Question

alan baker interested in the number of chairs per household people have. please finish the calculation below using data he collected here
the mean (\\( \bar { x } \\)): chairs (please show your answer to 1 decimal place.)
the median: chairs
the mode: chairs (please separate your answers by , in bimodal situation. enter dne if there is no mode.)
question help: message instructor

Explanation:

Step1: Calculate the total number of households

$$
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$$

Step2: Calculate the sum of \(x\times f\)

$$
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$$

Step3: Calculate the mean

$$ \bar{x}=\frac{\sum_{i = 1}^{k}x_{i}f_{i}}{n}=\frac{171}{57}=3.0 $$

Step4: Calculate the median

Arrange the data in ascending order (using frequencies). The cumulative frequencies:
For \(x = 1\), \(cf=14\); for \(x = 2\), \(cf=14 + 12=26\); for \(x = 3\), \(cf=26+11 = 37\). Since \(n = 57\), \(\frac{n + 1}{2}=\frac{57+1}{2}=29\). The median class is \(x = 3\) (because \(26<29<37\))

Step5: Calculate the mode

The mode is the value with the highest frequency. The frequency of \(x = 1\) is \(14\), which is the highest.

Answer:

The mean: \(3.0\) chairs; The median: \(3\) chairs; The mode: \(1\) chair