Question

the following refer to the following data set:
46.4 22.8 45.4 64.4 38.2
64.4 44.9 54.4 34.6 53.9

what is the arithmetic mean of this data set?

mean =

what is the median of this data set?

median =

what is the mode of this data set?

mode =

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question 5

the highway mileage (mpg) for a sample of 8 different models of a car company can be found below. find mean, median, and mode. round to one decimal place as needed.
19, 23, 26, 27, 30, 31, 33, 33

mean =

median =

mode =

Explanation:

First Data Set (46.4, 22.8, 45.4, 64.4, 38.2, 64.4, 44.9, 54.4, 34.6, 53.9)

Arithmetic Mean

Step1: Sum all data points

Sum = \( 46.4 + 22.8 + 45.4 + 64.4 + 38.2 + 64.4 + 44.9 + 54.4 + 34.6 + 53.9 \)
Calculate each addition:
\( 46.4 + 22.8 = 69.2 \)
\( 69.2 + 45.4 = 114.6 \)
\( 114.6 + 64.4 = 179 \)
\( 179 + 38.2 = 217.2 \)
\( 217.2 + 64.4 = 281.6 \)
\( 281.6 + 44.9 = 326.5 \)
\( 326.5 + 54.4 = 380.9 \)
\( 380.9 + 34.6 = 415.5 \)
\( 415.5 + 53.9 = 469.4 \)

Step2: Divide by number of data points (n=10)

Mean = \( \frac{469.4}{10} = 46.94 \)

Step1: Sort the data set

Sorted data: \( 22.8, 34.6, 38.2, 44.9, 45.4, 46.4, 53.9, 54.4, 64.4, 64.4 \)

Step2: Find middle value (n=10, even, average of 5th and 6th)

5th value: \( 45.4 \), 6th value: \( 46.4 \)
Median = \( \frac{45.4 + 46.4}{2} = \frac{91.8}{2} = 45.9 \)

Step1: Identify most frequent value

Check frequencies: \( 22.8(1), 34.6(1), 38.2(1), 44.9(1), 45.4(1), 46.4(1), 53.9(1), 54.4(1), 64.4(2) \)
Most frequent: \( 64.4 \) (appears twice)

Answer:

Mean = \( 46.94 \)

Median