Track 15 · Applied Statistics for Professionals · Lesson 1 of 12

Sales performance and KPIs

Calculate period and compound growth rates and make seasonality-aware sales comparisons that a manager can act on.

30 minIntermediate8 graded exercisesFree

On a Monday morning the weekly dashboard shows chain sales up 43% on the previous week, and the marketing team is already celebrating. It was a holiday week. Whether that number is good news depends entirely on what you compare it with — and choosing the comparison is the most important statistical decision in sales reporting.

A key performance indicator (KPI) is a number a business tracks to judge performance: weekly sales, sales per square metre, average spend per visitor. On its own a KPI says little. It becomes information only when it is compared with something — last week, the same week last year, a target, or another store — and most reporting mistakes are mistakes of comparison, not of arithmetic.

g_t = \frac{x_t - x_{t-1}}{x_{t-1}} = \frac{x_t}{x_{t-1}} - 1

Growth rate from one period to the next (multiply by 100 for a percentage)

$x_t$: the KPI in the current period (this week, this month, this year)
$x_{t-1}$: the KPI in the comparison period — the base. Growth is always measured relative to the base, never to the new value.
$g_t$: the growth rate; negative values are declines

Growth rates compound. A 10% rise followed by a 10% fall does not return you to the start: $1.10 \times 0.90 = 0.99$ , a 1% loss. For the same reason the average growth per year over several years is not the total growth divided by the number of years but the compound annual growth rate (CAGR), which is a geometric mean of the yearly growth factors.

\text{CAGR} = \left(\frac{x_{\text{end}}}{x_{\text{start}}}\right)^{1/n} - 1

Compound annual growth rate

$x_{\text{start}}, x_{\text{end}}$: the KPI at the start and at the end of the period
$n$: the number of years (growth steps) between them — not the number of yearly values

Dataset

Weekly store sales

4,160 rows · one row = one store-week · synthetic data

About this dataset Open in the lab

Store	Region	Store size	Week number	Holiday week	Promotion	Footfall (visitors)	Weekly sales (SAR)
ST01	Central	Small	1	false	true	1986	214951.9
ST01	Central	Small	2	false	false	1811	201838.41
ST01	Central	Small	3	false	true	2045	217021.33
ST01	Central	Small	4	false	true	1947	212706.67
ST01	Central	Small	5	false	false	1798	193921.23
ST01	Central	Small	6	false	false	1894	201477.48

Lumen Bay Stores (fictional): 40 stores × 104 weeks of sales, footfall and holiday/promotion flags.

Weekly sales of one store (ST01) over two years. The sharp spikes are holiday weeks; the gentle wave is annual seasonality with a summer dip.

Show the data as a table

Week number	Weekly sales
1	214952
2	201838
3	217021
4	212707
5	193921
6	201477
7	197267
8	206280
9	211218
10	201213
11	206739
12	199819
13	209185
14	197123
15	293939
16	313148
17	203765
18	197709
19	232446
20	246758
21	212820
22	205871
23	216734
24	205562
25	198589
26	266500
27	236579
28	204712
29	225071
30	177968
31	189915
32	194620
33	171665
34	166083
35	181943
36	199899
37	185408
38	296005
39	189010
40	179410
41	186868
42	195030
43	185182
44	176416
45	197533
46	188537
47	192513
48	178527
49	192016
50	187312
51	309569
52	203754
53	166637
54	210566
55	214755
56	195425
57	184641
58	250361
59	199192
60	205819
61	241159
62	209134
63	223981
64	213078
65	211331
66	334444
67	369291
68	215761
69	212458
70	208998
71	222373
72	228725
73	231077
74	227540
75	210337
76	204514
77	323839
78	227540
79	218137
80	221926
81	188962
82	235957
83	192834
84	214758
85	198978
86	197903
87	205242
88	236614
89	202619
90	259522
91	194378
92	189092
93	203780
94	206979
95	213130
96	193551
97	215059
98	197784
99	234531
100	190308
101	198242
102	199824
103	308311
104	195791

Retail sales are seasonal: they follow the calendar. In this (synthetic) chain, total weekly sales are usually between 11 and 14 million SAR, but holiday weeks jump to 16–19 million. That is why week-on-week growth is a poor guide in a seasonal business: from week 14 to the holiday week 15, chain sales rose by 42.9% — almost all of it the calendar, not performance.

Worked example

Comparing a holiday week fairly

In Year 1 the festival holiday fell in weeks 15–16; in Year 2 it fell in weeks 66–67 (lunar-calendar holidays move about 11 days earlier each year). Chain sales were 12.70M SAR in week 14, 18.15M in week 15, 18.43M in week 16, 13.33M in week 65, 18.90M in week 66 and 18.64M in week 67. How did the Year 2 holiday perform?

Week-on-week. Week 66 vs week 65: $18.90 / 13.33 - 1 = 41.8\%$ . This compares a holiday week with an ordinary week, so it measures the holiday, not the business.
Same week number last year. Week 66 is week 14 of Year 2, so a naive year-on-year comparison uses Year 1 week 14: $18.90 / 12.70 - 1 = 48.8\%$ . The holiday moved, so this compares a holiday week with a normal week again. One week later the same method gives week 68 vs week 16: −26.7%, an apparent collapse.
Align the calendars. Compare the holiday period with the holiday period: $\dfrac{18.90 + 18.64}{18.15 + 18.43} - 1 = 2.6\%$ .

