Maths Flashcards

Question

PPDAC cycle - Analysis: Name the 5 types of sample distribution

Answer 1

Centre (median), Shape, Spread, Overlap, Unusual Features.

Answer 2

Which subgroup is higher? State the median and how big the difference is between group 1 median and group 2 median. Provide reasons (prior knowledge, or what you noticed that supports your point) and online research (with link) that supports your point.

Answer 3

Looking at the sample distribution, I notice that the median (variable) for (group 1)(group 1 median) is (difference) (input calculation: larger median - smaller median) greater than the (group 2) (group 2 median).

Answer 4

This means that on average, the (variable) for (group) tends to be larger/smaller than that of (group). However, it should be noted that in this sample, the difference in the (variable) for (group) and (group) is relatively small/clear but not very large/big and significant.

Answer 5

I expected the (group) (variable) to be larger than the (group) (variable) because... (list reasons). However, the data shows the opposite trend, suggesting factors such as sampling variation and __ may influence the results.

Answer 6

Research, with link, that confirms/supports reasons from Pt 3.

Answer 7

1) Look at the overall shape of the sample. 2) Write what you see: give numerical values as to where there is more data. 3) State if box & whisker plot is left or right skewed, or symmetrical. 4) State if dot plot is bi-modial, unimodial, etc. 5) State the approximate shape using the phrase, "Tends to be..."

Answer 8

Normal Distribution: hill/mound shape, symmetrical, bell-shaped curve. Right Skew: Tail on the right side. Left Skew: Tail on the left side. Bimodial: 2 peaks. Triangular: triangular Irregular: No real pattern.

Answer 9

In the sample distribution, I notice that the dot plot for (group 1) tends to be (shape). The box and whisker plot also shows that the (group 1) sample is left/right skewed. This may be due to (reason/outlier description) than the rest of the (group 1). In particular, (outlier description). This may be due to (plausible reason). The (group 2) dot plot sample shows (shape) with the box and whisker plot being left/right skewed. This may be due to (reason/outlier description). This again may be due to (reason). Research to back up.

Answer 10

Talk about position and size of IQR IQR = Max – Min (show calculations)

Answer 11

Looking at the sample distribution, I notice that the box and whisker plot for (group 1) shows that the width of the box (which represents the interquartile range, IQR) is (IQR) (UQ - LQ). In comparison, the IQR for (group 2) is (IQR) (UQ - LQ). This means that the IQR for (group) is (difference between IQR's) wider/more than for (group), indicating that the middle 50% of (group) are more/less spread out compared to (group). Incorporate reasons then research to back it up.

Answer 12

Refers to how much the datasets overlap.

Answer 13

The sample distribution box plot shows that _% of (group 1) (variable) is greater than the median (variable) for (group 2). This means that the majority of the sampled (group 1 as a population) have a greater (measurement: weight, percentage, height, etc) of (variable) than (group 2). This suggests that (group 1 as a population) will on average have a greater (variable) than (group 2 as a population) out of all (participant title: students, kiwis, rugby players, etc) from (source of data). A reason for this could be that...(research). This will mean that...(one sentence explanation/result of research).

Answer 14

Can be unusual clusters, unusual points, outliers, extreme values Identifying outliers: 1.5 x IQR Identifying extreme values: 3 x IQR NZ Grapher tip: Select “Box plot (no outlier)” to easily identify outliers.

Answer 15

Looking at the sample distribution for (occupation: rugby players, students, etc) for (group 1) and (group 2), I can see that there is (#) (occupation) in the (group 1) who has a (measurement: weight, height, etc) of (#). The IQR for (group 1) is (IQR) (UQ-LQ). 1.5 x IQR = 1.5 x (IQR) = (V). The UQ for (group 1) is (UQ) and therefore, (UQ) + (V) = (#). Therefore, this player can/cannot be considered as an outlier because the (measurement) is within/not within 1.5 times the IQR. However, this can be considered as an unusual point. Reasons and research to back it up.

Answer 16

Interval within which we expect the population median to lie.

Answer 17

We would expect the (group 1) median (measurement) to lie between (#) and (#), and we would expect the (group 2) median (measurement) to lie between (#) and (#). Comparing the confidence intervals, there is enough evidence for us to see that the confidence intervals do/do not overlap and therefore we can/cannot conclude that the median (measurement) for (group 1) is greater/smaller than the median (measurement) for (group 2).

Answer 18

Describe confidence intervals. Make the call (second part of confidence interval outline). Describe sampling variability. Describe how the confidence intervals will be affected by a bigger sample size. Add reflections.

Answer 19

Each time a sample is taken from the same population (with the same population size), it is likely that the sample estimate (mean/median) and the confidence intervals will be different because different members of the population can be selected, which will have different sample data. However, we would expect the median of the population to still lie within the confidence intervals generated by the sample.

Answer 20

If we take another sample from the population and investigate if (variables in context), we will get a different mean, median, etc. This is because each time we take a sample, different (variables in context) will be selected (each data has equal chance of being selected). However, we would expect the median of the population to still lie within the confidence interval generated by each sample.

Answer 21

No overlap. Overlap.

Answer 22

The confidence intervals will be shorter if I increase my sample size. A larger sample will produce shorter informal confidence intervals, decrease sample variability, and result in more accurate sample estimates. Since my results already do not overlap, further shortening the intervals will make it even less likely that they will overlap. Therefore, I do not think increasing the sample size will change my overall inference.

Answer 23

The confidence intervals will be shorter if I increase my sample size. A larger sample will produce shorter informal confidence intervals, decrease sample variability, and result in more accurate sample estimates. Since my results already overlap, further shortening the intervals will make it even more likely that they will continue to overlap. Therefore, I do not think increasing the sample size will have any impact on my inference.

Answer 24

Was my sample size adequate? Was there any bias in my samples? How did I minimize any bias in my samples? Was my sample representative of the population? Was the source of my data reliable? Is my sample data taken from my target population? Do my conclusions seem reasonable? What are some limitations of my investigation?

Answer 25

I believe that my sample size of (#), consisting of (#) (group 1) and (#) (group 2), was appropriate given that the population included only (population total). If my sample size had been smaller, I would not have had enough data to draw meaningful conclusions. I felt that my sample provided adequate representation.

Answer 26

I minimized bias in my samples by using the stratified sampling method, ensuring (advantages of stratified sampling method)

Answer 27

My data source is reliable... (reasons)

Answer 28

If I were to repeat my investigation around the median (variable) of (group 1) and median (variable) of group 2) from NZ and a sample of 100 (groups category - e.g. students) from the NZ Grapher (URL to NZ Grapher relevant data) database. I would perhaps consider (at least 3 considerations): - the location of (group category) because (reasons). This means (explanation). This external/internal factor would influence our investigation because (explain/reasons - e.g. not one of the focused on variables). - Consider anything that can affect the chosen variables of the investigation (e.g. species, fertility stage, gender, etc.), with reasons. Therefore, if I were to repeat my investigation, I would consider the 3 factors of (list 3 factors).