Question

find the measures of center (mean, median, and mode) for the following data set \by hand.\
123.2 105.8 123.2 108.6 123.2
102.4 87.2 113.8 94.4 96.3
what is the mean of this data set? round to the nearest hundredth as needed.
mean =
round to the nearest hundredth as needed.
what is the median of this data set?
median =
what is the mode of this data set? round to the nearest hundredth as needed.
mode =
question 12
robin and evelyn are playing a target game. the object of the game is to get an object as close to the center as possible. each player’s score is the number of centimeters away from the center. robin and evelyn’s results from five rounds are shown.
robin’s scores: 99, 108, 102, 107, 119
evelyn’s scores: 125, 137, 138, 145, 145
the mean of robin’s scores is 107. what is the mean of evelyn’s scores?

Explanation:

First Part: Measures of Center for the First Data Set

Mean Calculation

Step1: Sum all data points

The data set is \(123.2, 105.8, 123.2, 108.6, 123.2, 102.4, 87.2, 113.8, 94.4, 96.3\).
Sum \(= 123.2 + 105.8 + 123.2 + 108.6 + 123.2 + 102.4 + 87.2 + 113.8 + 94.4 + 96.3\)
\(= 1078.1\)

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

Mean \(= \frac{1078.1}{10} = 107.81\)

Median Calculation

Step1: Order the data set

Ordered data: \(87.2, 94.4, 96.3, 102.4, 105.8, 108.6, 113.8, 123.2, 123.2, 123.2\)

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

5th term \(= 105.8\), 6th term \(= 108.6\)
Median \(= \frac{105.8 + 108.6}{2} = \frac{214.4}{2} = 107.2\)

Mode Calculation

Step1: Identify the most frequent value

In the data set, \(123.2\) appears 3 times (more than any other value).
Mode \(= 123.2\)

Second Part: Mean of Evelyn’s Scores

Answer:

s:

• First Data Set Mean: \(107.81\)
• First Data Set Median: \(107.2\)
• First Data Set Mode: \(123.2\)
• Evelyn’s Mean: \(138\)