Charlene Brown
Kentucky
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Project:
  This is the second lesson in a two-part project consisting of:
(1) Statistics: Reading and interpreting production graphs
(2) Statistics: Determining mean, range, median, mode and probability

Subjects:
  Adult basic education, Critical thinking, Educational technology, Employability, General education development (GED), Interpersonal relationships, Job skills, Life skills, Mathematics, Numeracy, Problem solving, Sciences, Vocabulary development, Work environment

Learner Level:
  Multi-level if all groups are carefully grouped so that lower level learners are mixed with higher level ones.

Time Frame:
  2 hours

Learner Grouping:
  Individual, Small group, Whole class

Setting:
  This activity was part of a unit taught at a manufacturing plant where employees were having problems understanding the concepts involved in collecting data for quality control purposes.

Email:
  Not available

Program:
  Bryan Adult Learning Center

Type of Program:
  ABE

Student Population Served:
  Basic skills (grade levels 5-8.9)

 
Statistics: Determining mean, range, median, mode and probability

This lesson teaches how to calculate mean, median, range, mode and probability. As a class, learners explore the differences in meaning among mean, range, median, and mode. Then working in teams, they use data from their workplace to compute values for these terms. Finally the class explores the term “probability” using a die. __________________________________________________________

Learning Objective:
Participants will be able to compute the mean, range, median, mode and probability using the problems given them. They will be able to work as a team to collect and analyze data. Learners will be able to design and execute appropriate illustrations to show the mean, range, median, and mode of the data they collect.

Primary Skill:
Use math to solve problems and communicate

Secondary Skills:
Decision making, Reflect and evaluate

Learner Needs & Goals:
Frequently employees are asked to participate in team discussions and meetings to make decisions based on data. When employees are unable to interpret the data correctly, they are unable to participate fully and competently in the decision-making process.

Learning Activity Description:
Participants should have completed a lesson on reading and interpreting production graphs. If they have not, the Workplace Essential Skills video is recommended. This lesson is designed to follow the Graphs lesson; however, either lesson could be taught first.

1. Ask the participants what their average take home pay is per month. (Be sure to preface this question by stating that they are not to say this aloud.) Ask them how they calculated this. Was it by adding up their take home pay for each month and then dividing it by the number of months in the year? Tell the class that the word mean is often used instead of average. Explain that average or mean is the resulting value from adding a group of numbers together and dividing the sum by the number of items in the group. Demonstrate the concept by working through several sample problems on the board. Ask individuals how old they think the President of the United States is. Show them how to calculate the average age that individuals have guessed.

2. Ask if anyone can explain the term range. Point out that the range is the difference between the greatest and the smallest value (number) in a group. Use the numbers from the previous exercise to demonstrate.

3. Show the class a picture of a divided highway and ask the participants to define what the strip of grass between the two sides of the highway is called - a median. Lead the participants to discuss the similarities between the two sides of the highway, for example, there are two lanes on each side of the median. Explain that the median is the number at which half the values in a sample fall above and half fall below. It may or may not be the same as the mean or average. To demonstrate how to find the median, list all the numbers in a population (a group of very similar or like items) from the highest value to the lowest, and the middle number is the median or midpoint. If there is an even number of values, use the average of the two middle numbers for the midpoint or median.

4. Next, explain that mode is the most frequently used number in a sample population. For example, in the list: 11; 12; 45; 23; 24; 23, the 23 is the mode. It is the most frequently occurring value or number.

5. Have the participants compute the mean, range, median, and mode for a fictitious employee’s earnings for the past six months. Have participants check their answers as you read the correct answers.

6. Divide the class in teams according to the color of the dots placed on the backs of their chairs. The teams should assign the following roles to group members: recorder, reporter, facilitator, and timekeeper. Together the teams find the answers to a handout that lists several work-related problems.

7. Ask the teams to go into the facility and collect the assigned information from which they will figure the mean, range, median, and mode. Some possible assignments may be employee hair color, age, or birth month. List twice the number of choices as the number of teams. Have each team select one problem.

8. The teams should return to the classroom and prepare their information for reporting. If the class has completed the lesson on graphs, learners may choose to use graphs to present the information during the reporting period. Have the teams report their findings.

9. Introduce probability by rolling a die and asking the learners what the chances are of rolling a snake eye (one) on the next roll. Explain that probability is the likelihood of an event occurring. Point out that this is important for quality control in a manufacturing plant. It is an important part of statistical information.

10. Ask what the chances are of rolling an odd number? An even number? Explain that there are six sides to a die and that each side is equally likely to be turned up after the die is thrown. The probability that the side with one dot lands up is 1 in 6 or 1/6. Write the formula that goes along with figuring probability on the board.

P = number of favorable ways
total number of ways

11. Explain that the secret to using a formula is to replace the words with the numbers meaning the same thing. The line between the numbers means to divide. Have participants practice by rolling die and completing some sample problems.

Materials and Resources:

  • PBS/LiteracyLink #61650 Workplace Essential Skills Series video titled Trends and Predictions: Graphs and Data available through KET, The Kentucky Network - Enterprise Division, 560 Cooper Drive, Lexington, KY 40502-2200, phone (800) 354-9067.
  • Earnings statements from a fictitious employee for the past six weeks
  • Game board and markers
  • Picture of divided highway, enlarged if possible
  • Set of problems based on the workplace, for example, the number of parts produced daily for several days on one of the assembly lines or the number of letters mailed out each day for the past several days
  • Clipboards for each team
  • Checklist for groups to evaluate their data collection
  • Die
  • Sample probability problems featuring scenarios from the participants’ workplace, for example, the number of defects per thousand or the number of customer complaints per day

Assessment:
Have the teams evaluate themselves with an instructor-prepared checklist.

Reflection:
I would begin with the probability part of the lesson because this helped the participants understand the purpose of gathering data.

Because the business used these principles to report the producton of each machine and part, the participants were able to use the skills learned in class the very next day. __________________________________________________________

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