Reporting on a distribution - Categorical The distribution of 'most common use of wearable technology' is shown in Figure 1. In this sample of 65 STA10003 students, 55.4% reported that they check their step counter first. A similar percentage of students checked either their active minutes [16.9%], or 'other' activities [15.4%]. The remaining students suggested they checked their heart rate in the first instance [12.3%]. Most COMMON use of wearable technology CO 45 Percent 15 10 Step Counter Heart Rate Active Minutes Most COMMON use of wearable technology Other Figure 1: Distribution of most common use of 'wearable' technology KNOW ING 38 Reporting on a distribution- Metric ( Include labelled histogram) · Shape · Approximately symmetric · Positively Skewed · Negatively Skewed · Centre · Symmetric with no outliers - mean and include standard deviation · Skewed or Symmetric with outliers - median · Spread · 'Typical' - Middle 50% [IQR] from Percentiles table · Use 25th and 75th percentiles · Outliers · Any values extremely high / low? State figures and direction
Sampling distribution . Z scores are helpful in determining where sample statistics lie in a distribution IS THE SAMPLE TRULY REPRESEN- TATIVE OF THE POPULATION? - with multiple samples there may be slight differences Sample variability differences between samples A sampling distribution If we take lots of random samples from the population, we can build a picture of the samples Distributions of Sample means . the distribution of sample means Is ALL possible random samples of size obtained from a population pop. would be covered Entire with samples · Need all possible random sample values to be able to calculate probab
Characteristics - Sample means should cluster around the population mean Random Sampling [ to truly reflect the population ] > Should form a Normal distribution · larger sample size = narrower distribut > closer sample meanto pop. mean Central Limit Theorem Shape Normal distribution · If samples from nom. distrib. pop, they should be normally distributed . regardless of the shape of the OG distribution, If samp size is n = 30, the sampling distribution Is almost 'perfectly normal' -