Question

the fuel efficiency, in miles per gallon, of 12 small utility trucks was measured are recorded as follows:

21, 24, 24, 26, 14, 23, 25, 33, 24, 22, 25, 22

for this sample, calculate the following measures:
mean round to the nearest hundredth (2 decimals)
median
mode

Explanation:

Order the data set

To find the median, we first arrange the 12 data points in ascending order:

$$ 14, 21, 22, 22, 23, 24, 24, 24, 25, 25, 26, 33 $$

Calculate the mean

Using the Rounding Numbers knowledge point, we sum the values and divide by the sample size \(n = 12\):

$$ \text{Sum} = 14 + 21 + 22 + 22 + 23 + 24 + 24 + 24 + 25 + 25 + 26 + 33 = 278 $$

$$ \text{Mean} = \frac{278}{12} \approx 23.1666... \approx 23.17 $$

Find the median

Since there are \(n = 12\) data points (an even number), the median is the average of the 6th and 7th values in the ordered list:

• 6th value: \(24\)
• 7th value: \(24\)

$$ \text{Median} = \frac{24 + 24}{2} = 24 $$

Find the mode

The mode is the value that appears most frequently in the data set:

• \(14\) appears 1 time
• \(21\) appears 1 time
• \(22\) appears 2 times
• \(23\) appears 1 time
• \(24\) appears 3 times
• \(25\) appears 2 times
• \(26\) appears 1 time
• \(33\) appears 1 time

The value \(24\) has the highest frequency.

$$ \text{Mode} = 24 $$

Answer:

• Mean: 23.17
• Median: 24
• Mode: 24