1. A doctor ordered four separate blood tests to measure a patient’s total blood cholesterol levels. The test results were as follows. (See Example 1 in this section.)
   285, 265, 230, and 210
   Find the mean of the blood cholesterol levels._
2. Find the median of the data in the following lists. (See Example 2 in this section.)
   (a) 51, 27, 82, 4, 64, 34, 8, 14
   __
   (b) 21.9, 37.4, 11.6, 82.5, 17.2

3. Find the mode of the data in the following lists. (If there is more than one mode, enter your answers as a comma-separated list. If an answer does not exist, enter DNE.
   ( a ) 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 8
   _
   (b) 93, 48, 12, 34, 93, 74, 34
   ___
   8.1 Preliminary Exercises (Homework)
4. A doctor ordered four separate blood tests to measure a patient’s total blood cholesterol levels. The test results were as follows. (See Example 1 in this section.)
   285, 265, 230, and 210
   Find the mean of the blood cholesterol levels._
5. Find the median of the data in the following lists. (See Example 2 in this section.)
   (c) 51, 27, 82, 4, 64, 34, 8, 14
   __
   (d) 21.9, 37.4, 11.6, 82.5, 17.2

3. Find the mode of the data in the following lists. (If there is more than one mode, enter your answers as a comma-separated list. If an answer does not exist, enter DNE.
   ( a ) 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 8
   _
   (b) 93, 48, 12, 34, 93, 74, 34
   ___
   8.1 Preliminary Exercises (Homework)
4. A doctor ordered four separate blood tests to measure a patient’s total blood cholesterol levels. The test results were as follows. (See Example 1 in this section.)
   285, 265, 230, and 210
   Find the mean of the blood cholesterol levels._
5. Find the median of the data in the following lists. (See Example 2 in this section.)
   (e) 51, 27, 82, 4, 64, 34, 8, 14
   __
   (f) 21.9, 37.4, 11.6, 82.5, 17.2

3. Find the mode of the data in the following lists. (If there is more than one mode, enter your answers as a comma-separated list. If an answer does not exist, enter DNE.
   ( a ) 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 8
   _
   (b) 93, 48, 12, 34, 93, 74, 34
   ___
   8.1 Hmwk Measures of Central Tendency (Homework)
4. Find the mean, the median, and the mode(s), if any, for the given data. Round noninteger means to the nearest tenth. (If there is more than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.)
   30, 38, 39, 34, 5, 14, 48, 32
   mean _ median
   mode(s) _
5. Find the mean, the median, and the mode(s), if any, for the given data. Round noninteger means to the nearest tenth. (If there is more than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.)
   2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2

mean _ median __
mode(s) _

3. Find the mean, the median, and the mode(s), if any, for the given data. Round noninteger means to the nearest tenth. (If there is more than one mode, enter your answer as a comma-separated list. If an answer does not exist, enter DNE.)
   −8.9, −2.4, 4.1, 4.1, 6.6, 8.1, 9.7
   mean __

median __

mode(s) __

6. In some 4.0 grading systems, a student’s grade point average (GPA) is calculated by assigning letter grades the following numerical values.
   A = 4.00 B− = 2.67 D+ = 1.33
   A− = 3.67 C+ = 2.33 D = 1.00
   B+ = 3.33 C = 2.00 D− = 0.067
   B = 3.00 C− = 1.67 F = 0.00
   Use this grading system to find this student’s GPA. Round to the nearest hundredth.

Tessa’s cumulative GPA for 3 semesters was 3.35 for 46 course units. Her fourth semester GPA was 3.78 for 12 course units. What is Tessa’s cumulative GPA for all 4 semesters? __

7. A professor grades students on four tests, a term paper, and a final examination. Each test counts as 15% of the course grade. The term paper counts as 20% of the course grade. The final examination counts as 20% of the course grade. Alan has test scores of
   84, 98, 92, and 80.
   Alan received an 86 on his term paper. His final examination score was 90. Use the weighted mean formula to find Alan’s average for the course. (Round your answer to one decimal place.) __
8. Another measure of central tendency for a set of data is called the midrange. The midrange is defined as the value that is halfway between the minimum data value and the maximum data value. That is,
   midrange =
   minimum value + maximu value
   2
   The midrange is often stated as the average of a set of data in situations in which there are a large amount of data and the data are constantly changing. Many weather reports state the average daily temperature of a city as the midrange of the temperatures achieved during that day. For instance, if the minimum daily temperature of a city was 60° and the maximum daily temperature was 90°, then the midrange of the temperatures is
   60° + 90°/2 = 75°
   The following daily temperatures were recorded at three-hour intervals.
   54°, 68°, 69°, 71°, 74°, 73°, 68°, 67°, 61°
   Determine the following in degrees.
   (a) the minimum data value
   °
   (b) the maximum data value
   °
   ( c ) the midrange
   _____ °
9. Another measure of central tendency for a set of data is called the midrange. The midrange is defined as the value that is halfway between the minimum data value and the maximum data value. That is,
   Midrange = minimum value + maximum value
   2
   The midrange is often stated as the average of a set of data in situations in which there are a large amount of data and the data are constantly changing. Many weather reports state the average daily temperature of a city as the midrange of the temperatures achieved during that day. For instance, if the minimum daily temperature of a city was 60° and the maximum daily temperature was 90°, then the midrange of the temperatures is
   60° + 90°/2 = 75°
   During a two-minute period, the temperature in a town increased from a low of −2°F to a high of 45°F. Find the mid-range of the temperatures during this two-minute period.
   __ °F
10. After six biology tests, Ruben has a mean score of 80. What score does Ruben need on the next test to raise his average (mean) to 82? _
11. For the first half of a baseball season, a player had 86 hits out of 279 times at bat. The player’s batting average was 86/279 = 0.308. During the second half of the season, the player had 57 hits out of 281 times at bat. The player’s batting average was 57/281 = 0.203. (Round your answers to three decimal places.)
    (a) What is the average (mean) of 0.308 and 0.203?
    (b) What is the player’s batting average for the complete season? __
12. Mark averaged 60 miles per hour during the 30-mile trip to college. Because of heavy traffic he was able to average only 40 miles per hour during the return trip. What was Mark’s average speed for the round trip?
    __ mph

8.2 Preliminary Exercises (Homework)
1.Find the range of the numbers of ounces dispensed by Machine 2 in the table below.

Soda dispensed ( ounces )
Machine 1 machine 2
9.52 8.01
6.41 7.99
10.07 7.93
5.85 8.05
8.15 8.02
X = 8.0 x=8.0
_ oz

2. A student has the following quiz scores.
   5, 8, 16, 17, 18, 20
   Find the standard deviation for this population of quiz scores. Round your answer to the nearest hundredth.
3. Use a graphing calculator to find the mean and the population standard deviation (in sec) of the race times in the following table. ( Round your answers to the nearest thousandth.)
   Men’s 400 meter dash result, in seconds
   49.4 , 48.2 , 53.2 , 50.0, 48.2 , 49.6 , 47.6 , 47.8 , 47.2,
   46.4, 46.2 , 45.9 , 46.7 , 45.9 , 45.1 , 43.8 , 44.66 , 44.26
   44.60 , 45.27 , 43.87 , 43.50 , 43.29 , 43.84 , 44.00, 43.75, 43.94

Mean _ sec
population standard deviation _ sec

5. Find the population variance for the measured speeds, in gigahertz, of five computers given as 5.1, 4.7, 5.3, 4.9, and 5.0. _

Sample Solution