The waiting time, in seconds, of 300 customers at a...

The waiting time, in seconds, of 300 customers at a supermarket cash register are recorded in the table below. $$\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text { Time } & <60 & 60-120 & 120-180 & 180-240 & 240-300 & 300-360 & >360 \\ \hline \text { Frequency } & 12 & 15 & 42 & 105 & 66 & 45 & 15 \\ \hline \end{array}$$ a) Draw a histogram of the data. b) Construct a cumulative frequency graph of the data. c) Use the cumulative frequency graph to estimate the waiting time that is exceeded by $25 \%$ of the customers.

The waiting time, in seconds, of 300 customers at a supermarket cash register are recorded in the table below.
$$\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text { Time } & <60 & 60-120 & 120-180 & 180-240 & 240-300 & 300-360 & >360 \\ \hline \text { Frequency } & 12 & 15 & 42 & 105 & 66 & 45 & 15 \\ \hline \end{array}$$
a) Draw a histogram of the data.
b) Construct a cumulative frequency graph of the data.
c) Use the cumulative frequency graph to estimate the waiting time that is exceeded by $25 \%$ of the customers.

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Key Concepts

Percentiles and Quantile Estimation

Percentiles are measures that indicate the relative standing of a value within a data set. They represent the values below which a given percentage of observations fall. Estimating a particular percentile, such as the 25th percentile, from a cumulative frequency graph involves finding the point on the graph that corresponds to the cumulative frequency equal to that percentage of the total data. This method helps in summarizing and interpreting the distribution of data.

Histogram

A histogram is a type of bar graph that represents the frequency distribution of numerical data by grouping the data into bins or intervals. It provides a visual impression of the underlying frequency distribution and can help in identifying the shape of the distribution, such as whether it is skewed or symmetric, and can highlight the spread and central tendency of the data.

Cumulative Frequency Graph

A cumulative frequency graph, also known as an ogive, is a graphical representation where the cumulative frequencies are plotted against the upper class boundaries. This tool helps in visualizing the accumulation of data and is particularly useful for finding percentiles, medians, and other quantiles by showing how the total frequency builds up across the range of data.

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