uses of mean – JDM Educational

Mean tells us the average of a data set, which can help us to understand the data and make predictions about the future. However, there are lots of other uses for the mean of a data set. So, what is mean used for? Mean is a measure of central tendency that is used in business, finance, research, and everyday life for comparing companies, tracking population changes, performing medical research, advertising, selecting from a group of job candidates, making predictions, and calculating unit price. Of course, mean can be far above the median if the data set has one or more large outliers that skews the mean high or low. In this article, we’ll talk about what the mean is used for in various applications. We’ll also look at some examples with numbers so that you can see how mean is used. Let’s get started. What Is Mean Used For? Mean (also called average or arithmetic mean) is a measure of central tendency that is used for various purposes in business, finance, research, and everyday life, including: Analyzing companies (comparing stock prices over time, comparing two companies, or comparing a company to the overall market).Tracking a population over time (or comparing two populations).Researching effectiveness of a treatment (average time to recovery, average improvement in key metrics).Deciding when it makes sense to advertise on a platform (based on LTV, or lifetime value of a customer, and CAC, or cost to acquire a customer).Comparing two candidates (for a sports team, academic institution, or job opening).Making predictions based on past data (mean and standard deviation to forecast a range of values).Unit price (to compare two bulk packages of an item in the same store or at different stores) Let’s take a look at each one of these in turn, starting with comparing company stock. Analyzing Companies As Investments When analyzing investments, mean is one of the most helpful tools to understand one or more companies at a glance. Mean is a tool used to compare stock market investment opportunities and companies. For example, mean can be used to: Analyze the historical performance of a company (by finding average stock price, earnings per share, profit margin, volatility, and other metrics over 5, 10, or 20 year periods).Compare a stock to the overall market (by comparing the company to the market average for earnings per share, dividend yield, and other metrics over various time periods).Comparing two companies side-by side (by comparing their average revenue, profit, profit margin, growth, and other metrics over the past 6, 12, 18, or 24 months). Example 1: Analyzing Historical Performance Of A Company We can use the historical performance of a company to decide if we want to invest or not. Let’s say that a company has the following metrics: Average price per share of $40 over the past 20 yearsAverage price per share of $20 over the past 10 yearsAverage price per share of $10 over the past 5 years The falling average share price in more recent years suggests that the company is on a decline, and that it is declining more rapidly as time goes on. Example 2: Comparing A Company Stock To The Overall Market We can compare an individual stock to the entire market to see where it stands in comparison. Let’s say that all dividend-paying stocks have the following metrics: Average dividend yield of 6% over the past 20 yearsAverage dividend yield of 5% over the past 10 yearsAverage dividend yield of 4% over the past 5 years On the other hand, the company in question has the following metrics: Average dividend yield of 2% over the past 20 yearsAverage dividend yield of 3% over the past 10 yearsAverage dividend yield of 4% over the past 5 years In the past 5 years, the company’s dividend yield (annual dividend payment divided by stock price) is on par with other dividend-paying stocks, so it might be reasonable to buy it. Looking at a longer time horizon (10 or 20 years), we see that the average dividend-paying stock has decreased its dividend yield, while this particular company has increased it. This may confirm our decision to buy the company, since it may outperform its peers in the years to come. Example 3: Comparing Two Companies Let’s say that you are considering two companies for purchase: Carl’s Car Wash and Larry’s Laundry. We can use mean profit, revenue, and profit margin to compare two companies (such as a car wash or laundromat) to see which might be a better investment. Both companies have an average profit of $10,000 per month for the last 12 months and an average profit of $8,000 per month in the past 24 months (so, both are growing, and at about the same rate). This makes it sound like either company is a good bet. However, we can dig deeper to get a better idea of how each company is performing. After some more research and number-crunching, we find that Carl’s Car Wash has average revenue of $50,000 per month over the last year. Larry’s Laundry has average revenue of $20,000 per month over the past year. This means that Carl’s Car Wash has a profit margin (profit divided by revenue) of $10,000 / $50,000 = 20%, while Larry’s Laundry has a profit margin of $10,000 / $20,000 = 50%. This makes Larry’s Laundry more attractive if we are worried about cost increases. This is because Larry’s Laundry could see a doubling of costs and still break even, while anything more than a 25% increase in costs would mean that Carl’s Car Wash would be losing money every month. Tracking Or Comparing Populations The mean is often a good approximation for the average person in a group, as long as there are not huge outliers skewing the data in one direction. Example: GDP (Gross Domestic Product) Per Capita Of Two Countries We can use GDP (Gross Domestic Product) and GDP per capita to compare two countries as a whole and by average citizen. Let’s say that the U.S. has a GDP of $21 trillion, with a population of 330 million, while Luxembourg has a GDP of $73 billion, with a population of 630,000. The U.S. has a higher “national income” (GDP) by far. However, the average person might not be better off, since: GDP per capita = GDP / population So, for the U.S., we have: U.S. GDP per capita = $21 trillion / 330 million = $63,636.36 For Singapore, we have: Luxembourg GDP per capita = $73 billion / 630,000 = $115,873.02U.S. GDP per capita = $21 trillion / 330 million = $63,636.36 So the GDP per capita (per person) in Luxembourg is 82% higher than the GDP per capita in the U.S. Researching Effectiveness Of Medical Treatments In medical or psychological research, we can compare the effectiveness of treatments by studying two groups: a treatment group (that receives the treatment) and a