Question

the number of days in each month (excluding leap years) is given in the table below. using technology, such as a ti-83, ti-83 plus, or ti-84, determine the mean, median, and mode for the number of days in a month (round your answers to one decimal place).
month | days in month
jan | 31
feb | 28
mar | 31
apr | 30
may | 31
jun | 30
jul | 31
aug | 31
sep | 30
oct | 31
nov | 30
dec | 31
provide your answer below:
mean = \square, median = \square, mode = \square

Explanation:

Step1: Calculate the Mean

First, we sum up all the days in each month. The data set is: 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31.
The sum \( S = 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31 \)
Let's calculate step by step:
\( 31\times7 = 217 \) (since 31 appears 7 times: Jan, Mar, May, Jul, Aug, Oct, Dec)
\( 30\times4 = 120 \) (Apr, Jun, Sep, Nov)
\( 28\times1 = 28 \) (Feb)
So \( S = 217 + 120 + 28 = 365 \)
There are 12 months, so the mean \( \bar{x} = \frac{365}{12} \approx 30.4 \) (rounded to one decimal place)

Step2: Calculate the Median

First, we need to order the data set from smallest to largest: 28, 30, 30, 30, 30, 31, 31, 31, 31, 31, 31, 31
There are 12 data points, so the median is the average of the 6th and 7th values.
The 6th value is 31 and the 7th value is 31. So median \( = \frac{31 + 31}{2} = 31.0 \)

Step3: Determine the Mode

The mode is the value that appears most frequently. Looking at the data set, 31 appears 7 times, 30 appears 4 times, and 28 appears 1 time. So the mode is 31.

Answer:

Mean = \( 30.4 \), Median = \( 31.0 \), Mode = \( 31 \)