Question

question 9
the following refer to the following data set:
83 43 52 92 75 92 54 55 38 93
what is the mean ($\bar{x}$) of this data set?
mean = (please show your answer to one decimal place.)
what is the median of this data set?
median =
what is the mode of this data set?
mode =

Explanation:

Mean Calculation

Step1: Sum all data points

The data set is \( 83, 43, 52, 92, 75, 92, 54, 55, 38, 93 \).
Sum \( = 83 + 43 + 52 + 92 + 75 + 92 + 54 + 55 + 38 + 93 \)
\( = 83+43=126 \); \( 126+52=178 \); \( 178+92=270 \); \( 270+75=345 \); \( 345+92=437 \); \( 437+54=491 \); \( 491+55=546 \); \( 546+38=584 \); \( 584+93=677 \).

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

Mean \( \bar{x} = \frac{677}{10} = 67.7 \)

Median Calculation

Step1: Order the data set

Ordered data: \( 38, 43, 52, 54, 55, 75, 83, 92, 92, 93 \)

Step2: Find middle values (n=10, even)

Middle positions: 5th and 6th values.
5th value: \( 55 \); 6th value: \( 75 \).

Step3: Calculate median (average of middle values)

Median \( = \frac{55 + 75}{2} = \frac{130}{2} = 65 \)

Mode Calculation

Step1: Identify most frequent value

Check frequencies: \( 38(1), 43(1), 52(1), 54(1), 55(1), 75(1), 83(1), 92(2), 93(1) \).
\( 92 \) appears twice, others once.

Answer:

s:
Mean: \( 67.7 \)
Median: \( 65 \)
Mode: \( 92 \)