- Level: AS and A Level
- Subject: Maths
- Word count: 5070
To test if my secondary evidence is correct and therefor to find if adult men have a higher pulse rate or adult women and the average pulse rate for both sexes.
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Introduction
(Page 1 of 24)
MOHAMMED EMAMY
MODUAL 2 UNIT 5 COURSEWORK. AQA
PULSE RATES
Introduction
Not everyone has the same pulse rate, and pulse rate cane be effected by a number of different variables. For my task I will be investigating the difference in MEN and WOMEN’S pulse rates.
In order to form my hypotheses I have used secondary data from the Internet, cited at: www.vitalstatistcs.htm. Statistics show that the average male pulse rate is about 72, and the average adult female is between 76 to 80, and the average pulse rate for men and women is between 60 – 80.
AIM
To test if my secondary evidence is correct and therefor to find if adult men have a higher pulse rate or adult women and the average pulse rate for both sexes.
HYPTHESIS
On average Adult men will have a pulse rate between 71 – 73, adult women will have a pulse rate of 76 – 80, and the average pulse rate for both sexes will be between 60 – 80.
OBJECTIVES
1.To collect data from a suitable number of individuals using an appropriate sampling method.
2. To present the data in a meaningful way.
3. To interpret data and analyse results and diagrams.
4. To draw conclusions on analysis, state weather the prediction was correct.
(Page 2 of 24)
METHOD
In order to test my hypothesis I will use stratified random sampling, as it is more accurate then random sampling. Therefore I can take into account the age of my subjects, since age is also an important factor in individuals pulse rates.
For each sex I have used a total sample of 60 people and divided them into 3 categories (sratum) of age groups. Using random sampling (Giving each individual a number and selecting random numbers by using the RAN button on my calculator.) A sample of 10 is then taken from each group, giving me a total sample of 30 for each sex.
Middle
93
1
1
2
93
93
186
380.25
282.24
388.09
Totals
30
30
60
2205
2285
4490
2017.5
2201
4051.31
MEN | WOMEN | MEN & WOMEN | |
Standard deviation √∑F(x - )2 () | 8.20 (to3sf) | 8.57 (to3sf) | 8.22 (to3sf) |
(Page 5 of 24)
My results for men show that the mean obtained from the grouped data is outside the predicted pulse rate range for men. However as the mean and the standard deviation obtained from the grouped data can only be an estimate, since there is a spread in each group where the mid interval is applied. Therefor I have used the standard deviationand the mean obtained from the raw data. I can also use the raw data to find the median, interquartile range and the semi-interquartile range for each gender.The mode however is not relevant in this case, as there are several identical pulse rates in each group.
Also In relation to the second part of my hypothesis, by adding the frequencies of men and women I have a larger total frequency of 60. I can find the mean and the standard deviation for the frequency of both sexes added by using the raw data.
(See overleaf, page 6)FORRAW DATA SORTED IN ORDER AND BY GENDER.
My next step is apply the data collected in a frequency distribution table for each sex and represent it in a population pyramid, as this will allow me to compare the distribution of two sets of data at a glance. I will also be able to see in which modal classes the largest frequency occurs.
(See overleaf, page 7)FOR POPULATION GRAPH AND FREQUENCY DISTRIBUTION TABLE FOR MEN AND WOMEN.
(Page 8 of 24)
As the range is a very crude measure of spread I have chosen to use the 10-90thpercentiles to avoid the extreme outliers of my data from each sex and the frequency of both sexes added together. Hence I have drawn the respective cumulative frequency curves for each sex and both sexes added together and found the 10-90thpercentile range.
BELOW FOLLOWES MY CUMALATIVE FREQUENCY TABLE BY GENDER AND THE TOATAL FREQUENCY OF MEN AND WOMEN ADDED:
Pulse Rates | Frequency for men | Frequency for Women | Frequency for Men & Women | Cumulative Frequency for Men | Cumulative Frequency for Women | Cumulative Frequency for Men & Women |
56 - 60 | 2 | 1 | 3 | 2 | 1 | 3 |
61 - 65 | 3 | 3 | 6 | 5 | 4 | 9 |
66 - 70 | 5 | 4 | 9 | 10 | 8 | 18 |
71 - 75 | 9 | 5 | 14 | 19 | 13 | 32 |
76 - 80 | 5 | 7 | 12 | 24 | 20 | 44 |
81 - 85 | 4 | 6 | 10 | 28 | 26 | 54 |
86 - 90 | 1 | 3 | 4 | 29 | 29 | 58 |
91 - 95 | 1 | 1 | 2 | 30 | 30 | 60 |
(See overleaf, page 9)FOR PERCENTILE RANGE, REPRESENTINGEACH SEX.
(See overleaf, page 10) FORPERCENTILE RANGE, REPRESENTINGFREQUENCY OFBOTH SEXES ADDED.