control group (that receives a placebo, or no treatment). Comparing the mean between a treatment group and a control group can give us an idea of the effectiveness of a treatment. Example: Effectiveness Of A Medical Treatment A medical study for a cholesterol-lowering drug has a treatment group and a control group. The cholesterol of each member of the group is taken at the beginning of the study and at the end of the study (1 year later). After 12 months, the treatment group saw an average decline of 30 mg per dL in total cholesterol. The control group saw an average decline of 3 mg per dL in total cholesterol. This suggests that the treatment may be effective in reducing cholesterol. We should dive deeper into the data (using the sample mean and standard deviation for both groups) to compare the means by using hypothesis testing. Deciding Whether To Advertise Companies need to make good decisions to stay in business. One decision involves where to spend money on advertising. A company can find out its return on investment for various advertising channels (Google Ads, Facebook Ads, YouTube ads, etc.) to help them make this decision. They can also compare the CAC (cost to acquire a customer) for a given channel with the LTV (lifetime value) of a customer. Usually, it does not make sense to advertise if CAC is higher than LTV, unless the company is willing to lose money in the short term to increase market share in the long term. Comparing the average cost to acquire a customer (CAC) and average lifetime value of a customer (LTV) can help us to figure out when and where it makes sense to advertise. Example: Deciding Whether To Continue Advertising A company is advertising its products on a well-known blogger’s website. The company pays the blogger an advertising fee of $5,000 per month. The company studies its analytics and finds that the blogger’s website sends an average of 2,000 visitors per month to the company’s sales page. Out of these visitors to the sales page, an average of 10% convert (that is, buy the company’s product). This means that an average of 10% x 2,000 = 200 paying customers per month come from the blogger’s website. This means that the CAC (average cost to acquire a customer) through the blogger’s website is: CAC = (total spent in acquiring customers) / (total customers acquired)CAC = $5,000 / 200CAC = $25 So, the company’s cost to acquire a customer is $25. If the company is making a profit of $100 per product sold, then they should continue advertising on the blogger’s website. If the company is making a profit of $10 per product sold, then they should stop advertising on the blogger’s website (unless they want to temporarily lose money on every sale to increase market share). At the “breakeven” point (profit of $25 per product sold), the company may wish to continue advertising to increase market share, even though it won’t bring any more immediate profit. Comparing Two Candidates We can use mean to compare candidates in many situations: GPA (grade point average) for academic scholarships and college admissionsBatting average for baseball recruitingAptitude test scores for hiring job candidates Example: Batting Averages The batting average for a baseball player is the number of hits divided by the number of times at bat: Batting Average = (Number Of Hits) / (Number Of Times At Bat) One potential recruit, Joseph, has had 15 hits in 60 times at bat this year. So, Joseph’s batting average is: Joseph’s Batting Average = (15) / (60) = 0.250 (read as “two fifty”) Another potential recruit, Kyle, has had 12 hits in 50 times at bat this year. So, Kyle’s batting average is: Kyle’s Batting Average = (12) / (50) = 0.240 (read as “two forty”) Joseph’s batting average is slightly higher than Kyle’s (Joseph is at 250, or 25%, while Kyle is just behind at 230, or 24%). Batting average is one measure that helps to determine who makes it to the next level in baseball. Making Predictions We can use the mean, calculated with historical data, to make predictions about future events. This method can be used with everything from weather prediction to sales. Example: Sales Projections Let’s say that you have been working in a sales job for about a year. You have made 4,000 calls during that time and made 200 sales. On average, it takes 4,000 / 200 = 20 calls to make one sale. Another way to say this is to take the reciprocal (200 / 4,000 or 1 / 20) to get an average 5% success rate for sales calls. You can use this historical data to make a prediction about next month’s sales. You are faster at making sales calls now, and you are using new software that helps you to work faster. Next month, you are poised to make 500 calls. Using the average sales success rate, you can predict the number of sales you will make next month: Sales Made = (Success Rate)*(Sales Calls Made)Sales Made = 5%*500Sales Made = 25 This is a big improvement, since you made an average of about 16.7 sales (200 sales / 12 months) during your first year on the job! You can use the average close rate to predict the sales you will make in the future. Calculating Unit Price When deciding which package of items to buy, we can use the mean to find the average price per unit and see which package is a better deal. Example: Comparing Unit Price Per Package Let’s say that Bob’s Pencils are sold in a package of 12 for $8.40, while Carl’s Pencils are sold in a package of 8 for $6.40. We can calculate the mean price per pencil to compare the two for value: Average Cost Per Pencil = (Total Cost Of Package) / (Total Number Of Pencils) For Bob’s Pencils, we get: Bob’s Average Cost Per Pencil = $8.40 / 12 = $0.70 For Carl’s Pencils, we get: Carl’s Average Cost Per Pencil = $6.40 / 8 = $0.80 So, Bob’s Pencils is a better package deal, since the cost per pencil is 70 cents (compared to 80 cents per pencil for Carl’s Pencils). We can use mean to calculate unit prices for packages of goods to compare them and see which is the best value. Conclusion Now you know some of the uses of mean in everyday life. You also have some examples that show how the calculations are done to use the mean in helping to make decisions. You can learn more about the difference between mean and standard deviation in my article here. You can learn more about when the mean increases or decreases here. You might also want to read my article on weighted average, a more general form of mean. The geometric mean is another measure of central tendency - you can learn about it here. I hope you found this article helpful. If so, please share it with someone who can use the information. Don’t forget to subscribe to my YouTube channel & get updates on new math videos! ~Jonathon