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#### Learning Objectives

- The student will complete product analyses by calculating the mean, median, mode, and range for a given set of item retail prices.
- The student will complete sales analyses by calculating mean, median, and range using daily sales data.
- The student will understand how statistics are used to collect, organize, and interpret data.

#### Connection to Bloom’s Taxonomy

- Comprehension
- Application
- Analysis
- Synthesis

## Lesson Materials

- Calculators
- Crayons or Colored Pencils
- Index Cards
- Pencils
- Worksheets for lesson plan 6 (see sidebar)

## Making Connections

Ask students to define the word statistics. As a class, brainstorm possible definitions. Then provide students with dictionaries or access to on-line dictionaries to develop one definition that describes the term accurately. In general, statistics is a mathematical or scientific term to describe the collecting, organizing, and interpreting of data. Statistics may include creating graphs, calculating averages, or determining probability.

We live in a world filled with statistics, yet we are often unaware of their usefulness in our daily lives. Have students think about statistics by asking them to identify and list when averages are used. Provide newspapers as one possible way to jump start the activity.

**Some possible responses may include the following:**

- The average price of a gallon of gasoline
- Baseball batting averages
- Bowling averages
- Average temperature
- Average rainfall or snowfall
- Average hospital stay for patients
- Average income or age, collected as census data
- Average wait time (on the telephone) when on-hold for customer service
- Product price averages for dairy products
- Average grade on a test
- The Down Jones Industrial Average (stocks)
- Average weight or height for a child of a certain age (used by pediatricians)

## Exploring and Learning

- Four common statistical terms used to analyze data are
*mean*,*median*,*mode*, and*range*. Review the following definitions and how to calculate each:- The
*mean*is the average. It is calculated by adding values (data) and dividing by the number of values (sample). - The
*median*is the middle value in a series of values placed in numerical order. For odd sample sizes, simple use the middle value. For even sample sizes, take an average of the two middle values. - The
*mode*is the most common value in a series of values. If no value occurs more than once, then there is no mode. If two values occur more than once and the same number of times, the sample is called bimodal. - The
*range*is the difference between the largest and smallest values in a sample.

- The
- Pair students together and provide each pair with a copy of Weather Data Worksheet (PDF). Student will analyze a sample 5-day weather forecast to calculate the following statistics:
- Average (Mean) High Temperature
- Average (Mean) Low Temperature
- Median High Temperature
- Median Low Temperature
- Mode High Temperature
- Mode Low Temperature
- Range for High Temperatures
- Range for Low Temperatures

- Together as a class, review the calculations for each weather temperature statistic. It maybe helpful to guide students through each of the calculations in order to reinforce the concept of how to calculate the mean, median, mode and range. Refer to the Weather Data Worksheet Key (PDF) for answers.
- Based on the calculated weather temperature statistics, discuss the following questions:
- Was the Average (Mean) High Temperature above 85 degrees?
- (No)

- Was the Average (Mean) Low Temperature below 60 degrees?
- (Yes)

- What two values were exactly the same?
- (The Median High Temperature and the Mode High Temperature)

- Which had a larger range over a 5-day period, high temperatures or low temperatures?
- (High temperatures ranged 21 degrees versus low temperatures that ranged 18 degrees)

- Was the Average (Mean) High Temperature above 85 degrees?
- Present students with the following scenario:
RG and Hannie are working at the Raymond Geddes Elementary School Store. Sniffer has asked them to analyze their top 20 school store items. He would like to know the average (mean) retail price of those items, the median retail price, the mode, and the range. In addition, Sniffer would like RG and Hannie to analyze a week’s worth of sales by calculating several statistics: average daily total sales amount, the median daily total sales amount, and the range for daily total sales amounts for the week.

Can you help RG and Hannie calculate and analyze the statistics?

Challenge: If you run your own school store, or ran the school in a previous Geddes lesson plan, update the sales spreadsheet with your own sales data.

- To help complete the scenario, pair students together and provide each group with the following:
- Explain and list on the board, or as a transparency, the following instructions to complete the scenario:
- Place the items in the Geddes Kit List (PDF) in order by retail price from lowest to highest. If students are familiar with using spreadsheet software, encourage them to input the list into a spreadsheet to complete the product analysis.
- Calculate
- Record answers on the Product Analysis Worksheet (PDF)
- Next, use the Weekly Sales Results Excel Spreadsheet to analyze sales results for one week.
- Place the daily total sales amounts in order from lowest to highest.
- Calculate the average daily total sales amount for this week.
- Calculate the median daily total sales amount.
- Calculate the range for the daily total sales amounts.

- Record answers on the Sales Analysis Worksheet (PDF).

- As a class, review the results. Refer to the Product Analysis Worksheet Answer Key (PDF) and the Sales Analysis Worksheet Answer Key (PDF) for answers.
- Discuss the following sales analysis questions:
- Which day of the week generated the most sales? (Friday)
- Which day of the week generated the least sales? (Monday)
- What was the range between the highest sales day and the lowest sales day? ($14.76)

- Brainstorm some possible reasons to explain why sales on Friday were so much better than sales on Monday for this week. Some possible explanations include the following:
- Students may not remember to bring in their money when returning back to school after the weekend.
- The school may be able to send out more reminders during the week advertising the school store and its products.
- Teachers may have completed their lessons with students providing students more time at the end of the week to shop at the school store.
- Students purchased more of the most expensive item (6-Color Pens) on Friday. This may have helped to boost sales for the day.
- There may not be any particular reason since we have only one week’s worth of sales. Students would need multiple weeks of sales results to determine if Friday always remained the best day of the week.

- Review the definition of statistics—collecting, organizing, and interpreting data. Do students feel they were successful using statistics to analyze product and sales data?
- Lead a short discussion on some of the shortcomings of statistics. Statistics can be helpful to analyze data. However, statistics may also be misleading. As shown above, students cannot pinpoint the exact reasons why Friday generated the highest sales for the week. Statistics do not take into account the human factor - why people make the decisions they do. Averages, in particular, can be misleading. They may be affected by outliers, extreme high and low values. Often times, mathematicians will drop the highest and lowest values in a sample in order to arrive at a more representative average.

## Extended Learning and Practice

- Spend more time analyzing the Weekly Sales Results Excel Spreadsheet.
- What was the average daily number of items sold for the week? ( 656 ÷ 5 = 131 items )
- What was the median number of daily items sold? ( 134 items )
- What was the range? ( 148 - 105 = 43 items )

- Visit the PBS Kids ZOOM website at for another in-class activity to calculate averages. How heavy are your students’ backpacks? Collect, organize, and calculate data just like ZOOM did.

## Assessment

The lesson objectives can be assessed by evaluating the Weather Data Worksheet (PDF), the Product Analysis Worksheet (PDF), and the Sales Analysis Worksheet (PDF) with the Weather Data Worksheet Answer Key (PDF), the Product Analysis Worksheet Answer Key (PDF), and the Sales Analysis Worksheet Answer Key (PDF).

Use the Assessment of Student Progress PDF to assess students’ overall abilities to meet the lesson’s learning objectives, which include analyzing product price and sales data by calculating mean, median, mode, and range; and understanding how statistics are used to collect, organize, and interpret data.

## Closure

Provide each student with an index card and have them answer the following questions on one side of the card:

- What are two new things that you have learned?
- What else would you like to learn about this topic?

On the back side of the index card, instruct the students to draw a picture of something they learned about during this lesson. The index cards can be hole punched and held together with a simple shower curtain ring.