Mean, median & grouped summaries

Understand the concept

The mean adds values and divides by their count. The median is the middle value after sorting, or the average of the two central values for an even count. Large extremes can move the mean much more than the median.

A grouped summary reveals differences that an overall average can hide. Include sample sizes: a mean from two observations has a different evidential weight from a mean from two thousand. Missing values are excluded by many Pandas aggregations, so report them when relevant.

Descriptive patterns do not establish cause and effect. A relationship between study time and marks could also reflect prior preparation or other factors. Here, use a deliberately tiny sample to practise calculations rather than make claims about learners. The code uses only Python’s standard library.

from statistics import mean, median
hours = [1, 2, 2, 3, 12]
print(f"Mean: {mean(hours):.1f}")
print(f"Median: {median(hours):.1f}")
print(f"Count: {len(hours)}")

Output / what to expect

Mean: 4.0
Median: 2.0
Count: 5

Try it yourself

Calculate the mean and median after removing 12. Explain what changed, without assuming the extreme value is an error.

from statistics import mean, median
hours = [1, 2, 2, 3]
print(mean(hours))    # 2
print(median(hours))  # 2.0
# The mean falls; the median stays the same.
# Investigate whether 12 is valid before deciding to exclude it.

Concept samjho

Mean ke liye sab values jodo aur count se divide karo. Median sorted data ki middle value hai; even count mein beech ki do values ka average hai. Bahut badi ya chhoti values mean ko median se zyada move kar sakti hain.

Group-wise summary differences dikhati hai jo overall average mein chhup sakte hain. Sample size bhi batao: do observations ka average aur do hazaar ka average ek jaisa evidence nahi dete. Pandas ki kai aggregations missing values ko skip karti hain, toh zarurat par missing count bhi report karo.

Pattern dekhne se cause prove nahi hota. Study time aur marks ka relation prior preparation ya dusre factors se bhi ho sakta hai. Yeh chhota sample calculations practice karne ke liye hai, learners par claim karne ke liye nahi. Code standard library se chalega.

from statistics import mean, median
hours = [1, 2, 2, 3, 12]
print(f"Mean: {mean(hours):.1f}")
print(f"Median: {median(hours):.1f}")
print(f"Count: {len(hours)}")

Output / kya expect karein

Mean: 4.0
Median: 2.0
Count: 5

Ab khud try karo

12 hatane ke baad mean aur median nikalo. Kya change hua explain karo, lekin extreme value ko automatically error mat samjho.

from statistics import mean, median
hours = [1, 2, 2, 3]
print(mean(hours))    # 2
print(median(hours))  # 2.0
# The mean falls; the median stays the same.
# Investigate whether 12 is valid before deciding to exclude it.