Week 9 - Measurement and Analysis

Question 1

what are the methods of summarising data

Answer 1

descriptive statistics
- central tendancy (mean, median, mode)
- spread/ dispersion (range, interquartile range, standard deviation, variance)
- shape (skewness, kurtosis)

Question 2

what are the methods for organising data

Answer 2

• data tables
• coding

Question 3

what are the methods of representing data

Answer 3

• graphs
  (bar charts, histograms, pie charts, box plot, frequency polygons)

Question 4

what is mean, median and mode

Answer 4

mean = sum of all values divided by the number of values

median = middle value when all numbers are arranged in order

mode = most frequent value

Question 5

What is range

Answer 5

range = max val - min val

difference between the highest and lowest values in a dataset

Question 6

what is the interquartile range (IQR)

Answer 6

the IQR is the range between the Q1 and Q3
represents middle 50% of data

quartile 1 (Q1) is the lowest 25% of the numbers
quartile 2 (Q2) is the next 25% of numbers (up to the median)
quartile 3 (Q3) is the second-highest 25% of numbers (above the median)
quartile 4 (Q4) is the highest 25% of numbers

Question 7

What is variance

Answer 7

variance measures how far each value in a dataset is from the mean, on average

Question 8

What is standard deviation (SD)

Answer 8

SD is the square root of the variance, tells you how much on average values in a dataset differ from the mean

Question 9

What are the types of measurement scales

Answer 9

1. Nominal scales
   - catagorises data without any order or ranking e.g. ethnic background
2. Ordinal scales
   - Categorises data with a clear order, but the difference between ranks is not defined e.g. age groups ranked
3. Interval scale
   - Numeric data with equal intervals, but no true zero e.g. body temperature in °C
4. Ratio scale
   - Numeric data with equal intervals and an absolute zero e.g duration since diabetes diagnosis (0 days, 20 days)

look at page 3 of week 9

Question 10

What is a frequency polygon

Answer 10

A line graph created by connecting points plotted at the midpoint of each data class

used with continuous data

Question 11

How is normal distribution demonstrated and what is it

Answer 11

a symmetrical probability distribution where data values are clustered around the mean, with fewer values further away from the mean

Normal distribution of data can be demonstrated with a symmetrical curve of data results

Question 12

What is a frequency polygons two main purposes

Answer 12

interpolation = estimate the frequency of missing values

shape characterisation = understand teh distribution of the data

Question 13

what are the 3 shapes that can occur on a frequency data plot

Answer 13

1. positivley skewed
   - Tail is longer on the right.
   - Most data are clustered at lower values.
   - Example: Income distribution.
2. symmetrical
   - Data are evenly spread around the centre.
   - Most values cluster around the mean.
   - Ideal for many statistical analyses.
3. negatively skewed
   - Tail is longer on the left.
   - Most data are clustered at higher values.

Question 14

what is kurtosis

Answer 14

measures tail heaviness and peak sharpness

Question 15

How is kurtosis measured

Answer 15

if the data range is
- meokurtic
- platykurtic
- leptokurtic
different heights through normal distribution

normal distribution of each
meo = 3
platy = less than 3
lepto = greater than 3