The maths data analysts and data scientists actually use

Level 1: the arithmetic analysts use every week

These look easy. They are also where most reporting errors come from. Run this block; every number is synthetic.

# Synthetic weekly orders for one store (hypothetical data)
last_week, this_week = 1240, 1395
change = (this_week - last_week) / last_week * 100
print(f"Orders changed by {change:.1f}%")

# Conversion went from 3.0% to 3.6%: points vs percent
old, new = 3.0, 3.6
print(f"Up {new - old:.1f} percentage points, which is {(new - old) / old * 100:.1f}% relative")

# Average order value across two cities: weighted, not simple
orders = {"Noida": (800, 650.0), "Pune": (200, 1200.0)}  # (orders, avg value in rupees)
simple = sum(v for _, v in orders.values()) / len(orders)
weighted = sum(n * v for n, v in orders.values()) / sum(n for n, _ in orders.values())
print(f"Simple average of averages: Rs {simple:.0f}; true average: Rs {weighted:.0f}")

Three lessons sit in that block:

• Percentage change is (new − old) / old. Orders rose from 1,240 to 1,395, which is 12.5%.
• Percentage points vs percent. Conversion moving from 3.0% to 3.6% is up 0.6 percentage points, but up 20% in relative terms. Reports that confuse the two can overstate or understate a change a lot.
• Averages of averages. Averaging the two cities' order values gives ₹925. The true average, weighted by number of orders, is ₹760. When groups have different sizes, a simple average of their averages is wrong.

If these three feel natural after a week of practice, you have the maths for the core of a data analyst role.

Level 2: the statistics both roles need

Once you describe data, you need to describe how spread out it is and how much to trust a pattern.

import statistics as st

# Synthetic delivery times in minutes; one very late order
times = [28, 31, 30, 27, 33, 29, 32, 30, 180]
print("mean  ", round(st.mean(times), 1))
print("median", st.median(times))
print("stdev ", round(st.stdev(times), 1))

# Least-squares slope by hand: ad spend (Rs '000) vs leads, synthetic
x = [10, 20, 30, 40, 50]
y = [12, 19, 33, 41, 48]
mx, my = st.mean(x), st.mean(y)
slope = sum((a - mx) * (b - my) for a, b in zip(x, y)) / sum((a - mx) ** 2 for a in x)
intercept = my - slope * mx
print(f"leads = {intercept:.1f} + {slope:.2f} * spend")

# Conditional probability from a synthetic 2x2 table
converted_mobile, total_mobile = 90, 3000
converted_desktop, total_desktop = 60, 1000
print(f"P(convert | mobile)  = {converted_mobile / total_mobile:.3f}")
print(f"P(convert | desktop) = {converted_desktop / total_desktop:.3f}")
print(f"P(mobile | convert)  = {converted_mobile / (converted_mobile + converted_desktop):.3f}")

What each part shows:

Mean vs median. One order took 180 minutes; the rest took about 30. The mean is 46.7 minutes, a delivery time almost no customer experienced. The median, 30, describes the typical order. Use the median for skewed data such as delivery times, salaries and house prices.

Standard deviation. At 50 minutes, it is larger than the median, which tells you the spread is dominated by that one outlier. Standard deviation is useful, but only after you have looked at the values.

A slope. The least-squares line says each extra ₹1,000 of ad spend is associated with about 0.94 more leads in this synthetic data. That is the core idea behind linear regression: a line chosen to make the squared errors as small as possible. Data scientists use libraries to fit it; understanding the formula helps you notice when a result is implausible.

Conditional probability. Mobile converts at 3%, desktop at 6%. Yet 60% of conversions come from mobile, because mobile traffic is three times larger. "Most conversions are on mobile" and "mobile converts better" are different statements, and only one is true here.

Level 3: what data science adds on top

Data science uses more maths, but mostly as ideas you need to recognise in code rather than calculations you do by hand.

You can start a data science course without these and learn them as the course reaches them. You will find it much easier if Level 1 and Level 2 are solid first.

What you can leave for later

Unless you move into research or specialised ML roles, you rarely need:

• Proving theorems, or deriving algorithms from scratch.
• Advanced calculus beyond the idea of a derivative and a gradient.
• Measure theory, abstract algebra, or other university-maths topics.

People who worry most about maths are often picturing these. They are not the daily work.

A two-week check before you choose a programme

1. 1Week 1: redo the Level 1 block with your own made-up numbers until you can predict each output before running it.
2. 2Week 2: do the same with Level 2. Change the outlier from 180 to 60 and predict what happens to the mean and median.

If both weeks feel manageable, either the Data Science programme or the Data Analyst programme is within reach mathematically. If Level 2 feels like a wall, start with analytics and add statistics as you go; the DA, DS or FDE decision tree walks through that choice.