1 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Since We Have the Means, Let’s Find the 

Happy Median

Frank A. Cirillo, MS

Economist

Division of Consumer Expenditure Surveys

Bureau of Labor Statistics

EEA 2/27/21
2 — U.S. BUREAU OF LABOR STATISTICS • bls.gov

Introduction

 When looking at data, the way we present it frames our 

understanding of the world around us.

Hypothetically, if New York City has a homicide rate of 1 per 100,000 people in 

April 2019 and in May of 2019 it has a homicide rate of 2 per 100,000 people, it 

would be true to say that there was a 100% increase in the homicide rate from April 

to May. However, it would also be true to say that the homicide rate increased by 1 

in 100,000 people from April to May 2019. 

A headline stating, “Homicide rates double in NYC from April to May” gets a lot 

more clicks than “Homicide rate increases by 1 per 100,000 people from April to 

May”
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The CE Connection

 How does this relate to BLS Consumer Expenditure Surveys 

(CE) data?

 When we publish annual and semi annual reports, we decide how 

to frame and present our data. This can affect how the outside 

world perceives and reports on issues pertaining to Consumer 

Expenditure Data. 

 All data and calculations in today’s presentation were made with 

internal CE Microdata; replicating with CE Public-use microdata 

files might yield slightly different results. 
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Medians vs Means

 Currently, the CE program only reports mean values for the data 

we collect and release in our tables and annual reports. These 

mean values include null values for consumers who don’t report 

any purchase of that item. 

 What if there was another way to present our data, what would 

that show us?

 Medians are another measure of centrality that have distinct 

advantages and disadvantages compared to means. 
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Outliers

 One of the advantages of using medians over means is the lack of 

sensitivity to outliers.

 Means can be highly sensitive to extreme values on either end of data sets 

and this bias is reflected in the mean value.

 Medians on the other hand, are resistant to outliers, meaning you can get a 

more representative picture of the data using medians when outliers are 

included in your data. 

 For example, if you take the numbers 0 through 10 as your sample, the 

mean and the median are both 5. But if you change the 10 to 1,000, the 

mean jumps to 95 while the median is unchanged.
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Population Distribution

 Another advantage of using 

medians compared to means is 

how they are affected by skewed 

data sets.

 Means are pulled up or down 

depending on the skew of the 

data where as medians maintain a 

more stable representation of the 

data as shown in chart 1.

Chart 1
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Percent Reporting

 When sampling a large group of respondents, many times you will have 

null or 0 values for certain reported categories, and the CE data are no 

exception. 

 Currently, CE includes null values in our mean calculations. This creates a 

problem if we were to adapt medians as a new measure of our data. 

 For any category that does not have at least 50% of respondents reporting, 

the median value will be 0. For this reason we will use this value (50% 

reporting) as a bench mark when looking for medians in CE data.

 We can also compare the median and mean values of only those 

consumers who reported data for certain categories to see if the reported 

values skew in any direction. 
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All 2019 categories with percent reporting >50%

Category % reporting Category % reporting Category % reporting

Bakery products [D] 65.16 Fruits and vegetables [D] 73.03 Pensions and Social Security [I] 77.21

Cable and satellite television services 

[I] 56.66 Gasoline [I] 88.61 Personal care services [I] 60.17

Cellular phone service [I] 76.9 Gasoline, other fuels, and motor oil [I] 89.57 Personal insurance and pensions [I] 83.4

Cereals and bakery products [D] 70.75 Health insurance [I] 76.41

Personal taxes (contains some imputed 

values) [I] 81.72

Computer information services 

(internet) [I] 72.85 Housekeeping supplies [D] 52.12 Property taxes [I] 62.61

Dairy products [D] 67.39 Income after taxes [I] 99.89 Shelter [I] 97.82

Deductions for Social Security [I] 76.84 Income after taxes [I] 99.8 State and local income tax (imputed) [I] 62.18

Electricity (owned home) [I] 62.36 Lunch [D] 52.46 State and local income taxes [I] 62.18

Electricity [I] 91.71 Meats, poultry, fish, and eggs [D] 66.21 Telephone services [I] 87.77

Estimated market value of owned home 

[I] 63.69 Miscellaneous foods [D] 72.78 Utilities, fuels, and public services [I] 97.19

Estimated monthly rental value of 

owned home [I] 63.8 Money income before taxes [I] 99.76 Vehicle insurance [I] 73.09

Federal income tax (imputed) [I] 76.12 Net change in total liabilities [I] 57.89

Vehicle rental, leases, licenses, and 

other charges [I] 53.67

Federal income taxes [I] 76.12 Nonalcoholic beverages [D] 59.42 Wages and salaries [I] 75.23

Fresh fruits [D] 56.29 Other dairy products [D] 54.75 Water and other public services [I] 67.04

Fresh milk and cream [D] 50.46 Owned dwellings [I] 64.16 Water and sewerage maintenance [I] 59.79

Fresh vegetables [D] 56.36
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Ease of Use

 Mean values have a few advantages that medians do not have, mainly the 

ability to sum mean values of smaller groups to easily calculate the mean 

value of a larger group made up of the smaller groups. 

 For example, adding the means of Fresh Milk, Cream, Butter, Cheese, Ice 

Cream and related products, other dairy products, and Miscellaneous diary 

products yields the mean of Diary products.

 In terms of general use, medians have no other functional downside 

compared to means and shouldn’t be substituted in lieu of means.

