Arithmetic Mean and Central Tendency

Answer the following problems showing your work and explaining (or analyzing) your results.
1. Describe the measures of central tendency. Under what condition(s) should each one be used?
Mean- Works good when it comes to test scores
Median- should be used when describing something like average income.
Mode= is good is you want to see what is you best seeing product in a store situation.
2. Last year, 12 employees from a computer company retired. Their ages at retirement are listed below.First, create a stem plot for the data. Next, find the mean retirement age. Round to the nearest year. 55 77 64 77 69 63 62 64 85 64 56 59
8
5
7
77
6
234449
5
569

Mean = 66
3. A retail store manager kept track of the number of car magazines sold each week over a 10-week period. The results are shown below. 27 30 21 62 28 18 23 22 26 28
a. Find the mean, median, and mode of newspapers sold over the 10-week period. 285
Mean= 28.5
Median=26.5
Mode=28
b. Which measure(s) of central tendency best represent the data?
Mean
c. Name any outliers. 62

d. Joe wants to pass his statistics class with at least a 75%. His prior four test scores are 74%, 68%, 84% and 79%. What is the minimum score he needs on the final exam to pass the class with a 75% average?

70%
4. Nancy participated in a summer reading program. The number of books read by the 23 participants are as follows: 10 9 6 2 5 3 9 1 6 3 10 4 7 6 3 5 6 2 6 5 3 7 2
Number of books read
Frequency
1–2 4
3–4
5
5–6
8
7–8
2
9–10
4
a. Complete the frequency table.
b. Find the mean of the raw data.

c. Find the median of the raw data
.
6. The chart below represents the number of inches of snow for a seven-day period.
Sunday
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
2
5
3
10
0
4
2
a. Find the mean, median, and mode.
Mean= 3.71
Median=3
Mode=2
b. Which is the best measure of central tendency? Mean
c. Remove Wednesday from the calculations. How does that impact the three measures of central tendency? The only tendencies that change are mean and median the have a minor. Mean=2.66 Median=2.5 Mode =2

d. Describe the effect outliers have on the measures of central tendency.
They have the ability to largely skew the mean up or down.
7. A dealership sold 15 cars last month. The purchase price of the cars, rounded to the nearest thousand, is represented in the table.
Purchase price
Number of cars sold
$15,000
3
$20,000
4
$23,000
5
$25,000
2
$45,000
1

a. Find the mean and median of the data.

Mean= $22,333.33
Median= $23,000
Mode= $23,000

b. Which measure best represents the data? Use the results to support your answer.
The mode best represents the data. The mode and the median are the same, and when it comes to sales you want to know what your most popular vehicle is.
c. What is the outlier and how does it affect the data?
The outlier is $45,000 it raises the average of amount of money made that month.
8. What do the letters represent on the box plot?

A. Is you lowest number
B. Is the median between C & A
C. Median
D. Is the median between C & E
E. Highest number

9. The test scores from a math final exam are as follows: 64 85 93 55 87 90 73 81 86 79
a. Create a box plot using the data.

Median = 83

b. Label the five points on the box plot and include numerical answers from part "a."

10. Using the data and results from Question 9, answer the following questions.
a. What is the median?
83
b. What is the range?
38

c. What is the interquartile range?
17
d. In a short paragraph, describe the data in the box plot.
The data in graph above shows test scores of students the scores range from the highest score being 93 to lowest score being 55. There is a 38-point difference between the highest and the lowest and we can also see that the average students are getting around an 83. And the range with in the plot is 17. So by looking at this plot I think I should grade my test on a curve.