Statstics Sta101 Assignment

STA101 STATISTICS

LECTURE 3: DESCRIPTIVE ANALYSIS AND PRESENTATION OF SINGLE VARIABLE DATA (CONT)

Lecture Learning Outcomes:

1. Compute, describe, and compare the four measures of central tendency: mean,

median, mode, and midrange.

2. Understand the effect of outliers on each of the four measures of central tendency.

3. Compute, describe, compare, and interpret the two measures of dispersion: range

and standard deviation (variance).

4. Compute, describe, and interpret the measures of position: quartiles, percentiles,

and z-scores.

5. Create and interpret boxplots.

6. Understand the empirical rule and Chebyshev's theorem and be able to assess a

set of data's compliance to these rules.

7. Know when and when not to use certain statistics – graphic and numeric.

Lecture References:

Prescribed text 'Elementary Statistics' 11th Edition by Johnson & Kuby – Sections 2.3, 2.4, 2.5 and 2.6 of Chapter 2.

Lecture Concepts and Key Points:

• Measures of central tendency – refers to numerical values that locate the centre,

or average, of a set of data.

• Mean – the arithmetic average of a set of data, found by adding all the values of the variable and dividing the total by the number of values. The mean of a sample is denoted by 'x-bar'.

• Median – the value of the data that occupies the middle position after the data is ranked in order according to size.

• Mode – the value of the data that occurs most frequently.

• Midrange – the value exactly midway between the lowest and highest valued data. Found by taking the average of the low and high values.

• Measures of dispersion – refers to measures of dispersion or spread of data sets.

• Range – the difference in value between the highest-valued data and the lowest valued data.

• Deviation from the mean – the difference between the value of each of the data set and the mean of the data set.

• Sample variance – is calculated as the sum of the squares of the...