Mathematics 4024 · O Level · Cumulative frequency diagrams

Cumulative frequency diagrams — practice question

A sample of 100 electric light bulbs from Brand A was tested to measure the lifetime of each bulb. The findings are summarised in the table below.
(a)[1]

Fill in the cumulative frequency table.

(b)[2]

On the grid, sketch a smooth cumulative frequency curve for this data. Label the curve Brand A.

(c(i))[1]

Estimate the median from your graph.

(c(ii))[2]

Use your graph to estimate the interquartile range.

(d)[4]

The results for 100 Brand B bulbs are given below. 4 bulbs lasted 50 hours or less. The maximum lifetime recorded for any bulb was 300 hours. The median is 250 hours. The upper quartile is 275 hours. The interquartile range is 75 hours. On the grid, draw and label the cumulative frequency curve for the Brand B bulbs.

(e)[1]

Using your graph, estimate how many Brand A bulbs lasted 275 hours or less.

(f)[1]

Complete the statement below. Brand .......... had .......... more bulbs that lasted longer than 275 hours than Brand .......... .

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