S 14 Histograms with Unequal Class Intervals

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GCSE Maths Statistics & Probability. S 14 Histograms with Unequal Class Intervals. Subject Content Reference: S3.2h . 3. Frequency Density. 2. 1. 50. 100. 150. 200. 250. Time in minutes. A histogram with unequal class intervals uses the notion of frequency density . .

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GCSE MathsStatistics & Probability

S 14

Histograms with Unequal Class Intervals

Subject Content Reference: S3.2h

3

Frequency Density

2

1

50

100

150

200

250

Time in minutes

A histogram with unequal class intervals uses the notion of frequency density . .

Frequency Density = Frequency ÷ Class Interval

Example

The following table shows the time (in minutes) taken for 100 athletes to complete a marathon. Draw up a histogram and

from it, estimate the number of athletes who took between 21/2 and 3 hours to finish:

Step 1:

Draw the axes for time and frequency density . .

Step 2:

Draw in the bars . .

Step 3:

Shade in the parts of the histogram between

21/2 and 3 hours (150 and 180 mins) . .

. . and calculate the frequency represented

= 1/2(16)

+ 28

+ 2/5(35)

= 8 + 28 + 14

= 50

It’s important to realise that the area of each rectangle

represents the frequency (frequency density x time)

Exercise 1

1) The following table shows the time taken for members of a cycling club to finish a 100 km charity ride:

a) Complete the table by calculating frequency densities:

b) Draw a histogram to show this information:

c) Use the histogram to estimate the number of cyclists completing the ride between 21/2 and 31/2 hours:

Exercise 1 (cont’d)

2) The following table shows the distance covered by cars in a 24 hour race:

a) Complete the table by calculating frequency densities:

b) Draw a histogram to show this information:

c) Use the histogram to estimate the number of cars covering between 2650 and 3150 km: