Statistics 1 in the IITM BS Qualifier: Common Mistakes

Statistics 1 in the IITM BS qualifier has a few classic traps: treating every number as numerical data, taking a median of categories that have no order, trusting the mean when there is an outlier, and dividing by the wrong total in a table. The formulas are short. Most of the work is reading the question carefully and knowing which measure fits which kind of data.

What Statistics 1 covers in weeks 1 to 4

From the official course page for Statistics for Data Science I (BSMA1002):

Probability starts only from week 7, after the qualifier.

Trap 1: numbers that are not numerical data (week 1)

A PIN code, a roll number and a jersey number are all written in digits. But they are labels. Adding or averaging them means nothing. Treat them as categorical data.

A quick test: ask "does the average of this make sense?" The average height of a class makes sense. The average PIN code does not.

Trap 2: mixing up the scales of measurement (week 1)

Here is the usual four-way split, with one example each:

The classic mistake: saying 20 degrees Celsius is "twice as hot" as 10 degrees. You cannot, because 0 degrees Celsius is not "no heat". You can say 20 kg is twice 10 kg.

Trap 3: the median of categories (week 2)

You can find the mode of any categorical data. The median only works when the categories have an order.

• Survey answers "poor, fair, good, very good" have an order, so a median is fine.
• Favourite colours have no order, so there is no median. Only a mode.

Trap 4: mean versus median with an outlier (week 3)

Five monthly incomes, in thousands of rupees: 20, 22, 25, 27 and 200.

• Mean = 294 divided by 5 = 58.8.
• Median = 25, the middle value after sorting.

The mean is pulled up by one large value. Four of the five people earn far less than 58.8. When a question mentions skewed data or an extreme value, the median usually describes the typical case better.

Two smaller slips:

• Not sorting first. The median of 8, 3, 10, 5 is not 3 or 10. Sort to 3, 5, 8, 10, then take the average of the two middle values: 6.5.
• Quartile methods. Different books compute quartiles in slightly different ways. Use the method your lectures use.

Trap 5: which variance formula (week 3)

Take the values 2, 4 and 6. The mean is 4. The squared gaps from the mean are 4, 0 and 4, which add up to 8.

• Divide by 3 (the number of values) and you get about 2.67.
• Divide by 2 (one less) and you get 4.

Many textbooks use the first for a whole population and the second for a sample. Check which one the lecture uses for that type of question. The standard deviation is the square root of whichever variance you use.

Trap 6: dividing by the wrong total (week 4)

60 students from College A and 40 from College B wrote a test. 30 from A passed and 28 from B passed.

• By raw counts, A looks better (30 against 28).
• By share within each college, A is 30 of 60 = 50% and B is 28 of 40 = 70%. B did better.

In a contingency table, decide first whether the question wants shares of a row, of a column or of the whole table.

Trap 7: reading correlation wrongly (week 4)

• Pearson correlation is always between minus 1 and 1. An answer of 1.4 means an arithmetic error.
• A correlation near 0 means no straight-line pattern. There could still be a curved pattern, so look at the scatterplot.
• A strong correlation does not prove that one thing causes the other.
• Covariance changes when you change units (cm to m). Correlation does not.

A simple routine for Stats 1

• Keep a one-page sheet: each measure, when to use it, and one tiny example.
• Do every calculation once by hand before using a calculator.
• After each practice assignment, label every wrong answer as "concept", "reading" or "arithmetic". Reading errors are often the easiest to fix once you notice them.

For more, see our Statistics 1 course page, how to improve in Statistics 1 and 2, the 4-week qualifier study plan and the qualifier passing marks.

Common questions

Is Statistics 1 in the qualifier mostly calculation or theory?

The weeks 1 to 4 topics mix both. Week 1 is mostly ideas, such as types of data and scales. Weeks 3 and 4 need calculation, such as variance and correlation.

Do I need a scientific calculator?

The course page does not say. Check the exam instructions for your term. Either way, practise the formulas by hand so you understand every step.

What is point bi-serial correlation in simple words?

It measures the link between a numerical variable and a variable with only two categories. For example, hours studied and whether a student passed or failed.

Can I pass Stats 1 by scoring high in the other three courses?

No. Statistics 1 has its own minimum in both the hall ticket rule and the exam. For General candidates it is 40%, whatever you score elsewhere.