MEAN MEDIAN MODE

 

Statistical Analysis Summary

Central Tendency Metrics

I2.2 Suppose that the data for analysis includes the attribute age. The age values for the data tuples are (in increasing order) 13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70. (a) What is the mean of the data? What is the median? (b) What is the mode of the data?

Mean

29.96

Median

25

Mode

25, 35

Bimodal (Freq: 4)

Methodology & Calculations

Dataset Context

N = 27 observations (Sorted Age Attributes)

MEAN

Calculated by dividing the sum of all data elements by the total population size (N).

μ = 809 / 27 = 29.9629...

MEDIAN

Identified as the structural midpoint of the ordered dataset. For an odd population size (N = 27), the value aligns with position (N + 1) / 2.

Target Index: 14th position → 25

MODE

Determined by peak structural frequency. The values 25 and 35 share the highest recurring density within the sample profile.

Maximum Frequency: 4 occurrences each

import numpy as np

from scipy import stats

ages = [13, 15, 16, 16, 19, 20, 20, 21, 22, 22, 25, 25, 25, 25, 30, 33, 33, 35, 35, 35, 35, 36, 40, 45, 46, 52, 70]

# Total count

n = len(ages)

# Mean

mean_val = np.mean(ages)

# Median

median_val = np.median(ages)

# Mode

mode_result = stats.mode(ages, keepdims=True)

mode_val = mode_result.mode[0]

mode_count = mode_result.count[0]

# Find all modes just in case it is multimodal

from collections import Counter

counts = Counter(ages)

max_count = max(counts.values())

all_modes = [k for k, v in counts.items() if v == max_count]

print(f"Count: {n}")

print(f"Sum: {sum(ages)}")

print(f"Mean: {mean_val:.2f}")

print(f"Median: {median_val}")

print(f"Modes: {all_modes} with count {max_count}")