Median: 동영상 및 연습문제

The wait times (in minutes) for a popular theme park ride at $3$ PM are listed in increasing order: $12$, $18$, $22$, $28$, $30$, $34$, $40$, $48$, $52$, $170$. Find the mean and median of these $10$ values.

Exclude the value $170$, which appears to be an outlier, and then find the new mean and median. How were they affected by the outlier?

The following are the estimated annual incomes (in dollars) of students who graduated from a university with a major in history. The data are based on graduates from a particular year, and one exceptionally high income is included. Find the mean, median, mode, and the midrange to answer the given question:

16,920; 18,340; 17,750; 19,210; 19,800; 19,450; 18,100; 16,500; 1,950,000

Does the exceptionally high income significantly affect the measures of center? Based on these data, would the university be justified in claiming that the mean salary of history graduates exceeds \$200,000?

The following are selling prices (in dollars) of wireless security cameras tested by a consumer review agency.

240, 160, 220, 90, 240, 240, 120, 190, 140, 240, 160, 190, 170, 240

If you were selecting a security camera, what other statistic (besides measures of central tendency) would be useful for decision-making?

The following are measured amounts of caffeine (mg per 12 oz) found in a single can from each of 20 different beverages. Do these statistics represent the population of all cans of these same 20 beverages?

0,0,30,35,32,48,39,52,57,34,45,39,0,0,50,56,37,0,39,46

A sample of heart rate measurements (beats per minute, bpm) was collected, where each of 10 individuals has both resting heart rate and active heart rate recorded. The resting heart rate is measured when the person is at rest, while the active heart rate is measured after mild physical activity.

Resting Heart Rate: 62, 72, 88, 58, 90, 66, 64, 80, 70, 68

Active Heart Rate: 98, 110, 140, 85, 150, 102, 94, 120, 108, 100

Are the measures of center the best statistics to use with these data? What other statistical measures might be more appropriate?

Listed below are the drive-thru wait times (in seconds) at 12 PM for two different fast-food chains. Find the mean and median for each set of data, then compare the two sets of results. Does a comparison between the means and medians reveal that there is a difference between the two sets of data?

Use the following recorded weights (in kg) of a group of individuals measured in two different years. Find the mean and median for each set of data, then compare the two sets of results. How have the weights changed over time? 

Listed below are the heights (in inches) of a group of individuals. Find the mean and median for this set of data. Do the results support or contradict the belief that the average height of the adults in the group is $66$ inches?

$65$, $68$, $66$, $70$, $64$, $69$, $67$, $72$

Listed below are the number of books borrowed from a library by $8$ individuals.

a. What is the mean of the number of books borrowed?

b. What is the median of the number of books borrowed?

Listed below are the number of items purchased by a group of shoppers at a supermarket at 2:00 PM.

Find the median.

Listed below are the scores (out of $100$) achieved by a group of students in a math exam. Find the ranks corresponding to these scores.

$78$, $85$, $85$, $72$, $80$, $75$, $77$, $88$, $82$, $79$

The self-reported weights of adults aged 25 and over are provided below, along with their corresponding measured weights (based on data from a health survey). All weights are in pounds. Calculate the differences between the reported and measured weights. Then, determine the following using these differences:

(i) Mean

(ii) Median

(iii) Mode

The self-reported weights of adults aged 25 and over, along with their corresponding measured weights and the differences between reported and measured weights, are provided in the table below. All weights are in pounds.

Using the differences between reported and measured weights, determine the values of:

Q1 (First Quartile)

Q3 (Third Quartile)

Determine whether the statement is true or false. If it is false, choose the option that rewrites it as a true statement.

A data set can have more than one mode.

The following are the systolic blood pressure readings (in $\text{mmHg}$) for a group of $10$ patients:

$122$, $138$, $145$, $130$, $154$, $127$, $142$, $136$, $150$, $134$.

Find the mean, median, and mode of the data. If any measure cannot be found or does not represent the center of the data, explain why.

The responses of a sample of $30$ employees in a mid-sized company were collected after they were asked which aspect of their workplace was most negatively affected by poor management.

Find the mean, median, and mode of the data. If any measure cannot be found or does not represent the center of the data, explain why.

The quiz results for $10$ students in a chemistry class are:

$56$, $62$, $78$, $85$, $62$, $90$, $74$, $62$, $80$, $88$.

Determine the mean, median, and mode for this data set. Which measure is most appropriate to describe the center?

A nutrition company inspects six boxes of meal replacement bars and records their weights (in grams) as $1348$, $1352$, $1339$, $1345$, $1355$, and $1341$. What are the mean and median weights of these boxes?

The times (in minutes) it took nine students to complete a quiz are $18$, $22$, $15$, $25$, $20$, $16$, $19$, $24$, and $21$. What are the mean and median times?

A botanist measures the heights (in centimeters) of eight different plants. Suppose the botanist wants to convert all the heights to millimeters. How can the mean and median of the original data set be quickly found in millimeters?

The dot plot below shows the ages (in years) of participants in a workshop:

Calculate the mean, median, and mode of the ages. Which measure best describes the center of the data?

The following are the numbers of books sold (in thousands) by $18$ different bookstores in a city during $2023$:

Calculate the mean and median number of books sold.

A teacher recorded the following test scores for $32$ students:

$11$, $12$, $13$, $13$, $14$, $15$, $15$, $16$, $16$, $17$, $17$, $18$, $18$, $19$, $19$, $20$, $20$, $21$, $21$, $22$, $22$, $23$, $23$, $24$, $24$, $25$, $25$, $26$, $27$, $28$, $29$, $30$.

Calculate the mean and median of these test scores.

A poll asked $870$ adults how many books they read last year. The results were:

Find the mean, median, and mode of the data, if possible. If any measure cannot be found or does not represent the center of the data, explain why.

The median of these six ordered numbers equals $41$. What is the missing number?

$30$ $36$ $40$ ___ $46$ $52$

A sample of salaries in a small company produces a distribution with most employees clustered near the lower salaries but a few very large executive salaries produce a long right tail. Which measure will typically be greater, the mean or the median?

A survey yields the following grouped frequency distribution. Identify the modal class.

Find the median of the data set $18$, $7$, $12$, $25$, $9$, $14$, $11$ after arranging the values from smallest to largest.

Find the median of the data set: $31$, $8$, $17$, $12$, $26$, $14$, $19$, $10$.

A sample contains the values: $5$, $5$, $7$, $9$, $9$, $9$, $14$, $14$, $18$, $22$. Find the median.