Question

The following data represent the record high temperatures for 50 cities.

Temperature	42-44	44-46	46-48	48-50	50-52
Number of cities	10	18	13	7	2

(a) Prepare a cumulative relative frequency distribution table for this frequency distribution.
(b) Estimate the mean record high temperature from the grouped data (to one decimal digit).
(c) Construct two graphs: a histogram and an ogive.
(d) The actual mean (calculated using the individual, original set of data) of the record high
temperature of these 50 cities is 44.6 oC. Explain why the estimated mean from the grouped data (part b) is
different from the actual mean.

Answer 1

a)

temp	number of cities	cumlative	relative cummlative
42-44	10	10	0.2
44-46	18	28	0.56
46-48	13	41	0.82
48-50	7	48	0.96
50-52	2	50	1

b)

c)

Grouped data is organised into several group.To create grouped data the raw data has been sorted into several groups and tables showing how many data points occur in each group. Hence the means differ from un-grouped data to grouped data.

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