 Medians should be used to complement means to show a more holistic 

picture of CE data. Let’s look at a few examples of this.
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Apples (UCC=110110)

 To illustrate the problem of using a universal classification code (UCC) with a percent 

reporting under 50%, consider apples. The mean expenditure value for all consumer 

units (CU) on apples in 2019 was $43.71 while the median value was $0. However, 

the median of apple purchasers was $207.48 while the mean value of all purchasers 

was $255.61. (43.71/0.1710)

 What does this tell us about the distribution of apple consumption, how much apple 

purchasers pay, or what the average consumer spent on apples in 2019, etc.?

2019 AllCUPrePub Apples 2019 Diary Data Apples Apples (purchasers only)

Yrly Mean est. $43.71 Yrly Median est. $0 $207.48

Mean (purchasers) $255.61 Qtly Median est. $0 (10,682)a $51.87 (1,908)b

Percent reporting 17.10% Medians percent reporting 17.86% (b/a)
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Cellular Phone Service (270102)

 Cellular Phone Service (CPS) on the other hand did have a percent reporting above 

50%. When taking the median value of CPS we get something much more 

representative than with apples. Our median is $760 while our mean is $1,218.08

 If you look closely at the data you will realize that the median value of CPS 

purchasers alone ($1,080.00) was actually significantly lower than the mean value of 

purchasers ($1,583.98) 

 This shows that outlier values on the top end of our data or perhaps a heavy upper 

tail, skew our mean value in the extreme.

2019 AllCUPrePub CPS 2019 Interview Data CPS CPS (purchasers only)

Yrly Mean est. $1,218.08 Yrly Median est. $760.00 $1,080.00

Mean (purchasers) $1,583.98 Qtly Median est. $190.00 (24,956)a $270.00 (19,197)b

Percent reporting 76.90% Medians percent reporting 76.92% (b/a)
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Fresh Milk and Cream 

Fresh Milk, All types(090110) and Cream (090210)

 Unlike the prior examples, this category, Fresh Milk and Cream (FM&C) contains 2 UCC’s as well as a 

percent reporting above 50%.

 When comparing the median value of $51.48 for all consumers to the mean value of $140.39, there is 

very noticeable difference. The mean of all consumers is almost 3 times larger than the median value of 

all consumers. However, the median value of purchasers, $206.96, is actually pretty similar to the mean 

value of purchasers, $278.22. 

 In this case means can be a more accurate measure of centrality for FM&C, but medians can still be 

useful to check how much outliers are influencing the mean purchasers value. In this case, the mean 

purchasers value is not very different from the median purchasers value. 

2019 AllCUPrePub FM&C 2019 Diary Data FM&C FM&C (purchasers only)

Yrly Mean est. $140.39 Yrly Median est. $51.48 $206.96

Mean (purchasers) $278.22 Qtly Median est. $12.87 (10,682)a $51.74 (5,455)b

Percent reporting 50.46% Medians percent reporting 51.07% (b/a)
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Income Before Taxes (980000) 

Income After Taxes (980017) 

2019 AllCUPrePub Income before taxes 2019 Interview Data Income before taxes

Yrly Mean est. $82,852 Yrly Median est. $45,478.60

Percent reporting 100% Qtly Median est. $11,369.65

2019 AllCUPrePub Income after taxes 2019 Interview Data Income after taxes

Yrly Mean est. $71,487 Yrly Median est. $43,362.00

Percent reporting 100% Qtly Median est. $10,840.50
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Findings

 In all examples our median values were smaller than our mean values, regardless of the 

percent reporting. This means our data sample has a positive skew.

Chart 2
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Findings

 Sometimes the median value of purchasers was higher or lower than the mean value of 

all consumer units, but the median value of purchasers was always lower than the mean 

value of purchasers, further highlighting the positive skew of our data samples as 

shown in chart 2. 

Chart 2
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Findings

 Since medians show lower values of consumption than means, how does 

this affect our reports?

 How does this shift affect the public perception of CE data and reports? 

 Should certain published tables be republished with medians instead of 

means?

 Can we break populations up into subcategories and expect means to be an 

accurate reflections of these groups expenditures and other data points?
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Conclusion

 How we frame our data and our findings is extremely important. 

 By using new metrics (medians) along with current metrics (means) we 

can dive deeper into the makeup of US consumer expenditures, their 

distributions, skew, and resulting bias to show a more accurate 

representation of the data we are analyzing. 

 More analysis will be needed to further compare median value changes 

from year to year to see how else we can frame our CE data as well as how 

the non normal distribution of our data affects the methodology and 

outcomes of CE’s models.

 Hopefully you can apply this mindset to reexamine how you present your 

data or how you examine others in the future!
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Sources

1. https:/www.cdc.gov/csels/dsepd/ss1978/lesson2/section8.html

2. https://www.bls.gov/cex/2019/research/allcuprepub.pdf

3. https://codeburst.io/2-important-statistics-terms-you-need-to-know-indata-science-skewness-and-kurtosis-388fef94eeaa

Limitations of BLS Data

 All of the data calculations done in today’s presentation were done using CE’s current internal 

methodology including imputation, top coding, and model weighting.

 In future publications medians maybe published using different methodology than what was used in 

today’s presentation. 
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Frank A. Cirillo, MS

Economist

Division of Consumer Expenditure Surveys

www.bls.gov/cex

202-691-6905

cirillo.frank@bls.gov

Contact Information