The Year 2 holiday was about 2.6% above the Year 1 holiday — a little below the chain's underlying growth of 4.8% a year (two weeks are a noisy basis, so treat that gap as "no clear difference"), and nothing like the 41.8% the week-on-week view suggests.

Over a full year the calendar effects mostly cancel. The mean store-week sales were 315,402 SAR in Year 1 (weeks 1–52) and 330,639 SAR in Year 2, a growth of 4.83%. Every one of the 40 stores traded in both years, so this is also a like-for-like (same-store) comparison. In real chains, new store openings inflate total growth, so analysts report like-for-like growth on stores open in both periods.

Normalise before you rank. Large stores sell the most per week (513,322 SAR on average vs 210,274 SAR for small stores), but per square metre of floor the small stores lead: 245.8 vs 196.7 SAR per m² per week (total sales ÷ total floor area of each group: a ratio of totals, so every square metre counts equally). Sales per m², sales per visitor (here about 94.5 SAR) and like-for-like growth answer different questions; choose the KPI that matches the decision (space allocation, staffing, marketing).

Quick check

Sales rose 20% in March and fell 20% in April. What is the net change from the start of March to the end of April?

Comparison	Good for	Watch out for
Week-on-week	Spotting sudden operational problems	Seasonality, holidays and promotions dominate
Same period last year	Underlying growth in a seasonal business	Moving holidays, calendar shifts, store openings
Seasonally adjusted (÷ seasonal index)	Month-to-month trend reading	The index must come from several past years
Like-for-like (same stores)	Organic growth of the existing estate	Excludes the effect of openings and closures
Per m² / per visitor	Fair ranking of different-sized stores	Ratios hide total volume

Which comparison answers which question

Exercises

The lesson is complete when every exercise is answered correctly. Hints are free; viewing a worked solution before solving means the exercise won't count towards mastery.

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Exercise 1 · Guided, difficulty 1 of 3

Week-on-week growth

Not started

A store sold 227,506.00 SAR last week and 201,271.91 SAR this week. What is the week-on-week growth rate? Give a percentage to 2 decimal places (negative for a decline).

Exercise 2 · Practice, difficulty 2 of 3

Compound annual growth

Not started

A regional chain's annual sales were 17.3 million SAR in the base year and 21.5 million SAR 3 years later. What was the compound annual growth rate (CAGR)? Give a percentage to 2 decimal places.

Exercise 3 · Interpretation, difficulty 2 of 3

Choosing the comparison for a moved holiday

Not started

In this chain the festival holiday fell in weeks 15–16 of Year 1 and weeks 66–67 of Year 2 (weeks 14–15 of the second year). The regional director wants to know whether week 66 was a good week. Chain sales in week 66 were 18.90 million SAR. Which comparison should the report lead with?

Exercise 4 · Application, difficulty 2 of 3

Year-on-year growth of the chain

Not started

Use the retail_weekly dataset. Year 1 is weeks 1–52 and Year 2 is weeks 53–104; all 40 stores trade in every week. In the lab, filter on week and find the mean store-week sales for each year, then the year-on-year growth rate. (Because both years have the same number of store-weeks, the ratio of the means equals the ratio of the totals.)

Data: retail_weekly · Open in the lab to explore and calculate.

Exercise 5 · Application, difficulty 3 of 3

How big is the holiday effect?

Not started

In retail_weekly, compare store-weeks with holiday = true and false. Find the mean store-week sales in each group, the holiday uplift (holiday mean ÷ non-holiday mean − 1), and the percentage of store-weeks with a promotion in each group (a crosstab of holiday × promotion gives the counts).

Data: retail_weekly · Open in the lab to explore and calculate.

Exercise 6 · Practice, difficulty 2 of 3

Seasonally adjusted month-on-month change

Not started

A store's seasonal indices (from five previous years) are 0.94 for November and 1.27 for December: December sales are typically 27% above an average month. This year November sales were 880,000 SAR and December sales 1,168,700 SAR.

What is the seasonally adjusted change from November to December? Give a percentage to 1 decimal place.

Exercise 7 · Practice, difficulty 2 of 3

Fair or misleading comparison?

Not started

Classify each sales comparison as fair for the stated purpose or misleading.

Ranking stores of very different sizes by total weekly sales to decide which store managers get a bonus

Comparing this year's March with last year's March, when the same holidays fell in March both years

Reporting chain growth of 12% after opening eight new stores, as evidence that existing stores are doing better

Comparing a promoted week with an unpromoted week to judge a new window display

Comparing seasonally adjusted December sales with seasonally adjusted November sales

Comparing a holiday week with the same week number last year when the holiday has moved by 11 days

Exercise 8 · Interpretation, difficulty 3 of 3

Respond to the Monday dashboard

Not started

The marketing manager writes: "Chain sales jumped 41.8% in week 66 compared with week 65. Our new in-store display, launched in all stores in week 66, is clearly working." Week 66 was the first week of the Year 2 holiday. You know that the Year 2 holiday weeks 66–67 were 2.6% above the Year 1 holiday weeks 15–16, and that the chain's underlying growth is about 4.8% a year. Write a short reply (3–4 sentences) explaining what the 41.8% does and does not show, what comparison you would use instead, and what that comparison suggests.

What you can now do

Calculate period-on-period growth relative to the correct base, and compound annual growth (CAGR) over several years
Choose seasonality-aware comparisons: same period last year aligned on calendar events, or seasonally adjusted figures
Normalise KPIs (per m², per visitor, like-for-like) before ranking units of different size
Explain why a jump in sales cannot be credited to an initiative without a fair comparison group