The cumulative frequency graph shows distribution of the waiting times before being served, in minutes, of 60 customers at restaurant A on a particular day.

  1. (a)

    Use the curve to estimate

    1. (i)

      the median waiting time,

      Answer ... min

    2. (ii)

      the interquartile range,

      Answer ... min

    3. (iii)

      the 35th percentile of the waiting time.

      Answer ... min

  2. (b)

    Given that 20% of the customers waited more than x minutes to be served, find the value of x.

    Answer x = ...

  3. (c)

    The data below represents the waiting times of 10 customers from restaurant B on the same day.

    10, 12, 14, 14, 15, 17, 17, 18, 22, 28

    Calculate

    1. (i)

      the median waiting time,

      Answer ... min

    2. (ii)

      the interquartile range.

      Answer ... min

  4. (d)

    The owner of restaurant B claims that his restaurant is more efficient and consistent in their service compared to restaurant A based on the data given. Give a reason why this is not a fair comparison.

    ...

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Worked solution

6(c)(i)

1. Identify the two middle values and calculate the median.

The data is already in ascending order:

10,12,14,14,15,17,17,18,22,2810, 12, 14, 14, 15, 17, 17, 18, 22, 28

There are 1010 values, so the median is the average of the 5th and 6th values.

Median=15+172=16\text{Median} = \frac{15+17}{2}=16

Answer

1616 min

6(c)(ii)

1. Find the lower quartile and upper quartile from the ordered data.

The data is already in ascending order:

10,12,14,14,15,17,17,18,22,2810, 12, 14, 14, 15, 17, 17, 18, 22, 28

Lower half: 10,12,14,14,1510, 12, 14, 14, 15, so Q1=14Q_1=14.

Upper half: 17,17,18,22,2817, 17, 18, 22, 28, so Q3=18Q_3=18.

2. Calculate the interquartile range.

Interquartile range=Q3−Q1=18−14=5\text{Interquartile range}=Q_3-Q_1=18-14=5

Answer

55 min

6(d)

1. Give a valid reason why the comparison is unfair.

Restaurant A's data is based on 6060 customers, while restaurant B's data is based on only 1010 customers. Since the sample sizes are very different, the data from restaurant B may not be representative enough to compare fairly with restaurant A.

Answer

It is not a fair comparison because restaurant A has data from 6060 customers, but restaurant B has data from only 1010 customers, so B's data may not be representative.

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