000
08/12/2000
15/04/2001
12/06/2001
23/04/2001
02/10/2000
29/01/2001
14/11/2000
5480
5167
5427
5222
5280
5222
5272
5475
5356
5432
1
0
8
5
10
0
18
3
3
4
Let 𝑥 = the number of cups of coffee drunk in the past week
Let ∑ = the sum
Let 𝑛 = the number of pieces of data
̅) number of cups of coffee:
Mean (𝒙
𝑥̅ =
𝑥̅ =
∑𝑥
𝑛
1+0+8+5+10+0+18+3+3+4
10
𝑥̅ = 5.2
Standard deviation (𝝈) of number of cups of coffee:
6
2
∑(𝑥−𝑥̅ )
𝜎= √
𝑛
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))
2
10
𝜎 = 5.55377749
𝜎 = 5.55 (𝑡𝑜 3 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑓𝑖𝑔𝑢𝑟𝑒𝑠)
Year 9
Figure 5: table showing date of birth, age and number of cups of coffee drunk in the past
week for year 9
Date of Birth
Age in days
Number of cups
(as of 29/09/15) of coffee drunk
in the past week
24/11/2001
23/06/2002
06/11/2001
26/10/2001
13/03/2002
27/07/2002
08/09/2001
30/12/2001
15/02/2002
09/09/2001
5057
4846
5075
5086
4948
4812
5134
5021
4974
5133
14
0
6
2
0
3
4
12
0
9
Let 𝑥 = the number of cups of coffee drunk in the past week
Let ∑ = the sum
Let 𝑛 = the number of pieces of data
̅) number of cups of coffee:
Mean (𝒙
𝑥̅ =
𝑥̅ =
∑𝑥
𝑛
14+0+6+2+0+3+4+12+0+9
10
𝑥̅ = 5
7
Standard deviation (𝝈) of number of cups of coffee:
2
∑(𝑥−𝑥̅ )
𝜎= √
𝑛
2
∑((14−5)+(0−5)+(6−5)+(2−5)+(0−5)+(3−5)+(4−5)+(12−5)+(0−5)+(9−5))
𝜎 = √
10
𝜎 = 5.12076383
𝜎 = 5.12 (𝑡𝑜 3 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑓𝑖𝑔𝑢𝑟𝑒𝑠)
Year 8
Figure 6: table showing date of birth, age and number of cups of coffee drunk in the past
week for year 8
Date of Birth
Age in days
Number of cups
(as of 29/09/15) of coffee drunk
in the past week
23/04/2003
06/07/2003
14/10/2002
07/01/2003
02/12/2002
17/12/2002
30/09/2002
22/05/2003
01/11/2002
24/03/2003
4542
4468
4733
4648
4684
4669
4747
4513
4715
4572
2
0
0
5
1
0
3
7
4
0
Let 𝑥 = the number of cups of coffee drunk in the past week
Let ∑ = the sum
Let 𝑛 = the number of pieces of data
̅) number of cups of coffee:
Mean (𝒙
𝑥̅ =
𝑥̅ =
∑𝑥
𝑛
2+0+0+5+1+0+3+7+4+0
10
𝑥̅ = 2.2
8
Standard deviation (𝝈) of number of cups of coffee:
2
∑(𝑥−𝑥̅ )
𝜎= √
𝑛
2
∑((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))
𝜎 = √
10
𝜎 = 2.48551358
𝜎 = 2.49 (𝑡𝑜 3 𝑠𝑖𝑔𝑛𝑖𝑓𝑖𝑐𝑎𝑛𝑡 𝑓𝑖𝑔𝑢𝑟𝑒𝑠)
Year 7
Figure 7: table showing date of birth, age and number of cups of coffee drunk in the past
week for year 7
Date of Birth
Age in days
Number of cups
(as of 29/09/15) of coffee drunk
in the past week
06/04/2004
29/10/2003
12/09/2003
22/08/2004
26/02/2004
01/12/2003
09/03/2004
18/11/2003
04/11/2003
02/07/2004
4193
4353
4400
4055
4233
4320
4221
4333
4347
4106
0
0
0
3
0
7
2
0
0
1
Let 𝑥 = the number of cups of coffee drunk in the past week
Let ∑ = the sum
Let 𝑛 = the number of pieces of data
̅) number of cups of coffee:
Mean (𝒙
𝑥̅ =
𝑥̅ =
∑𝑥
𝑛
0+0+0+3+0+7+2+0+0+1
10
𝑥̅ = 1.3
9
Standard deviation (𝝈) of number of cups of coffee:
2
∑(𝑥−𝑥̅ )
𝜎= √
𝑛
2
∑((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))
𝜎 = √
10
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 group
Year group
Mean number of coffees
Standard deviation of
drunk in a week
number of coffees drunk in
a week (to 3 significant
figures)
Year 13
Year 12
Year 11
Year 10
Year 9
Year 8
Year 7
8.9
8.2
7.8
5.2
5
2.2
1.3
8.80
8.46
7.58
5.55
5.12
2.49
2.26
There 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 growth4.
4
http://kidshealth.org/teen/expert/nutrition/coffee.html, 17/01/16, 12.19
10
Figure 9: scatter graph showing age in days against number of cups of coffee drunk in the
past week
Scatter graph showing age in days against number of cups
of coffee drunk in the past week
30
28
number of cups of coffee drunk in the past week
26
24
22
20
18
16
14
12
10
8
6
4
2
0
3500 3700 3900 4100 4300 4500 4700 4900 5100 5300 5500 5700 5900 6100 6300 6500 6700
age in days
The 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 Coefficient
Let 𝑥 = the age
𝑥̅ = the mean age
∑ = the sum
𝑛 = the total number of the sample
Let 𝑆 = the variance
𝑦 = the number of coffees drunk in the week
𝑦̅= the mean number of cups of coffee
𝑟=
𝑆𝑥𝑦
√𝑆𝑥 𝑆𝑦
11
𝑆𝑥𝑦 = ∑
𝑆𝑥 = (
(𝑥− 𝑥̅ )(𝑦−𝑦̅)
∑ 𝑥2
𝑛
𝑥
𝑛
2
− 𝑥̅ )
𝑥2
𝑆𝑦 = (
𝑦2
𝑦
𝑥 − 𝑥̅
∑ 𝑦2
𝑛
𝑦 − 𝑦̅
6535
42706225
0
0
1179.929
-5.51429
6527
42601729
6
36
1171.929
0.485714
6292
39589264
26
676
936.9286
20.48571
6417
41177889
0
0
1061.929
-5.51429
6502
42276004
21
441
1146.929
15.48571
6534
42693156
13
169
1178.929
7.485714
6298
39664804
9
81
942.9286
3.485714
6366
40525956
1
1
1010.929
-4.51429
6471
41873841
7
49
1115.929
1.485714
6513
42419169
6
36
1157.929
0.485714
5983
35796289
6
36
627.9286
0.485714
6208
38539264
12
144
852.9286
6.485714
6129
37564641
1
1
773.9286
-4.51429
6063
36759969
9
81
707.9286
3.485714
6019
36228361
7
49
663.9286
1.485714
6165
38007225
0
0
809.9286
-5.51429
5982
35784324
28
784
626.9286
22.48571
5955
35462025
5
25
599.9286
-0.51429
6144
37748736
14
196
788.9286
8.485714
6088
37063744
0
0
732.9286
-5.51429
5758
33154564
3
9
402.9286
-2.51429
5834
34035556
9
81
478.9286
3.485714
5538
30669444
4
16
182.9286
-1.51429
5685
32319225
1
1
329.9286
-4.51429
5704
32535616
0
0
348.9286
-5.51429
5844
34152336
15
225
488.9286
9.485714
5768
33269824
5
25
412.9286
-0.51429
5795
33582025
18
324
439.9286
12.48571
5625
31640625
21
441
269.9286
15.48571
5842
34128964
2
4
486.9286
-3.51429
5480
30030400
1
1
124.9286
-4.51429
5167
26697889
0
0
-188.071
-5.51429
5427
29452329
8
64
71.92857
2.485714
5222
27269284
5
25
-133.071
-0.51429
5280
27878400
10
100
-75.0714
4.485714
5222
27269284
0
0
-133.071
-5.51429
5272
27793984
18
324
-83.0714
12.48571
− 𝑦̅ 2 )
(𝑥 − 𝑥̅ )(𝑦
− 𝑦̅)
(𝑥 − 𝑥̅ )(𝑦 − 𝑦̅)
𝑛
-6506.46
-92.9495
569.2224
8.131749
19193.65
274.195
-5855.78
-83.654
17761.01
253.7287
8825.122
126.0732
3286.78
46.95399
-4563.62
-65.1946
1657.951
23.68501
562.4224
8.034606
304.9939
4.357055
5531.851
79.02644
-3493.73
-49.9105
2467.637
35.25195
986.4082
14.09155
-4466.18
-63.8025
14096.94
201.3848
-308.535
-4.40764
6694.622
95.63746
-4041.58
-57.7368
-1013.08
-14.4725
1669.408
23.84869
-277.006
-3.95723
-1489.39
-21.277
-1924.09
-27.487
4637.837
66.25481
-212.363
-3.03376
5492.822
78.46889
4180.037
59.71481
-1711.21
-24.4458
-563.963
-8.05662
1037.08
14.81542
178.7939
