Handout_3 Descriptive statistics - measures of dispersion

# Handout_3 Descriptive statistics - measures of dispersion -...

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DESCRIPTIVE STATISTICS – MEASURES OF DISPERSION #3 The mean is the measure of central tendency most frequently used to describe statistical data. The mean, however, does not give us sufficient information about the data to draw a conclusion. Below are frequency diagrams for two sets of data illustrating a distribution of sizes of shoes in two different groups of students. Each set includes n = 13 values. ^ | Frequency f i | Fig. 1 Fig. 2 | | * | * * * | * * * * * | * * * * * * * | * * * * * * * * * * | -+----+----+----+----+ -+----+----+----+----+ 7.5 8.0 8.5 9.0 9.5 7.5 8.0 8.5 9.0 9.5 Size of shoes x i ==> Size of shoes x i ==> (A frequency f i is the number of students having shoes of a given size; we see from the Fig. 1 that three students have the shoes of size 8.0 , five – the size 8.5, etc). It is easy to see that for each set of data displayed in Fig. 1 and Fig. 2 the mean size is 8.5 . Using the data in Fig.1 and Fig. 2 we can complete the following frequency tables . Table 1 (based on Fig. 1) Table 2 (based on Fig. 2) =============== ============== | x i | f i | f i * x i | | x i | f i | f i * x i | =============== =============== | 7.5 | 1 | 7.5 | | 7.5 | 4 | 30 | ------------------------- ------------------------ | 8.0 | 3 | 24 | | 8.0 | 2 | 16 | ------------------------- ------------------------- | 8.5 | 5 | 42.5 | | 8.5 | 1 | 8.5 | ------------------------- ------------------------- | 9.0 | 3 | 27 | | 9.0 | 2 | 18 | ------------------------- ------------------------- | 9.5 | 1 | 9.5 | | 9.5 | 4 | 38 | =============== =============== Σ f i * x i = 110.5 Σ f i * x i = 110.5 Using the formula for

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## This note was uploaded on 11/24/2011 for the course MATH 3000 taught by Professor Kzaer during the Spring '05 term at St. Johns College MD.

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Handout_3 Descriptive statistics - measures of dispersion -...

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