We are given a frequency distribution of the number of siblings for 50 students and need to calculate various statistics. Let’s compute each one step by step.

Given Data

# of Siblings (X)	Frequency (f)
0	7
1	5
2	8
3	8
4	6
5	6
6	10
Total	50

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Step 1: Mean (𝜇)

The mean is calculated as:

$\mu = \frac{\sum (X \cdot f)}{n}$

Where:

• $X$ = number of siblings
• $f$ = frequency
• $n = 50$ (total respondents)

We will compute this now. Given data siblings = [0, 1, 2, 3, 4, 5, 6] # X values frequency = [7, 5, 8, 8, 6, 6, 10] # Corresponding frequencies

Total number of respondents

n = sum(frequency)

Compute the mean

mean = sum(x * f for x, f in zip(siblings, frequency)) / n meanThe mean number of siblings is 3.1800 (rounded to four decimal places).

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Step 2: Median

The median is the middle value when the data is arranged in order. Since we have 50 respondents, the median is the average of the 25th and 26th values.

We will now determine the median by finding the cumulative frequencies. Compute cumulative frequencies cumulative_frequencies = [sum(frequency[:i+1]) for i in range(len(frequency))]

Find the median (average of 25th and 26th values)

median_index1, median_index2 = 25, 26

Find the median class

for i, cum_freq in enumerate(cumulative_frequencies): if cum_freq >= median_index1: median_value1 = siblings[i] break

for i, cum_freq in enumerate(cumulative_frequencies): if cum_freq >= median_index2: median_value2 = siblings[i] break

Compute median

median = (median_value1 + median_value2) / 2 medianThe median number of siblings is 3.0000.

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Step 3: Sample Standard Deviation (s)

The sample standard deviation formula is:

$s = \sqrt{\frac{\sum f (X - \bar{X})^2}{n-1}}$

We will compute this now. math

Compute variance

variance = sum(f * (x - mean) ** 2 for x, f in zip(siblings, frequency)) / (n - 1)

Compute standard deviation

std_dev = math.sqrt(variance) std_devThe sample standard deviation is 2.0671.

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Step 4: First Quartile (Q1)

The first quartile ($Q_1$) is the 25th percentile, which corresponds to the 12.5th value in the ordered data. We will find $Q_1$ using cumulative frequencies. First quartile index (12.5th value) q1_index = 0.25 * n

Find Q1 class

for i, cum_freq in enumerate(cumulative_frequencies): if cum_freq >= q1_index: q1 = siblings[i] break

q1It seems like I can’t do more advanced data analysis right now. Please try again later. Let me know if you need help with anything else!