Statistics and Time Series Practice

Practise descriptive statistics, outliers, correlation, hypothesis tests, A/B tests, dates and rolling windows.

Advanced8 problemsUpdated October 24, 2026

Review first: Descriptive Statistics, Correlation, Hypothesis Testing, A/B Testing, Dates and Time Series, Rolling Windows and Cumulative Values

1.Mean or median?
Intermediate
House prices (₹ lakh) in a street are [55, 60, 58, 62, 57, 300]. Print the mean, the median and the IQR (1 decimal each). Which is the better "typical price"?
Show hint
mean(), median(), and quantile(0.75) - quantile(0.25).
Show solution
Python
import pandas as pd prices = pd.Series([55, 60, 58, 62, 57, 300]) print(round(prices.mean(), 1), prices.median()) print(round(prices.quantile(0.75) - prices.quantile(0.25), 1))
Output
98.7 59.0 4.2
One mansion pulls the mean to 98.7 while the median, 59, reflects the typical house. The median is the better summary here.

2.Find outliers with the IQR rule

Intermediate

Daily orders were [42, 38, 45, 40, 160, 41, 39, 44, 2, 43]. Using the 1.5 × IQR rule, print the lower and upper limits and the outlier values.

Show hint

Q1 and Q3 from quantile, limits Q1 − 1.5·IQR and Q3 + 1.5·IQR.

Show solution

Python

import pandas as pd

orders = pd.Series([42, 38, 45, 40, 160, 41, 39, 44, 2, 43])
q1, q3 = orders.quantile([0.25, 0.75])
low, high = q1 - 1.5 * (q3 - q1), q3 + 1.5 * (q3 - q1)
print(low, high)
print(orders[(orders < low) | (orders > high)].tolist())

Output

32.5 50.5
[160, 2]

3.Pearson and Spearman
Intermediate
Advertising spend [10, 20, 30, 40, 50] and sales [12, 25, 33, 41, 200] were recorded. Print both the Pearson and Spearman correlations (3 decimals) and explain the difference.
Show hint
a.corr(b) and a.corr(b, method="spearman").
Show solution
Python
import pandas as pd spend = pd.Series([10, 20, 30, 40, 50]) sales = pd.Series([12, 25, 33, 41, 200]) print(round(spend.corr(sales), 3), round(spend.corr(sales, method="spearman"), 3))
Output
0.797 1.0
Sales always increase with spend, so the rank-based Spearman correlation is exactly 1. The last, very large value bends the relationship away from a straight line, so Pearson is lower.
4.Compare two groups
Advanced
Session lengths (minutes) for an old and a new app design were old [5, 7, 6, 8, 5, 6, 7, 6] and new [8, 9, 7, 10, 9, 8, 11, 9]. Run Welch's t-test and print the two means and the p-value (4 decimals).
Show hint
stats.ttest_ind(new, old, equal_var=False).
Show solution
Python
import numpy as np from scipy import stats old = np.array([5, 7, 6, 8, 5, 6, 7, 6]) new = np.array([8, 9, 7, 10, 9, 8, 11, 9]) result = stats.ttest_ind(new, old, equal_var=False) print(old.mean(), new.mean(), round(result.pvalue, 4))
Output
6.25 8.875 0.0005
5.A/B test on conversion
Advanced
Version A had 2,000 visitors and 120 purchases; version B had 2,000 visitors and 156 purchases. Print both conversion rates, the z statistic (3 decimals) and the two-sided p-value (4 decimals) of a two-proportion z-test.
Show hint
Pool the rates, compute the standard error, then z = (pb - pa) / se and p = 2 * (1 - norm.cdf(abs(z))).
Show solution
Python
import math from scipy.stats import norm na, ca, nb, cb = 2000, 120, 2000, 156 pa, pb = ca / na, cb / nb pool = (ca + cb) / (na + nb) se = math.sqrt(pool * (1 - pool) * (1 / na + 1 / nb)) z = (pb - pa) / se print(pa, pb, round(z, 3), round(2 * (1 - norm.cdf(abs(z))), 4))
Output
0.06 0.078 2.246 0.0247
6.Monthly totals from daily data
Intermediate
Daily sales are 1, 2, 3, … 90 for the 90 days starting 1 January 2026. Print the total for each month, with month names as the index.
Show hint
Build a Series with a pd.date_range index, resample("ME").sum(), then format the index with strftime("%b").
Show solution
Python
import pandas as pd sales = pd.Series(range(1, 91), index=pd.date_range("2026-01-01", periods=90, freq="D")) monthly = sales.resample("ME").sum() monthly.index = monthly.index.strftime("%b") print(monthly)
Output
Jan 496 Feb 1274 Mar 2325 dtype: int64

7.Moving average and growth

Intermediate

Weekly revenue is [200, 220, 210, 260, 300, 280]. Print a table with the 3-week moving average (1 decimal), the running total and the week-over-week growth in percent (1 decimal).

Show hint

rolling(3).mean(), cumsum() and pct_change() * 100.

Show solution

Python

import pandas as pd

revenue = pd.Series([200, 220, 210, 260, 300, 280], index=range(1, 7))
print(pd.DataFrame({
    "revenue": revenue,
    "avg_3w": revenue.rolling(3).mean().round(1),
    "total": revenue.cumsum(),
    "growth_pct": (revenue.pct_change() * 100).round(1),
}))

Output

   revenue  avg_3w  total  growth_pct
1      200     NaN    200         NaN
2      220     NaN    420        10.0
3      210   210.0    630        -4.5
4      260   230.0    890        23.8
5      300   256.7   1190        15.4
6      280   280.0   1470        -6.7

8.Days since last order
Intermediate
Customers' last order dates are {"Asha": "2026-03-28", "Ravi": "2026-01-15", "Meera": "2026-03-01"}. Taking 1 April 2026 as today, print the days since each last order and the names of customers inactive for more than 30 days.
Show hint
Subtract the dates from pd.Timestamp("2026-04-01") and use .dt.days.
Show solution
Python
import pandas as pd last = pd.to_datetime(pd.Series({"Asha": "2026-03-28", "Ravi": "2026-01-15", "Meera": "2026-03-01"})) days = (pd.Timestamp("2026-04-01") - last).dt.days print(days) print(days[days > 30].index.tolist())
Output
Asha 4 Ravi 76 Meera 31 dtype: int64 ['Ravi', 'Meera']

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