import pandas as pd

Data extracted from the table

data = { "Height Range (cm)": ["140-150", "150-160", "160-170", "170-180", "180-190"], "Frequency": [3, 5, 12, 15, 5] }

Converting the data into a DataFrame for better manipulation

df = pd.DataFrame(data)

Calculating the mid-points of the height ranges

df["Midpoint"] = df["Height Range (cm)"].apply(lambda x: (int(x.split("-")[0]) + int(x.split("-")[1])) / 2)

Adding a column for the product of frequency and midpoint (fx)

df["fx"] = df["Frequency"] * df["Midpoint"]

Calculating the mean

total_frequency = df["Frequency"].sum() mean = df["fx"].sum() / total_frequency

Calculating the cumulative frequency for median

df["Cumulative Frequency"] = df["Frequency"].cumsum()

Median calculation

n = total_frequency / 2 # Median class is where cumulative frequency >= n median_class_index = df[df["Cumulative Frequency"] >= n].index[0] median_class = df.iloc[median_class_index] median_l = int(median_class["Height Range (cm)"].split("-")[0]) # Lower boundary of median class median_h = 10 # Width of the class interval median_f = median_class["Frequency"] # Frequency of the median class cumulative_f_prev = 0 if median_class_index == 0 else df.iloc[median_class_index - 1]["Cumulative Frequency"]

median = median_l + ((n - cumulative_f_prev) / median_f) * median_h

Mode calculation

The modal class is the one with the highest frequency

mode_class_index = df["Frequency"].idxmax() mode_class = df.iloc[mode_class_index] mode_l = int(mode_class["Height Range (cm)"].split("-")[0]) # Lower boundary of modal class mode_f1 = mode_class["Frequency"] # Frequency of modal class mode_f0 = 0 if mode_class_index == 0 else df.iloc[mode_class_index - 1]["Frequency"] # Frequency of class before modal class mode_f2 = 0 if mode_class_index == len(df) - 1 else df.iloc[mode_class_index + 1]["Frequency"] # Frequency of class after modal class

mode = mode_l + ((mode_f1 - mode_f0) / ((mode_f1 - mode_f0) + (mode_f1 - mode_f2))) * median_h

mean, median, mode(168.5, 170.0, 172.30769230769232)(168.5, 170.0, 172.30769230769232)successThe measures of central tendency for the given data are:

• Mean: 168.5 cm
• Median: 170.0 cm
• Mode: 172.31 cm (approximately)

Would you like a detailed explanation of these calculations or assistance with something else?

Here are 5 follow-up questions to explore further:

1. How are the mean, median, and mode applied in real-life scenarios?
2. What would happen if the class intervals were uneven?
3. How does the calculation change if new data points are added to this set?
4. Why is the mode less accurate than the mean or median in some cases?
5. Can we visually represent this data to better understand these measures?

Tip: When working with grouped data, always calculate class midpoints for frequency distributions to simplify computations for the mean.