2.554198
68.43673
0.977668
-336.749
-4.8107
733.7939
10.48277
-1037.21
-14.8172
12
∑
𝑆𝑥 =
5475
29975625
3
9
119.9286
-2.51429
5356
28686736
3
9
0.928571
-2.51429
5432
29506624
4
16
76.92857
-1.51429
5057
25573249
14
196
-298.071
8.485714
4846
23483716
0
0
-509.071
-5.51429
5075
25755625
6
36
-280.071
0.485714
5086
25867396
2
4
-269.071
-3.51429
4948
24482704
0
0
-407.071
-5.51429
4812
23155344
3
9
-543.071
-2.51429
5134
26357956
4
16
-221.071
-1.51429
5021
25210441
12
144
-334.071
6.485714
4974
24740676
0
0
-381.071
-5.51429
5133
26347689
9
81
-222.071
3.485714
4542
20629764
2
4
-813.071
-3.51429
4468
19963024
0
0
-887.071
-5.51429
4733
22401289
0
0
-622.071
-5.51429
4648
21603904
5
25
-707.071
-0.51429
4684
21939856
1
1
-671.071
-4.51429
4669
21799561
0
0
-686.071
-5.51429
4747
22534009
3
9
-608.071
-2.51429
4513
20367169
7
49
-842.071
1.485714
4715
22231225
4
16
-640.071
-1.51429
4572
20903184
0
0
-783.071
-5.51429
4193
17581249
0
0
-1162.07
-5.51429
4353
18948609
0
0
-1002.07
-5.51429
4400
19360000
0
0
-955.071
-5.51429
4055
16443025
3
9
-1300.07
-2.51429
4233
17918289
0
0
-1122.07
-5.51429
4320
18662400
7
49
-1035.07
1.485714
4221
17816841
2
4
-1134.07
-3.51429
4333
18774889
0
0
-1022.07
-5.51429
4347
18896409
0
0
-1008.07
-5.51429
4106
16859236
1
1
-1249.07
-4.51429
374855
2045140077
386
5132
∑ 𝑥2
𝑛
-301.535
-4.30764
-2.33469
-0.03335
-116.492
-1.66417
-2529.35
-36.1336
2807.165
40.10236
-136.035
-1.94335
945.5939
13.50848
2244.708
32.06726
1365.437
19.50624
334.7653
4.782362
-2166.69
-30.9527
2101.337
30.0191
-774.078
-11.0583
2857.365
40.8195
4891.565
69.8795
3430.28
49.00399
363.6367
5.19481
3029.408
43.27726
3783.194
54.04563
1528.865
21.84093
-1251.08
-17.8725
969.251
13.84644
4318.08
61.68685
6407.994
91.54277
5525.708
78.93869
5266.537
75.23624
3268.751
46.69644
6187.422
88.39175
-1537.82
-21.9689
3985.451
56.93501
5635.994
80.5142
5558.794
79.41134
5638.665
80.55236
1939.52
− 𝑥̅ 2
∑ 𝑥 2 = 2045140077
∑ 𝑥2
𝑛
∑ 𝑥2
𝑛
=
2045140077
70
= 29216286.8
374855
𝑥̅ = 70
𝑥̅ = 5355.071
𝑥̅ 2 = 28676790
13
𝑆𝑥 = 29216286.8 − 28676790
𝑆𝑥 = 539496.8
𝑆𝑦 =
∑ 𝑦2
− 𝑦̅ 2
𝑛
∑ 𝑦 2 = 5132
∑ 𝑦2
𝑛
∑ 𝑥2
𝑛
=
5132
70
= 73.31429
386
𝑦̅ = 70
𝑦̅ = 5.514286
𝑦̅ 2 = 30.40735
𝑆𝑦 = 73.31429 − 30.40735
𝑆𝑦 = 42.9069
𝑆𝑥𝑦 = ∑
𝑟=
𝑟=
(𝑥− 𝑥̅ )(𝑦−𝑦̅)
𝑛
𝑆𝑥𝑦
√𝑆𝑥 𝑆𝑦
1939.52
√539496.8×42.9069
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.
14
Conclusion
Having 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.
15
Bibliography
http://www.fgse.nova.edu/edl/secure/stats/lesson1.htm, 17/01/16, 12.12
http://www.bbc.co.uk/bitesize/standard/maths_ii/statistics/standard_deviation/revision/2/,
17/01/16, 12.14
http://revisionmaths.com/advanced-level-maths-revision/statistics/product-momentcorrelation-coefficient, 17/01/16, 12.17
http://kidshealth.org/teen/expert/nutrition/coffee.html, 17/01/16, 12.19
16