(Page 11 of 24)
However as averages can only provide a typical value for my data I need to know the spread (or dispersion) of my data to get a complete picture. As the standard deviation takes into account all the data, I have decided to use the interquartile range, which allows me to cut out any extreme values. It also allows me to find 50% of my values (pulse rates) that lie between the upper and lower quartiles, in comparison to the 80% of my values (pulse rates) obtained from the 10-90th percentile range. Furthermore it allows me to find the skeweness of my data, if skewed. Other advantages are that it permits me also to visually see the outliers of my data if any by drawing a box-and whisker diagram. The cumulative frequency curve (or ogive) is drawn using the same grouped data from the frequency distribution table used to find the percentile range (see page 8) in this way I can compare the interquartile range and the percentile range. The frequency distribution table used to find the percentile range is also used to draw a box and whiskers diagram for the frequency of both sexes added.
(See overleaf, page 12) FOR CUMALITIVE FREQUENCY CURVE & BOX AND WHISKER PLOT REPRESENTING FREQUENCY OF MEN AND WOMEN.
(See page 10)FOR CUMALITIVE FREQUENCY CURVE & BOX AND WHISKER PLOT REPRESENTING THE FREQUENCY OF MEN AND WOMEN ADDED.
In order to get a different perspective of the skewness that takes into account all of my data I will need to represent my data in form of histograms. This form of representation of data also gives me the added advantage of being able to draw a frequency curve by joining the midpoints and comparing the results at a glance. In relation to the higher standard deviation for women I would expect the frequency curve representing women to be less peaked and more spread out in comparison to men’s frequency curve, as they have a lower standard deviation. The frequency curve will also provide the means for me to be able to analyse if my graphs have a recognisable shape that illustrates the shape of distribution, such as skewness, bimodal or symmetrical.
(Page 13 of 24)
Moreover I have insured that my class boundaries are kept the same as the cumulative frequency table, due to the fact that a number of my values (pulse rates) are identical in both groups as evident in the raw data table (see page, 6). Hence any small change to the class boundaries will result in a large proportion of data falling into different groups. This in turn will effect the shape of distribution when comparing the skewness with the box-and whisker diagram. The added frequency of both sexes shown bellow will likewise enable me to draw a frequency curve and visually see the shape of distribution of all of my data in comparison to the middle 50% of data used in the box and whisker diagram.
FREQUENCY DISTRIBUTION TABLE SHOWING CLASS BOUNDERIES AND THE FREQUENCY OF MEN, WOMEN AND BOTH SEXES ADDED BELOW:
Pulse Rates | Class Boundaries | Frequency for Men | Frequency for Women | Frequency for Men & Women |
56 - 60 | 55.5 – 60.5 | 2 | 1 | 3 |
61 - 65 | 60.5 – 65.5 | 3 | 3 | 6 |
66 - 70 | 65.5 – 70.5 | 5 | 4 | 9 |
71 - 75 | 70.5 – 75.5 | 9 | 5 | 14 |
76 - 80 | 75.5 – 80.5 | 5 | 7 | 12 |
81 - 85 | 80.5 – 85.5 | 4 | 6 | 10 |
86 - 90 | 85.5 – 90.5 | 1 | 3 | 4 |
91 - 95 | 90.5 – 95.5 | 1 | 1 | 2 |
Conclusion
In interpreting the histograms of men and women I found that 68% of the total area fell into the pulse rate range predicted for the frequency of both sexes added (see pages 14, 15). I also found that the interquartile range for both sexes showed that 50% of my data collaborated with my hypothesis (see page 10). The only result that did not fall into the pulse rates identified in my hypothesis was the mean of grouped distribution for men (see page 3). However as this is not the exact mean but an estimate I have used the mean calculated from my raw data table, which collaborated with my hypothesis.
The results for the frequency of men and women added and represented in a histogram of equal widths showed a relatively bell shaped distribution which reflected the box plot as the median was close to the centre of the box. I could also observe that the majority of the frequency occurred at the pulse rate range predicted. The highest frequency density also occurred at the pulse rate range of 60 to 80, in the histogram of unequal widths (see page 19). Therefor proving my hypothesis to be correct.
In regard to my sample size, although I had a larger sample of 60 for men and women, I had a smaller sample of 30 for each sex. My investigation would have been more conclusive if I had a larger sample to test. However as I used stratified sampling method and obtained my final sample from an overall larger sample originally it was more difficult to obtain a larger sample due to time restrictions and availability of access to a large number of people. Likewise if there was more time I could have carried out wider investigations. As pulse rate can be effected by a number of other factors other then age, which was taken into consideration in the stratified sampling method, such as smoking, consumption of caffeine, and fitness levels of individuals tested.
This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.
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