sta(4)

<p>They are always the most accurate representation of the data. (B)</p> Signup and view all the answers

<p>Interpreting the meaning of the average value in the context of the data. (A)</p> Signup and view all the answers

<p>Descriptive statistics effectively simplifies complex data without losing important information. (A)</p> Signup and view all the answers

<p>It facilitates clear and concise communication of data insights to various audiences. (B)</p> Signup and view all the answers

<p>The simple arithmetic mean considers the frequency of each value, while the weighted arithmetic mean considers the importance of each value. (B)</p> Signup and view all the answers

<p>All the student marks are equally important, so a simple arithmetic mean is used assuming equal weight. (C)</p> Signup and view all the answers

<p>The arithmetic mean would stay the same. (D)</p> Signup and view all the answers

<p>2400 (C)</p> Signup and view all the answers

<p>50 (A)</p> Signup and view all the answers

<p>29.9 (C)</p> Signup and view all the answers

<p>50-59 (D)</p> Signup and view all the answers

<p>The arithmetic mean would increase. (A)</p> Signup and view all the answers

<p>Weighted arithmetic mean is used when values have varying importance. (C)</p> Signup and view all the answers

<p>Weighted arithmetic mean (A)</p> Signup and view all the answers

<p>$X_g = n \cdot x_1^{f_1} \cdot x_2^{f_2} \cdots x_n^{f_n}$ (B)</p> Signup and view all the answers

<p>The positive nth root of the product of the values. (D)</p> Signup and view all the answers

<p>Grouped data utilizes the sum of frequency counts. (C)</p> Signup and view all the answers

<p>72000 (D)</p> Signup and view all the answers

<p>30 (D)</p> Signup and view all the answers

<p>15.13 years (B)</p> Signup and view all the answers

<p>100 (C)</p> Signup and view all the answers

<p>13 (D)</p> Signup and view all the answers

<p>The data follows a normal distribution (B)</p> Signup and view all the answers

<p>454 (A)</p> Signup and view all the answers

<p>20-30 km (D)</p> Signup and view all the answers

<p>30 (C)</p> Signup and view all the answers

<p>Class intervals and their frequencies (D)</p> Signup and view all the answers

<p>Sum of squared deviations (D)</p> Signup and view all the answers

<p>It incorporates weights based on the number of observations in each mean. (B)</p> Signup and view all the answers

<p>It significantly skews the mean away from the central tendency. (C)</p> Signup and view all the answers

<p>55 marks/subject (D)</p> Signup and view all the answers

<p>Arithmetic mean (D)</p> Signup and view all the answers

<p>It is highly resistant to fluctuations. (B)</p> Signup and view all the answers

<p>It requires all items to be present for computation. (A)</p> Signup and view all the answers

<p>$X_{w} = \frac{\sum{wx}}{\sum{w}}$ (A)</p> Signup and view all the answers

<p>It is based on a multiplication process. (A)</p> Signup and view all the answers

<p>It is simple to compute from all observations. (A)</p> Signup and view all the answers

<p>They can render the mean less representative of the data. (C)</p> Signup and view all the answers

The average of a set of values calculated by dividing the sum of the values by the number of values.

A table that displays the number of occurrences of each value or range of values in a dataset.

Data that is summarized in classes or intervals rather than individual values.

A range of values used to group data in a frequency table.

The number of occurrences of each class interval in a dataset.

The total of the products of each class interval midpoint and its frequency.

The total count of all frequencies in the dataset.

The calculated average from grouped data using frequencies and midpoints.

The value in the middle of a class interval used for calculations in a frequency table.

A branch of statistics that summarizes data using numerical and qualitative measures.

Numerical summaries that describe the central position of data distributions.

Values that summarize a dataset by condensing it into a single representative figure.

Statistics that describe the center of a dataset, like mean, median, or mode.

A summary of how often each value occurs in a dataset.

Variables that can be measured and expressed numerically.

The limitation of the human mind in processing large sets of numerical data.

The value that represents the center of each class interval in data.

The number of occurrences of each interval or category in data.

The product of frequency (f) and mid point (x) for each interval.

An average where different values have different levels of importance.

The sum of all products of frequency and mid points across intervals.

The sum of all frequencies in the data set.

Compute mean by dividing total fx by total frequency.

A sample representation of frequency distribution for analysis.

The nth positive root of the product of n positive values.

Xg = n (x1 × x2 × ... × xn)^(1/n) for geometric mean calculation.

Xg = n (x1^f1 × x2^f2 × ... × xn^fn)^(1/n) for geometric mean calculation.

A mean calculated by giving different weights to observations based on their importance.

Xw = (Σwx) / (Σw) where wx is the product of individual observation and its weight.

Benefits of using arithmetic mean include ease of calculation and consideration of all data.

Drawbacks include sensitivity to extreme values and ineffectiveness with skewed data.

For marks 40, 50, 60, 80, 45 with weights 5, 2, 4, 3, 1, the weighted mean is 55.

Extreme values can distort the arithmetic mean, making it unrepresentative.

In the given example, the total weight of subjects was 15.

Weighted mean is particularly useful when different data points contribute unequally to the final mean.